Very poor take. The author clearly has very limited experience with raising kids. Most kids won't do difficult things if you don't push them. Playing music, learning to spell correctly, doing mathematics, and so on. A very small minority of kids will do all of that easily and for the fun, but you can't rely on it. If you don't push your kid to do their 20 minutes of piano every day, they will half-ass it and will stop after 1 year and conclude they are not good at music. Same for sport. Same for reading books. Same for maths. And you know what? It's your fault. You chose to be lazy and complacent and didn't push them because it's hard to be a good parent. And now you expect me to validate your laziness? Nah.
The really important thing is to teach kids to find their joy.
At the end of my second year of piano lessons, my teacher took me into her living room, and we listened to Glen Miller records for most of the hour. And then we had a cup of tea, and she told me, "this is the music that I love. I play piano because I love that music, and I want to be able to play it myself. What kind of music do you like?" I didn't really have an answer. So she told me that we should stop doing lessons, but once I found music that I loved, she'd be happy to teach me how to play it.
In my early teens, I discovered Miles Davis. Once I had found my passion, all the hard work became play. I actually ended up learning to play jazz guitar, not piano. Even the heavy lifting was pure joy, because it had purpose and meaning.
I didn't become great at mathematics until I discovered the joy in mathematics (another brilliant teacher handed me a stack of old math contests, and said here, you might find these fun. I placed 4th among 20,000 students).
I didn't learn to write well until I discovered the joy in writings. (An absolutely brilliant English teacher who made us assign ourselves our own grades, but broke his promise in the end by upgrading all my papers to A+'s).
And I gave my kids the room to find their joy as well.
A counter argument is simply the observation that some stuff, it takes time (and effort) before you find the joy in it. Following your recepie, unless (as you say yourself) lucky teacher or wealthy parents, anything that doesn't incite immediate reward will be of low interest. A kid will probably pick up that general pattern too:
if joy can not be found in <T time, don't bother. And kids are not particularly known to be good at long horizon credit assignments, so that T is often hours, day, or maybe a week.
My brother (now an professional artist) told me at teenage years "some stuff you just won't understand the beauty and the joy until you've at least put 100 hours in it". And that's true in so many things in life.
I'm happy that one of my parent forced me to do some stuff (sports, music, language) even when I complained about it. Only 10 years later did I understand how valuable being able to speak another language fluently with minimal accent is, and how some of my fellow second generation migrants lost that ability, and regret it.
(having to go to school on Saturday sucked as a kid)
> it takes time (and effort) before you find the joy in it.
And the right mentor.
I distinctly remember that for my master's thesis, I had initially chosen a topic that I loved deeply, but getting constantly rebuffed by my supervising professor who constantly berated me and insulted my intelligence led me to not only hate the dissertation topic (not to mention him also), but hate that field which I loved so much.
I later switched topics, to a very different field, under a professor who actually took stride in and complimented my achievements however meagre they were. Net result, we've collaborated on multiple papers together and even after 10 years or so, consider each other friends instead of a mere teacher-student relationship.
I could give multiple anecdotes in other completely unrelated fields, from painting and art to driving a stick. Guides and teachers matter in finding the joy in things, even more so than the time invested.
> "some stuff you just won't understand the beauty and the joy until you've at least put 100 hours in it"
Terrific quote and advice. 100 hours seems doable for a lot of things (even if it's not enough time.)
If you practice things, often you become better at them, at which point they become more enjoyable.
There's definitely a point of fun - the point where something challenging enough to be interesting, and where you can make progress, but not so punishing as to be discouraging. Games often target that fun point.
>“Joy” is not found in a day. People enjoy doing things they are good at.
There's got to be more to it than your simplified breakdown.
My first exposure to computer programming was fun and instantly addictive. There was no struggle to learn coding. Same childhood experience for guitar. Nobody was around to push me. There was no need for "discipline to practice". It was simply practice-was-natural-thing-to-do because I enjoyed it. I wasn't a child prodigy. I was finding early joy in programming and guitar -- even though I was very bad at it.
On the other hand, I'm very skilled at cooking and Microsoft Excel. But I do not enjoy making any meals or fiddling with spreadsheets. Likewise, there are a lot of kids out there that hate farming but are actually very good at milking cows and running the tractor because their parents made them do the chores every day. Some kids then grow up to move to the city and leave behind the farm life for good. On the hand, some siblings will cherish farming and happily take over from the parents.
That said, I'm aware of the "No True Scotsman" argument about "joy" : If you _truly_ were skilled at cooking and MS Excel and farming, you'd actually enjoy it.
ok... so the meta question is ..... how does one tell the difference between "skill precedes joy" vs "The beatings will continue until morale improves!" ?
There was a popular "Tiger Mother" book where Amy Chua's daughter has a meltdown in public and didn't want to be forced to play the violin anymore. That finally convinced the mom to stop. On the other hand, the older sister seemed ok with piano lessons. Maybe children are just different.
TLDR of anecdotes above is any theories of optimal child-development has to account for _counterexamples_ to the skill-vs-joy connection :
Kids can find joy in things they are bad at. Kids can hate doing things they are good at.
I find tremendous joy in playing the piano today. That mostly started when I was about 20, ~15 years after I started playing the piano.
It had its moments during the first 15 years of my life, but it was more of a competitive activity than an entertaining one. Conservatively, every fun hour had about 50 shitty hours when I was a serious piano student. Now it's 100% fun.
This is exactly the same for me—I grew up playing the piano for basically my entire childhood, but it was always a chore. I dropped it once I went to college and figured I'd never pick it up back up, but then I decided on a whim to learn a song I found online. But b/c now it's no longer just for the sake of lessons, it's become a hobby that I really enjoy in its own right (and indeed, all the forced practice growing up has greatly expanded the range of songs that I'm able to learn now).
Same for me, I've learned programming, reverse engineering, music production, cooking, etc. I learned all these things not because I'm intrinsically in love with doing them, I just love having done them. This quote fits it perfectly, "I hate writing, but I love having written."
> It takes a long time to get good at some things and those days suck.
If those days suck, chances are you won't get good at it. People like things that are engaging and develop their identity and understanding of themselves and the world, even more so than things they are good at.
But kids are going to have setbacks, they will reach a plateau in their craft (music, painting, art, sport, ...). You need also as a good parent to help your kids go through, to not give up, because even joy to do is not always enough. This is the hard part.
From my modest experience of being a ski/snowboard instructor and trying to raise 3 boys (now 12, 16 and 18).
why does a child need to break through a plateau at anything?
Of my five sample size of five, expose them and support them, some things can’t even hook you until your brain grows enough .. The musical one is in a band now the nerdy one likes inhaling solder. I did force both boys to Hockey but just to have passable skills so that he can enjoy that all that comes with the sport as an adult
> why does a child need to break through a plateau at anything?
Learning that they can hit a plateau and move beyond it with concerted effort is super important. After you've done it once, you can look back on that experience for inspiration when there's a plateau that you want/need to move beyond.
Having experience with struggling with something that is easy for some others is important too. Some kids are just naturally good at a lot of things when they're younger; which is nice in some ways, but makes it hard to learn skills to deal with challenges... It's great when they find something that challenges them (even if it doesn't seem great to them in the moment). Other kids have a hard time with most things; you've got to look out for things they can be good at.
The current trend, at least in Germany, is that as soon as a kid says "I do not want anymore.", this is normal to stop. With that, the kids do not have the experience that it can be hard, but going through can bring something.
Resilience, capacity to go through ups and downs, etc. are things you train by being exposed to it. If your life is only fun and joy as kid, the day you are hit hard as an adult, you have no training.
But, this is my very personal point of view, education is very personal and very context specific, every family is different (country, culture, education, etc.) and in every family education is difficult from one kid to another. I am not trying to tell you how to educate your kids.
This does need to be anchored in value though. They should be at least playing a part in deciding what those things are before they're pushed to persevere towards them.
> why does a child need to break through a plateau at anything?
Exactly! Why? The few things I do better than most people are things I've stayed engaged with during those plateaus because I wanted to, not because someone else told me I should or that it was important. The people who respond positively to being forced into things generally end up not knowing who _they_ are, and end up generally unwell people.
I feel false dichotomy here - you assume helping child to go through plateau must be forced.
It doesn’t have to be and some people need a little bit of help - you didn’t and that’s great.
Conversely there will be kids that need to be forced or nothing good will come out of them - there will be kids that should be left alone because pushing them will just break whatever they should be doing.
It is delicate balance and difficult choices - but there is no white and black here that will be right for everyone.
Yeah I didn't mean to suggest this dichotomy. And I agree with you. Just not sure how much you can force people, even the ones who "need" to be forced. Or what "good" will come out of that. Good in my mind is a person who knows themselves, is functional, and is comfortable in their own skin. That is, a person who won't lead a life of total suffering, which seems pretty common!
his whole point was that once he found joy in it, he could excel. I'm confident there's loads of things I could be good at - I'm only good at the things that I enjoy putting effort into.
There are tens of thousands of people who love basketball playing right now and only 300 places in the NBA. Most people are average and never excel at anything, ever. Being 4th out of 20,000 is excelling and the proper response to someone using their own freakishly unrepresentative self as an example for normal people is to point out that they have no idea what it’s like to be normal.
Yeah, but something vital happened: you learned the basics of music theory and how to sight read music - both prerequisites to jazz guitar (and something that most guitarists don’t know). Learning piano is a great way to step into other musical instruments.
Not forcing kids to learn mathematics and not becoming great at mathematics until you discovered the joy in them are not remotely the same thing.
Not learning to write and not learning to write well until... are not remotely the same thing.
Kids are inherently joyful, unless they are abused. One doesn't have to teach kids to find joy.
Whereas an admonishment to "teach kids to find joy", aka: "do what you feel like" according to the article, rings true as detached from reality self-talk meant to make adults feel good about themselves. Its almost a class signal, that is a privilege signal. With varying results across classes.
> The really important thing is to teach kids to find their joy.
As an adult, how can I find joy? I've been trying out various hobbies, but eventually, all of them became a chore. I really miss the feeling of fixating on something and getting lost in it, but it's not coming back. I'm so jealous of people who have a passion, because I just don't.
As a serial hobby-hopper myself, I have come to realize that anything worth doing is at times dull and tedious. Passion is not always intense joy, it's appreciating the highs and tolerating the lows. Don't get caught up chasing cheap thrills.
We fail at teaching a means with no end. Help them find an interesting end and they will achieve it by any means necessary.
Our job as parents is to expose our kids to a wide variety of disciplines so that they can find their interest.
I read that Elon Musk runs his private school this way. The kids narrow their focus quite early on. But of course there's tons of depth to study. So they actually get somewhere.
My parents pushed me hard to do piano when I was around 10-12. After a year that went pretty well I was starting to get lazy and put very little work and investment into preparing for the next lesson. They still had me play piano a full year until they eventually gave up and bitterly told me what a waste my resignation felt to them.
20 years later, I got back to playing piano, and I can't thank my parent enough for having me to continue playing in my teenage years. Because it only took me a few month to be able to play pretty advanced piano sheets compared to some of my relatives who are struggling with the basics starting it in their adulthood.
Same for maths. I feel that a lot of people like the author of this blog post are being extremely misdirected thinking math can and should be taught in a fun or amusing manner every time.
Sure, a lot of topics in Maths can be made more digestible by "gameification" to help younglings develop an intuition.
But a very big part of Maths actually requires you to sit down and painstakingly crunch down the numbers/equations, memorize and learn when to apply the correct methods to solve some problems. And even though this part can feel fun and engaging after a while, you can't expect children to exhibit such interest right of the bat without having them first struggle with the classics.
Kids don't know better. Your role as a parent is to navigate along the fine line of forcing your kid to get good exposure to the (boring) activities we adults value and letting him enjoy what he enjoys.
Only in doing that will your kid open up to the world and grow up into a functional human being.
"20 years later, I got back to playing piano, and I can't thank my parent enough for having me to continue playing in my teenage years."
One of the tragedies of being young is that few have the insight to realize that the 'boring' stuff parents and teachers are forcing us to learn will actually benefit us and that eventually we'll be very thankful that they did.
My parents nagged me all the time about studying and even though I did my fair share of it I never fully appreciated how important it was until much later.
It's a strange phenomenon, one cognitively understands the reasons but one is isolated from the reality so one is somewhat distant from it. For example, one can get upset watching war footage on TV but being there is on another level altogether (soldiers often do not talk of their experiences because they know those at home will never fully understand).
In the same way, wisdom gained through experience is almost impossible to impart to a younger generation who has no actual experience.
I upvoted all of the above posts because - all of them share some correct arguments.
* Training is hard.
* Using your training e.g. a bicycle race is fun.
* Training is easier, if you actually know why you’re doing it and recognize some progress.
> the 'boring' stuff parents and teachers are forcing us to learn will actually benefit us
My parents forced me to play the piano for more than 10 years because they were obsessed with the piano, and because they had a piano. I hated every second of doing that in order to please them, and I never got higher than beginner level because it was a torture for me. Being a beginner for 10 years should be considered as abuse and it messed me up big time, especially for my daily confidence.
30 years later, I still hate that fucking thing and I understand that they fucked up due to their delusion. They deny everything when we talk about it though.
Sometimes you have to listen to the kids and understand what they want do do, and accept it instead of feeding your Munchausen by proxy syndrome. All I wanted was a computer, even the cheapest computer ever would have been acceptable. Nowadays, I write C++ for a living and I still hate the piano. If only anyone listened to me back then... My hatred for that instrument is a mystery for some people, and some people think that "wisdom gained through experience is almost impossible."
Amen. And the surreal thing is to then hear the very same mentalities behind this uttered in this comment section.
It's like there's like a vehemence in people towards abuse. Reminds me of how Zweig said that people were in a state of jubilation in anticipation of WW1.
There's something dark in humans where they don't accept the absence of pain. They think to at least some extent, that hurting their kids is a good thing, perhaps under a twisted "toughen them up" mentality.
And the thing is, they get away with it. Maybe their kid gets a chip on their shoulder against them, or maybe even estranged from them. But they don't get hurt back.
"Sometimes you have to listen to the kids and understand what they want do do, and accept it instead of feeding your Munchausen by proxy syndrome."
I agree, and it's more than 'sometimes', kids have a right to be heard and that hearing should be fair and reasonable. Clearly, in your case it wasn't.
What you experienced was unacceptable by any measure, and in my opinion the fact that your parents were oblivious to your predicament is a damning indictment on their parenting skills.
Your extreme situation isn't what I was referring to, so let me explain by briefly describing what I experienced.
I learned the piano because I wanted to, not because my parents forced me. In fact, whilst my parents were both musical we didn't have a piano when I was young—so I started late and that's been to my disadvantage. I mention that to let you know I understand what you went through.
Whilst I like the piano learning it was no bed of roses and it's difficult for all but the most talented (anyone not wishing to learn it would be an unmitigated drag). For me, those fucking Czerny scales used to drive me to distraction, I'd goof off and play whatever took my fancy whenever I could. Also, my teacher used to reprimand me regularly for not reading score timings as written, I'd play the tempo as I felt felt like it and that always casued a ruckus.
At no time did my parents force me to take subjects that I did not like. That said, gentle persuasion was used. I was never much good at languages and despite my ambivalence for the subject I took French not so much at my mother's insistence but rather her desire that I do so (her sister married a Frenchman and was living in France and she thought it would be useful). Learning French used to drive me crazy, it's not that I detested it (I understood its value), rather the problem was that I wasn't much good at the subject. I'd sit on my bed at home doing my French homework and bash my textbook up and down on the bedclothes whilst tying to learn those fucking French nouns with their damn random genders—why the fuck can't they all be 'la' or 'le' and not random? Having a single 'the' in English is immanently sensible.
Well, despite being not much good at the subject in hindsight learning French turned out to be a blessing when I was living in Europe. I could never have foreseen that situation when I was at school.
Another example, my father used to nag me about not taking Latin, my usual retort being why the hell would I want to learn a dead language (although that was more in jest at his persistence). I sort of had a paltry excuse as my school didn't teach Latin but there were arrangements to do certain subjects by correspondence under teacher supervision in the library. So I never took the subject at school, so nowadays my Latin is at best a mess.
That was a fucking mistake of the first order on my part for reasons too long to describe here. It's only the wisdom of hindsight that I now know I should have taken my father's advice.
BTW, I understand your frustration over not having access to a computer, I'm an IT professional and I managed an IT department for years (I was one of those nerds university security would regularly chuck out of the computer room at 10pm at night). If I'd been in your position, I'd have been mightily pissed off at your parents' miserable attitude.
> One of the tragedies of being young is that few have the insight to realize that the 'boring' stuff parents and teachers are forcing us to learn will actually benefit us and that eventually we'll be very thankful that they did.
I'm 40. I don't know, perhaps I'm still young.
I did not appreciate having to learn the boring parts. Learning things for the next exam so as to forget them in two weeks... I didn't see the point then and still don't.
I managed to get by with the minimum possible, fluked my CS education, then had a career earning an order of magnitude more than the average salary. Shrug.
Maybe I'm missing something else because of my lack of education? I don't know...
We’re all going to have different paths but I’m certain that flunking CS education and then getting 10x the average salary is not going to be the common case and was probably only possible for a given point in time.
I’m in my late 40s. I left grad school to get a job in VLSI because it was possible to do so in the job market of the 90s. In today’s job market we wouldn’t even pickup the resume of a new college graduate that didn’t have at least a masters. I would’ve been totally passed by today.
Assuming the benefit we’re looking is getting a high paying job of course.
You (and I and many others on HN) were lucky enough to join the tech industry while it was still growing explosively and got outsized salaries because of it. If you were to do the same thing today, you'd be telling a very different and much grimmer tale.
I had way more than usual share of "life events". I threw my career out the window to care for my toddler and dying partner. Then my partner died and I'm left alone raising the kid. What else is going to happen to make me wiser?
My parents forced me to play piano, right up until I told them that I'll destroy our piano if they don't lay off, and any consequences they could think of would not stop me (I was normally an obedient child, but enough was enough).
That got their attention.
30 years later I picked up classical guitar and loved it! Do I thank my parents for forcing the piano on me? Hell no.
Like I commented in another post, piano gave you the foundation for learning classical guitar (and appreciating that genre of music). Very few guitar players can even recognize note names on a staff. You’re not going to get far with classical guitar without it.
That was ironic understatement. With classical guitar, you won’t really get anywhere without being able to read sheet music. It’s not like rock and pop guitar where you can just learn tabs and slightly develop your ear and that’s enough play along with all your favorite tunes.
If you’ve already picked up reading music for one instrument, it’s a ton easier for the next one.
You want to have fun playing along to your favourite song. Or impromptu jam with a friend. Or sing for yourself because a song reminds you of a memory.
They all have a minimum skill requirement, without which it isn't as enjoyable.
You need to know to play reasonably well by ear to have fun imo.
Sure, those are definitely fun things to be able to do, but it’s not some kind of essential life skill. If it’s not someone’s thing, why force it? There are plenty of other skills that are also fun to have.
I mean, fair enough. I had an aptitude for it.
If you're able to figure out what skills they might have fun with in the future, that's excellent.
If not - I'm not sure, you gotta shoot your shot I guess? Because the dislike might be for the process (practice) when they actually would like the end product (jamming)
I just had a kid so this is pretty real to me. How it will go is anybody's guess, but I hope it does go well :)
I guess I believe more in the Montessori idea that kids are intrinsically motivated to learn and excel, and they will tend to be naturally drawn to work hard at the skills that they are best suited for.
I understand the idea that some skills have a hump to get over and it’s good to encourage that determination, but I’d also guess that for every person like you who is glad they were pushed to learn some particular skill, there is another person who it affected very negatively. So I suppose it’s a bit of a gamble in that sense.
> Because eventually you plateau without proper foundations, and that's not fun.
This is a completely alien perspective to most people. Most people never even really try to be good at anything. That you think this quirk of your own psychology is the norm shows a deep disconnect with the mass of mediocre people who don’t care about being competitive because they’re not trying to get highs up on some leaderboard. https://danluu.com/p95-skill/
I get that. It’s satisfying to overcome those hurdles and frustrating to be blocked. Speaking for myself though, if I find I’m getting really frustrated by something that I’m supposedly doing for fun, it’s a sign that I might not be approaching it in the best way psychologically. I’m usually much happier when I try to have more of a zen ‘putting in the reps’ mindset. Then the periods of progress are like icing on the cake, not something I need to enjoy the thing.
Learning sight reading is the most natural on piano like instruments. The notes are literally arranged in the same order. Stringed instruments are much more difficult to learn sight reading from scratch on.
That's an odd take. Sight reading is about associating the mark on the paper with the actual note, duration, style etc. How that note gets played on a particular instrument is a different matter.
> piano gave you the foundation for learning classical guitar
Absolutely not. If you hate something and don't learn anything more that entry level, it won't give you any foundation, only hatred and bitterness. Also the piano and the guitar are very different beasts that you cannot compare at all.
The piano and the guitar are different in many ways, but they also have some similarities depending on how you play them.
Mechanically, sure, nothing transfers. Rhythm transfers pretty well. An ear for what sounds right would too.
If you're reading printed music, that transfers. A lot of guitar play comes from tabs though, which isn't really transferrable.
If you play chords on the piano and the guitar, and especially if you're thinking about chord progressions, that transfers. But you might play either instrument without a lot of chords.
Lead melody kinds of things can transfer a bit. Especially if you were thinking about how the notes in the melody fit with the chords, even if you didn't play the chords.
Even if you didn't think you were learning music fundamentals, you might have picked up something.
I’m happy that there was overlap between what your parents put in front of you and what you found passion in later in life.
I think that story happens to many but I cannot accept a premise that it is somehow universal.
The passions I found later in life were unrelated to what my parents put in front of me. I suspect that it’s because the activities I eventually found (distance running, volleyball, cooking) were not activities that my parents enjoyed or thought much about.
Moreover, I was unable to develop healthy models of internal motivation until mid life. I didn’t have to when the “why” was covered by my parents.
Childhood should be the lowest risk time in life for people to learn to fail and find the path back to success. This is what I worry about as a parent when I try to set my kids up for future success. I want them to fail now.
I see my role as a parent as coaching them to care about how they spend their time and how to recover from disappointment and failure. If they get that, then learning piano later in life is just work. They won’t be afraid of that.
> I can't thank my parent enough for having me to continue playing in my teenage years.
Counter-example to anyone reading this and thinking about imposing this misery on their child - I absolutely hated piano lessons, and nowadays I absolutely hate that my parents forced me to do it. Total waste of time, even spending more time on Civilization or whatever instead would've been more valuable to me.
> "Because it only took me a few month to be able to play pretty advanced piano sheets compared to some of my relatives who are struggling with the basics starting it in their adulthood."
I don't get it. you'll be a beginner in something that you weren't pushed to in your childhood. so what?
are you planning to only do things you were pushed to as a child? I learnt skiing in mid 30s , never even saw snow as a child. Its my fav thing to do all winter and spent like 40 days a season on snow. Not sure if i would've enjoyed it the same if i was "pushed" skiing as a child and hated it.
I’m not a parent myself, but something I’ve seen happen with an American family I know, is that they push their kids way too much to learn and do as many things as possible. They have their music lessons, their many clubs at school, several physical activities such as soccer, tennis, taekwondo. At some point you have to stop and wonder whether you’re taking their childhood away.
These kids barely have any free time. School during weekdays, activities during the weekend… worse than a full time job.
I think there’s a balance to be struck. Your kids don’t need to be good at everything.
Every parent is fighting an uphill battle against the technology now.
You either structure the day in such a way that there is literally no time for anything outside of activities, or you just observe the kid gets sucked into the screens with less and less will to do anything else.
Have you personally tried to keep a teen away from a screen? If you did with a success, I would really like to hear your story and what has worked for you.
Looking at my kids friends / classmates, almost all of the parents just gave up, with the exception of a small group that is still trying with the discussed approach.
"Keeping teens away from screens"? And why are there screens?
Sugar is addictive. One would not necessarily expect a teen to healthily control their sugar intake; accordingly, we don't put bowls of candy around the house, and if we did we certainly wouldn't be shocked when they emptied themselves, and then thrown up our hands and said "can't keep kids from candy, what can you do?".
Our kids aren't teens yet, but the plan is for screen time to be whitelisted, that is, there are certain times and circumstances where screens are okay and the rest of the time they are not.
EDIT: To elaborate on parenting philosophy a bit, one can provide structure (good) without being authoritarian (bad). Rather than bouncing between "you have all the options available, including screens, hope you make a good choice!" and "you are doing this specific activity now", one can provide unstructured time with lots of options available- reading, board game, doing something outdoors, creating a craft, etc- while having none of those options be screens.
There are screens because their entire social circle has phones, sometimes from an early age. If your kids don’t have them then they are the odd ones out, and excluded socially, which has their own extremely negative consequences.
And if the parent cannot find a single way to prevent the constant use of the screens beyond simply packing the day with activities, that says more about the parent than the kid.
If the only way a teenager knows how to make good choices is through outright avoidance of situations where a poor choice might arise, then they don't know how to make good choices.
I have three kids (19, 13, 11) and I agree with them completely.
My son at 19 is building websites for companies, still deep into manga and video games but is started to get out more with the gym. He still lives with us, but essentially has his own life and seems to be doing well.
My 13 year old daughter is the one who loves to try everything. She's in dance, show choir, volley ball, tennis, violin, clarinet, etc. She even signs up for college for kids classes over the summer. All self motivated. Just yesterday her and her friends walked about 5 miles around town to different stores. She has her own phone.
My 11 year old is the smartest of the bunch. She has an amazing vocabulary and reading has always seemed to be "natural" for her. She's straining my policy of buying my children any books they want. She's bored of the advanced learning classes she's been put in. She also plays tennis and flute and cello. She learns her own crafts and sciency projects to try at home from TikTok. She will likely get a phone this year, but has an iPad.
All of them have had practically unlimited screen time since they were double digit ages. They are on TikTok and YouTube and SnapChat. They just have many other interests as well and it doesn't consume their lives. They manage their own bedtimes (within reason) and are responsible for getting themselves up and ready in the morning.
The only times we've forced them into activities is when they were too young to make those sorts of decisions for themselves. So all of my kids played soccer while young until they could suggest an alternative activity they would rather do more. They all started in music, until they could find other creative alternatives. None of them are screen zombies that so many HN posters swear is inevitable without banning things. I'm not sure where the panic is coming from, but leave me and my children out of it.
Went fine. Quite happy with how my children are turning out. We don't even limit screen time anymore. They seem to have developed healthy habits and boundaries.
> At some point you have to stop and wonder whether you’re taking their childhood away.
At some point you have to stop and wonder if a great childhood is doing - music lessons, many clubs at school, several physical activities such as soccer, tennis, taekwondo etc.
They are occupied, they are trying new things, learning new skills, running around outside, interacting with their peers.
This. I have several people with kids similar age as mine in my circle, who seemingly gave up and now its all phone, pad or tv at all times. It is very easy to lose that kid to other distractions unless you provide enough of a structure for them.
Many kids will do difficult stuff, just not the stuff you'd have in mind. Sometimes parents are right in what the kids should be focusing on, but I'd guess more than not they are wrong. For example, all the parents who discouraged heavy computer use or video games, when this is how most millennials came into programming and IT. Then there's the thing where a kid who is interested, obsessed even, learns SO much faster. I recall a story of a parent who wanted their child checked for learning disabilities and the psychologist exclaimed "Your son has memorized 350 Pokemon! It's not a question of learning ability, it's a question of motivation".
In my view, if we let our children do what interests them, to some degree (of course anything taken to the extreme will likely fail, and it depends on the child), they are likely to cover way more territory, and probably more useful territory, than a child that is being forced and coerced. One of the many things my 7 year old has learned from Minecraft is an entire language (English), to a level which in the past (my generation) we didn't reach before perhaps 18 (and that was due to watching TV, not school). The other day I caught him taking notes on a piece of paper that said single = 1, double = 2, triple = 3, quadruple = 4, quintuple = 5, sextuple = 6. This is a child who should not be speaking English, but now he can write and spell it better than his native language, because we let him follow his passion. He's also learned a ton of engineering concepts and vocabulary, and has the ability to install mods, debug when they don't work, has a basic understanding of networking, IP addresses and on and on.
He has no interest in playing an instrument right now, why should we force him? If the time comes and he wants to, he will learn it so much faster because he wants to get better.
If the kid isn't enjoying the piano lessons, will forcing them to do it for 20 minutes every day really be beneficial? Sure, they will now be able to do something - something that they absolutely hate... (also, why is it always piano that parents try to force on children?)
"something they absolutely hate" is learning to read sheet music, training for skill, practicing for muscle memory.
The fruits are reaped when they (me!) get older.
Like I mentioned in another comment, I can play along to a song I like, play a song that is a certain memory, jam with friends at a whim.
Those are not things I necessarily wanted to do when I was a kid.
But the "forced" practice was required as a foundation to do what I want to today.
Similarly, it teaches the value of putting forth the minimum effort to appear to be doing the work. Putting forth more effort rewards one with more work.
That’s such a depressing way to see things. I’m sure most people do something they don’t utterly despise, is only because they select for their local optimum.
If you live in the bubble where you experience this, congratulation you live a wonderfully privileged life, never interact with anyone or are totally oblivious to the experiences of all the people you interact with on a daily basis.
But also, many people choose to do something they hate so they earn more money. They could be just as privileged and choose not to, just so they can compete with the Joneses and consume more...
I hate doing laundry and cleaning dishes. I still do it, though.
There are things in life that you won't enjoy but you need to do. Learning to do them anyway is in fact a life skill.
I've seen people follow their dreams into careers they chose because they wanted them, despite those careers not being paid well. They're all at least as miserable as the average person, because what they enjoyed is now work, and they don't have money for anything they now enjoy.
"Do whatever makes you happy" is a life plan for the financially independent. Most people simply don't have that luxury.
Parenting, having and raising children, including but not limited to the act of giving birth is the ultimate example. There are many "piano lessons" along that journey.
Sure, you can take off at 2am and leave a screaming 2 month old child in a room and never come back, because you have been trying for hours to stop it from crying and it is just too fucking hard - just like you can walk out of your piano lesson and never go back.
The primary design goal for most traditional instruments was making them as loud as possible.
I was briefly made to play violin as a child, and I definitely hated it (fortunately my parents recognized this and didn't push too hard). The reason is in retrospect obvious: violins are loud and piercing and played close to the ear. Nobody considered hearing protection back then. I learned recorder as an adult and the loud notes can exceed 100dB(A) measured at the ear (both alto and soprano recorders, and recorders have very limited dynamics). Violins seem to be at least as loud. I would hate to play without hearing protection no matter how skilled I become.
Even in instruments where you can more easily play softly like a piano, the design for loudness can cause suffering. Pianos are much bigger than they need to be now that we have amplification, with correspondingly wide and finger-straining keys. Steel string guitars are louder than nylon but hurt more to play (and even nylon can hurt depending on your individual hand size and shape). I expect there are many children suffering hand/finger pain from being forced to play various instruments and genuinely hating it regardless of their skill level.
When a child hates something, there's often a good reason for it that isn't obvious and that they don't have the communication skills to explain.
You have the worst case of Dunning-Kruger syndrome I have ever come across.
There are ages below which you are too young to play full-sized pianos, or play every interval an adult can play. That doesn't stop you playing it at all. What's more, your hands and fingers stretch. It isn't painful to play the piano.
The stuff about loudness is just rubbish. There is absolutely no need for hearing protection while playing the recorder (a very quiet instrument), the violin or the piano solo. You have no idea what you are talking about.
I never said it was painful for everybody to play instruments. I'm saying this is an underappreciated reason for children to hate playing. Maybe you are lucky enough that it doesn't affect you.
And I personally measured my recorders with an SPL meter and found them to reach over 100dB(A) at the ear (played indoors in an ordinary room with furniture but without acoustic treatment). The meter used does not have a traceable calibration but in all respects behaves as I would expect a correctly calibrated meter to behave. I have no reason to believe it is miscalibrated. Recorders are only quiet in the bass. The high notes require much higher air pressure and can be very loud. Perhaps you are fooled by the lack of distortion. I played without hearing protection at first, but I was disturbed by the prolonged discomfort this caused in my ears. I then recorded my playing and reproduced it with loudspeakers. I was shocked at how loud I had to turn the speakers up to reach a realistic level. I think it's easier to judge SPL from loudspeakers because they do have distortion which serves as a perceptual cue. Pure sounds can reach dangerous levels without sounding obviously loud. I also think the fact that I was playing the instrument myself and not just listening contributed to my misjudgement.
> I'm saying this is an underappreciated reason for children to hate playing.
I once shocked my mom by clearly hearing what she whispered from across a quiet room. And not like a room in a home, this room was about the width of a house. I think people massively underestimate how sensitive hearing can be for some people.
I think this is the crux. Nobody likes to fail, kids included. And their attention span is wonky too so they may not see much value in learning from failure/s since there are so many other attractive things asking for their attention and they would rather do them.
Insane you’re getting downvoted, this 100% and then some. There’s a clear difference in outcomes between kids taught self-discipline and those who are raised standard Anglo-American ADHD style once they become adults.
Different point of view: do you consider hunting in the wilderness to be difficult?
I do, it requires being still in miserable conditions for a long time, being cold, wet, mosquitos, and then usually still no success, but frustration.
But to my knowledge, no savage kid is in need of being forced to learn it.
"children sense your true passions and naturally want to join in"
And that is my experience as well. But if you stop childrens curiosity out of limited time and patience "Be quite now!" - stop them from helping, because they are not a help in the beginning and you are faster on your own - then of course they won't just start enthusiastically some years later doing with motivation whatever it is, you define as their arbitary target now.
> But to my knowledge, no savage kid is in need of being forced to learn it
Uhh then your knowledge is very limited because that is rather well documented. Also, why are you saying "savage" like an 18th century racist? Is that in fashion again?
Oh, I am obviously a racist, by glorifying indigineous teaching methods.
But otherwise can you show, where this is documented? The natives tribes where I have some knowledge, don't force their kids to learn in the sense that is talked about here. No need to - the whole culture is about becoming a good hunter (for male individuals). So indeed lots of peer pressure, but no individual forcing.
Talking about a specific ethnicity is not required to be racist in English. If a person were to use the word "Nazi" to describe any person who lives in an area that was Nazi-controlled in 1942, this would be roughly equivalent in terms of the connotation and in terms of the reasonable indignation the recipient might feel.
Furthermore, if you didn't have a specific ethnicity in mind, then when you're going off about "natural education", what you're really saying here is "all groups of people that are part of a group I consider 'uncivilized' are the same".
Or alternately, if ethnicity isn't what you're using as your basis for calling groups of people and their children "uncivilized", what is?
"Or alternately, if ethnicity isn't what you're using as your basis for calling groups of people and their children "uncivilized", what is?"
Culture.
And this debate is equally fascinating and frustrating.
I simply spoke of generic nomadic uncivilised hunters.
And not at all in a bad way, just to illustrate a point. Because to my knowledge yes, nomadic hunting cultures do have similarities. Education seems to be one of those.
This kind of forced practice can create the appearance of a certain level of competence, but it rarely produces a deep understanding or innate appreciation of any of those subjects.
Take music, for example. Many high schoolers play an instrument as part of the college admissions game. Almost none of those kids can play music with their friends and just enjoy it. To them music is this structured activity where they get paper with dots on it, and they have to play the right notes at the right time to pass the class. These kids never develop a true understanding or appreciation for music. They don't keep their instruments or practice as adults.
There's so many things to learn to be good at, why not find something that you actually like?
This is one of the reasons I'm really happy that my daughter found show choir. Choir sucks. My kids hated it. I hated going to watch it. Bunch of terrible old songs that no one knows. Now she's singing and dancing to pop songs and show tunes on the stage and it's far more engaging for her. I do think it also helps that show choir is a tryout based program so the floor for interest and talent is far higher than with the regular choir.
The really important part of this is that kids mimic what they see adults they like and respect doing. If their role models spend 6+ hours in front of the television every night, that’s what they’ll do. If their role models are playing music or sport, that’s what they’ll want to do.
Yes, but one of the problems with our civilization is that we typically do the important stuff out of our children's sight, and then come home tired and try to relax. So they do not naturally get a correct idea of what we do.
I don’t disagree with you. Parenting is hard, and some of the job is being a role model. If you show your kids the only way to relax is to beg in front of Netflix that’s what they’ll see. One of the nicest things I see on a weekday evening bfis kids with their parents at the driving range - it’s clearly 0 break for the parent, but the kids are usually having a great time doing what mom/dad like doing.
Oh yeah let's turn otherwise fun hobbies into a forced chore, that will surely be great for the kid. Forcing kids to learn to spell when they have learning difficulties (eg dyslexia) doesn't usually go well either it's just causing suffering for the kid.
The problem in this discussion is that people here seem to miss that both an excessively authoritarian parenting style is bad but also going full liberal and just letting them run wild is not the solution. Sometimes children need guidance an a gentle push.
Even as a adult I sometimes need to get pushed. I sometimes take guided courses so I don't skip over the hard but important parts of learning a new thing.
Just don't push your children too hard or you do more harm than good. Accept that they are not you and have different interests and needs. Like make them practice an instrument but give them a choice which one. And if after a few years they still hate it, well you tried. Maybe it is not for them.
I think much can be learned from modern American kids sports vs the Soviet youth sports system.
Kids specialize almost immediately now in a sport that is most likely because the parent likes that sport and wants the kid to be good at it.
The Soviet system was the athlete as a kid should try as many different sports as possible until 12 or 13 because you don't know what the kid will have natural talent at for before then.
That is not pushing the kid to practice something they hate but it is also not letting the kid be free to not do anything besides play on the phone.
Kids ultimately like what they are good at. If I had a kid, I feel like my job would be to figure out what they have some talent at and then fan the flames so that talent turns into a passion. I think many parents though are trying to live out their own dreams through the kid, if the kid has talent for the activity or not.
I think the most important part is to start early. Make your kids interested in math, music, art, and sport, before they start school. Doesn't have to be anything sophisticated, simple addition and puzzles will do for math, etc. Then you have something you can later build on.
There are also ways to make things funny, including math. Most people say that they hate math, but then they do Sudoku. So, try to make more math like this. Not all math can be transformed to funny puzzles, but after a few the kids will get positive associations with the subject, and will be more willing to learn more.
Doesn’t seem to be an issue for Asian families or ones coming the from former Soviet block as well as Jewish ones. These groups as adults tend to outperform others. There’s a reason for that: early childhood discipline and consistency being built into their cultures.
> Forcing kids to learn to spell when they have learning difficulties (eg dyslexia) doesn't usually go well either it's just causing suffering for the kid.
I greatly valued the tutoring that I received for that (personally wish it had not been cut short). I was somewhat fortunate and received one-on-one tutoring in a secluded room.
They provided me with clearer definition of rules (instead of sayings like "i before e...", proper phonetics, and a history of where English came from.
That said, there's research into trying to determine which children with Dyslexia should receive specialized treatment as a segment just cannot learn to read at all.
Double-edged sword IMO. I was mandated to a half hour of piano practice early on, and I came to dread it. But in my experience that was less having to do with being pushed to practice, and more I loathed my parents overhearing my piano playing and thinking they'd come down and criticize me for not trying hard enough. This was an uncommon occurrence, but it occurred enough to plant the seeds of anxiety in my mind.
The nature of pushing needs to be considered in the sense of the overall parent-child relationship, and not just being handed a Mikrokosmos and an egg timer. If my parents were more proud of my ability to push forward and took interest in the piano and my playing beyond just performing good at recitals, I probably would have grown up to truly enjoy performing music. Today I'm left with a bit of a bad taste in my mouth that would require conceited effort to overcome. So I guess my parents weren't "lazy" in your terms but a bit too strict for me to conclude I would be "good at music" that early.
> A very small minority of kids will do all of that easily and for the fun, but you can't rely on it
This may be true, but explain to me what are the returns you get on forcing math (or anything) on kids? They won't like it, they won't learn it intimately, the won't internalize it, it'll be unusable knowledge and mostly a waste of time with lots of bad vibes and probably even a little trauma...
I spent a lot of time with math in high school and college but that was because I had a couple teachers who really elucidated why *I* might find math to be interesting (in my case, it was physics and computing). Forcing people to do anything generally leads to nothing worthwhile.
I think there's also a significant cultural dimension to this discussion.
For example, in many Middle Eastern and Asian cultures (pardon my generalization here), there's an ingrained expectation that children should be pushed, often quite hard, especially in areas like mathematics, science, engineering, and law. Hence the old cliche: "You have three career options: doctor, lawyer, or engineer.".
I've seen this firsthand as a Middle Easterner (I was born in IRAN). My father is an engineer, and both my parents were relentless when it came to academic discipline. I ended up in computer science, and my brother became a pharmaceutical researcher after obtaining his PHD.. There's no question that this kind of structure and pressure produced tangible results. But I'd be lying if I said it was an easy or joyful process. It ended up costing me plenty of social anxieties and now I struggle with social dynamics.
That said, I have mixed feelings about it. While the rigor pays off in terms of career and technical competence, it often comes at the cost of creativity, intrinsic motivation, and the space to explore things like literature, music, and the arts. I sometimes wonder what paths we might have followed if exploration had been valued as highly as performance.
So I _partially_ agree with you that some degree of external motivation is necessary, especially with children who haven't yet developed discipline. But I also think we should be careful not to frame this solely as a matter of "lazy" vs. "good" parenting. Upon reflection, I think that there's a balance between encouragement, discipline, and allowing for the development of intrinsic interest. Different families, cultures, and even individual children may need to strike this in different ways.
But should the parent decide if the kid will become a musician?
What if its not talented and pushing it with force to mechanically play Mozart?
I later became interested in playing bass guitar, nobody forced me.
I did it for leisure.
Children are and will not be experts in all fields.
Sure you are right that some discipline is needed to move forward and to keep up with something.
Do you remember and use everything you ever learned in school, if its not needed for your current job?
Kids nowadays spent half to 3/4 of the day in school or outside their own home.
When should they be kids?
I understand the pressure of parents to make sure they have good grades, some is necessary, but not really all of it.
I never learned touch type in school. I did that on my own after work within half a year. I did it because i was interested in. Worked 20 years in IT.
Now i am currently trying to get my amateur radio license, i use my knowledge that i collected so far, allthough i was bad at math in school.
Life is a journey, i got three professions so far.
> Most kids won't do difficult things if you don't push them.
I guess it's true for adult humans, and other creatures as well. Instead of pushing, however, you should consider using other motivational methods (a simple prize for accomplishing something that you want from your kids works very well). Pushing can cause alienation and hate, which could affect their entire adult life.
I think many adults don't push themselves because they were always pushed by others their entire lives. It's a form of learned helplessness. You never have a say in what to do, so you just do what you're told, nothing more.
Every kid that I know who was forced to do their 20 minutes of piano a day now doesn't play piano and can only play with sheet music in front of them. They can't improvise, they seem to take no joy in the music.
I was the kid who wanted a keyboard and guitar but didn't get one until I could afford one in my twenties, then I learned just enough to be able to be creative. People say I'm good at piano but technically I suck, I'm just creative and expressive with limited tools.
It's an interesting phenomenon, the adults who are technically great at piano, but can't play anything without it being written in sheet music.
I agree. I got frustrated a lot being forced to practice the piano as a child. Not a long practice, just like you mentioned, about 20 minutes a few days a week and an hour lesson every other week or so with someone in the neighborhood.
I look back at the memories very fondly now. As a pre-teen I got invited to play at my cousin's wedding and everyone still talks about it. It gave me a good foundation and I performed well in highschool band and small ensembles. I now play my instruments for my kids and it brings us all a lot of joy.
Both of my parents weren't especially musical. I'm not amazing or anything, but I've got enough skill to hear a tune from a show or someplace and play it at home for my kids reasonably enough. But I wouldn't be able to if my mom didn't make me practice.
Sample size 3 here and they are all adults and all STEM grads.
You have to push them, but push them right. That's a combination of coercion and encouragement and helping them avoid procrastination. There are hills to climb and they need helping over them to where the good stuff is.
I remember my eldest crying over ratios at the dining table. Then algebra at the kitchen table. Then crying again at real analysis in the pub with me. She graduated with a first in the end.
> My kid will do everything as long as it is interesting
Difficult things aren't interesting locally, you have to practice boring things in order to do interesting things in difficult subjects. Some kids do practice boring things if you just ask them, but most do not.
As an adult, you develop the agency to force yourself to do things you don't like doing
I can tell you as someone who was never forced into any extracurricular activities and was forced to go to church-schools that you probably should force your kids to learn something well (and not send them to religious schools)
You are not forced. You do stuffs you dont like because you racionally evaluate consequences that could probably not worth it if you don't do it. Why cannot we approach same attitude when raising kids?
I spend at least 40 hr a week doing something I have no motivation for. Most people do. Even if you don't hate your job, would you actually do it if you weren't getting paid?
> Most kids won't do difficult things if you don't push them.
I roughly classify parents in two groups: (1) like the author of the article, (2) like you. Based on my limited observation, neither can be claimed to give optimal results, and it more boils down to "see what actually works for your kid in the long term" which unfortunately far too often can only be definitely said in hindsight.
Just on this, do you factor in that maybe they don't practice the piano because they aren't interested in it, and that's fine because it has no practical utility? I.e. in contrast with things like spelling, which do.
Also in your opinion at what age should pushing start, and how much pushing per age group?
How do you know that the conclusion you’re drawing from your experience raising kids is correct? There are alternative conclusions that sound like they match your experience, such as “most kids won’t do difficult things that don’t interest them if you don’t push them.”
The world needs less Asian kids being forced to play piano since a very early age and it needs more kids (Asian and not only) that are left to explore the world.
Without that exploration the kids won't make the world their world, at best they'd only make it a bad approximation of what we, our (older) generation, best think that that world should be.
I prefer to live among educated people, thank you. I prefer my peers to go through forced history lessons, forced math lessons so they don’t tank my government, and biology lessons so they don’t tank the health system. Yes they won’t be able to determine their gender, but that will give me grandkids, thank you very much.
Same goes for piano or sports. Yes we need to pull people upwards, otherwise we’ll all become fat americans.
I kind of get the both sides of the argument. It kinda feels wrong on one hand. Lots of people agree. The other hand, it kinda, just works. Great. Everyone's hit with down-trend TFR anyway so maybe not it.
> at best they'd only make it a bad approximation of what we, our (older) generation, best think that that world should be.
Also, this part in GP doesn't feel exactly right to me. The problem doesn't seem to be in education, but rather lack of systematic resistance in current systems of society against humans weaponizing the system as tools to hamper progress of humanity as means to win minor inner struggles which is stupid. But the world doesn't seem to be moving in a wrong direction, only slowly.
Asian kids in 80s dreamed of bunches of permanent artificial space habitats running on fusion reactors. Still do. We've only gotten ground based fission reactors and space motor homes since then. But at least we are moving in that direction, just slower than at the ideal rate.
China's just done a humanoid robot marathon event. The winner completed the race. They're definitely in the future. US is, in a state not in line with site guideline to describe. And the latter is supposed to be more correct state than the other? How is that possible?
Because "forced history lessons" doesn't help said kids understand what history really is about, it just helps them accumulate facts, if that.
I'd say the same thing applies to math, where one can't really start understanding math until said kid is already an adolescent (unless they're a young Euler or something), so it always baffles me when I see parents filling their young kids with (fancy) arithmetics, most probably making said kids future therapy patients, all the while lauding themselves (the parents do, that is) that they're teaching their kids "maths".
Related, one of the best maths teachers I've had (this was back in high-school, in the mid-90s) was very quick to point out that we should forget almost all "maths" we had learned in elementary school, and the he very soon started to explain to us the definition of the real numbers. Or maybe this is just an Eastern-European thing, who knows? Maybe further West they do confuse arithmetics with maths until the Uni' years.
You’ve got it backwards: the future therapy patients are kids who are not taught discipline and persistence. Those who aren’t struggle as adults as the real world is harsh on vibe based living. Also, all those “useless facts” eventually build up on each other. They are prerequisites of knowledge and mastery.
You mention Eastern Europe, are you by chance familiar with the Hejný method of math education in Czechia? Because that introduces some "math beyond mere arithmetics" concepts to the elementary school education.
Sometimes, it is possible to create a less abstract version of a more abstract thing, and thus introduce the seeds of the concept to children much younger. For example, "solve the equation 2x+1=7" is abstract, but "Peter decided to use a # symbol for a specific number, and he didn't tell us which one, but we found in his notes that # + # + 1 = 7; can you figure out which number is # ?" is simple to understand for a very young child, even if the child can only solve it by trial and error.
Forced history lessons are just indoctrination and propaganda, since what you learn is dictated by the government. I wonder if there’s a single country on Earth that teaches e.g. the history of Israel-Palestine conflict in a way that even tries to approach objectivity.
All history lessons are indoctrination at the very least. There's not some "objective history book" where people can just learn "objective history" without zero doubts. Even for things that are taught more or less "objectively", no one alive has firsthand experience of them, unless they are recent. The end result of teaching critical thinking is that you shouldn't trust anyone completely, not yourself, and not your teachers. It's just that adding the layer of government propaganda makes things worse.
This is such an arbitrary and random choice. I don't give a ** if your child can play piano. It's negligible if you compare it with other hobbies.
Teach them (and me) how to pay taxes, do community service, partake in social events instead. I also don't want to live in a world where robots go to work for 40 hours, go home wasted and repeat for 40 years as they do in so many East Asian country. Its a stereotype yes, but you can't deny its unhealthy.
What do you mean by "science" in this context? For example, both biology and anthropology are sciences, but biology can tell us that people evolved from apes, while anthropology can tell us that a specific tribe believes that they were created by a flying serpent. Both of them are sciences, both of them can talk about the same topic (the origin of humans), but they take a completely different perspective on the topic.
Is the "transgender science" you talk about more like biology, i.e. describing how things are, or more like anthropology, i.e. describing what some (sub)cultures believe? Those are not the same things.
Biological and cultural/historical. There is rather strong clinical evidence on the healthcare side of things, and an understanding of intersex biology (including how the the brain develops, not just the classically understood intersexes) shows a complex picture of where various components of gender may originate from on a biological level.
But yes, much of what Foucault taught us about the arbitrariness of being a human in a culture does still ring true. No, it doesn't discount the hard evidence from biology and psychology.
Except they are now, wealthy Chinese are one of the most rapidly growing segment of tourists. Wanna guess what the wealthy successful ones learned as kids? That’s right: piano and math.
Not if access to those things are limited while providing opportunities for other things that people enjoy.
You don't replace enjoyable things with unenjoyable things and expect the child to become a well-adjusted adult. You give them alternative enjoyable things.
Managing a child's burgeoning dopamine regulation system is a primary function of a parent. Abdicating that function for quick fixes is a form of neglect, in my opinion, just like feeding kids sugary cereals.
It is not just me who "provides the world" to my children. Also their classmates, etc. And the internet: even when someone uses it to achieve a purpose, there are various ads and algorithms that try to turn you towards something else.
At first I am reluctant to agree. But I decided to take math and English every year. I sucked at math, and had to figure out how to get good on my own. Now I have a degree. Math and music go hand in hand. I hated the music I was learning, so I quit lessons, and got the music I wanted to learn and struggled to learn it and I got muh better. I am an avid reader.
I reluctantly admit that you are right, and I am the better for it because I overcame my lazyness and found joy, in math, English, reading, and music. I sing, play piano, guitar, and listen with appreciation.
Its not a good take because no alternative is provided, but the author does notice something important that 99% of other people don't notice today. They don't realize it explicitly, but the actions do recognize it implicitly.
The school system today uses elements, structures, and clusters, the same techniques used in real torture. Its embedded into the structure of by-rote pedagogy starting in the late 1970s, and it also goes by another name starting in the 90s, where Administrators, NEA representatives, and Teachers, call this "Lying to Children".
Most parents today seem to be simply too busy, treating school like daycare, or maybe they just don't love their children enough to put the time in to protect them and figure out what is actually happening to their kids.
Classic curricula followed the western philosophy of the greeks, you develop tools that let you reduce a working system to first principles (in guided manner), which are proven true, and then you use those principles to model the system accurate, and then predict the future parts of that system.
"Lying to Children" does the exact opposite in time. It starts with a flawed model that is useless teaching abstract concepts and includes other unrelated concepts that arise naturally from that flawed model. The student is then as mastery progresses forced to struggle to unlearn material that isn't correct, and then relearn the finer details with each new flawed model given in a progressive fashion, over, and over, and over, becoming more useful yes, but torturing themselves, and in a way destroying themselves in the process.
When questions or true insights occur, the flawed model breaks those insights requiring you to do things differently in earlier classes before you can use those, but not even this information is given so you can't leap frog the torture.
There are additional strategic structures that orchestrate failures to gatekeep technical fields like math. There is an Algebra->Geometry->Trigonometry sequence which uses a gimmick in undisclosed pass criteria between class 1 and class 3, so the student passes initially but then fails and has to go back to Algebra, but can't because its sequential.
Its called burning the bridge.
Regardless, the student is blamed, no help is given (because there is no cure for torture). They are told, "maybe you're just not a math person, you should choose a career that doesn't use this if your having trouble.
This gatekeeper is orchestrated to induce PTSD towards math in general, and as all technical fields require math this prevents them from entering those fields. Some are able to pass and enter these professions, but never the best and brightest, only the most compliant with blinders.
The exception to this is if you bypassed the entire process through private boarding school, and Ivy league college straightaway. If your an elite, you get a decent education.
These structures follow a false ideology based in gnosis/gnosticism which is long refuted, but that hasn't stopped these things from being used for purpose, or allowed others to remove these.
There is an all out war that has been happening for years, a war on our children. Compare low attention spans and other things with the documented characteristics of torture from PoWs and you'll see there are parallels everywhere.
The thousand yard stare. Hollowed out feelings. Lashing out. These are often referenced in the material on torture.
The problem is unlike adults, once broken and distorted by torture children carry that forward their entire lives, unable to change because its not learning, its torture, and there are very few who ever recover.
Failing to see the reality of what is happening and calling it lazy and complacent without understanding is problematic and most definitely not the sign of a good parent if that means you let your children's minds be destroyed under a false belief that its just laziness.
For those parents that are unaware of what I mean by torture. You can read books on the subject matter by Joost Meerloo, or Robert Lifton. From the case studies you can derive the requirements and you would be shocked to find and recognize these things being used everywhere today without you knowing. Robert Cialdini touches on the psychological blindspots used which bypass your and your children's perception to the issue.
The elements are isolation, cognitive dissonance, coercion with real or perceived loss, and lack of agency to remove oneself from the situation. Some would argue this also includes time and exposure.
Structuring and Clustering, forces active engagement through specially designed circular trauma loops, forcing the psyche back on itself to destroy itself, and narco-synthesis and narco-analysis which in the 50s used barbituates to trigger dopamine are used today through associative priming through many ways including your phone (gamification uses many of these things learned from research on torture).
It is established that those who are drugged have less resistance to torture, and those with faith-based beliefs tend to resist torture better. One of the first things to go under torture is rational thought.
The important part is to start as early as possible and absolutely not trust the school/teacher or kindergarden staff. They are badly programmed to reinforce kids in what comes easy to them and stop encouraging them after less than a handful of attempts.
If you have to restart later, no matter at which point, even up into 'the kids' 20s ( ultra late bloomers, slackers, kids disgusted by most people for reason Z, drug- or "condition X"-induced deadbeats, repressed kids with and without ADHD, failed or successful attempts by psycho-social environments ) understand three things:
1) you are not pushing, even if you are, you are demanding sth for the sake of your child AND yourself. YOU WANT THIS first and foremost. It's not a bad thing, fuck what the little fucker wants.
It's imperative for the kid to know that YOU WANT THIS no matter the obstacles. You want to see the process and result. It's a form of accountability, I guess. Kids pushing back is some dumb implicit way to check how important THEY and THE THING really are to you _or someone else_ (that counts for the ugly stuff, too). It's part of our evolutionary, hard-coded OODA loop.
2) just start at the very beginning, so that it's easy, almost effortless. The kid will be annoyed on most of the difficulty increases, it always depends on the sub-topic so don't back down. Even 20 year olds will catch up with their successful piers within some time. Neuro-genesis is awesome. Most 'grown up' stuff is child's play and a matter of baseline-human character anyway.
3) your stress level is what matters. Stay cool, be equanimous, serene, check your posture, voice, tone, the discussion won't last 5 min and will be worth it.
A friend of mine taught remedial math at UW to incoming freshmen. She would write:
x + 2 = 5
on the blackboard and ask a student "what is the value of x?" The student would see the x, and immediately respond with x means algebra, algebra is hard, I cannot do algebra.
So she started writing:
_ + 2 = 5
and ask the student to fill in the blank. "Oh, it's 3!"
The semantic meaning of a blank is much better understood to everyone than an arbitrary letter like 'x'.
People just want to know why it's x and not something else or how a letter can have value. They might even think how can 24 + 2 = 5? They just want something to grab onto and nobody is really teaching the concept of a symbol in a math class.
I will die on the hill that most of math would benefit from better naming, less short names and longer format.
Yes, the crack math guys have no problems with terse symbols. But most people do.
Good example is Greek letters for geometry. They are not really taught in school so an easy formula gets 'weird squiggly thing times another squiggly thing....' and that does not help understanding at all
This is like trying to change English or arguing that we should all speak Esperanto. Mathematical notation isn't the way it is to save ink or make it look difficult. It's that way because it works. Notation isn't set by committee, it's just a way of communication that works. If you read cutting edge research you'll find notations being invented all over the place. Most of them will never go anywhere, some will become standard in their field (like big-O) and others will become universally used (like dropping the multiplication symbol and using epsilon for a small number).
I think this is a very limited take for a hacker forum. We talk about how useful accurate names for variables are all the time, or generally how working to encode more natural/context-related semantics to code helps anyone reading it understand what the goal is better than an extremely terse symbology.
Yeah, lots of existing math texts will forever exist with greek alphabet soup, but we don't have to rely on those as our be-all-end-all teaching tools.
To operate at a high level in mathematics I would agree that having the skill of easily abstracting complex things into compact symbols is a necessary skill, just as I would agree to the same concept applied to software engineering or really any complex engineering system; by the same token, we don't have to START on hard mode with all of our students. Math is infamously difficult for some, largely (I think) because we make it unnecessarily opaque out of some misguided sense of traditionalism.
If we want to have lots of people who are good at math we should embrace whatever pedagogy is effective.
Math doesn't start on hard mode. Students spend years studying how numbers behave before doing symbolic math. That said, trying to cover the topics symbolic math does with a more verbose language would just make it into impossible mode. It'd be like trying to replace sheet music with words.
In fact the analogy to music notation is I think a fairly strong one. People's complaints always sound to me like asking why we don't write "C3 sixteenth note" for music instead of using dots and lines. After all, how are we meant to know what the dots mean and remember the difference between an eighth and sixteenth, or what flats/sharps do? And then the key signature can modify all of it!
The notation just isn't a barrier. Once you learn to read it, it's there because it's a clearer way to write the ideas. The hard part for people is they don't understand the ideas, and don't have the frameworks like key signatures, chord progressions, and meter to place them within. Longer words for variables won't help people understand e.g. inner and outer regular measures, or the open cover definition of compactness. That comes from a lot of work to understand what you're trying to say, the pitfalls of saying it wrong, and precisely how your slightly different way of saying it avoids those pitfalls (or selects the best set of pitfalls if you must pick some kind of degenerate behavior).
I hadn't thought of sheet music in this context before; that's a helpful counter-example, thanks.
Broadly I agree; the semantic density of domain-specific language is often required to operate well in that domain. I disagree some with the "Math doesn't start on hard mode," but I think that's just bikeshedding at some level.
The endemic "I just don't understand math" that my (American) peers have espoused, to me, points to a failure in our (American, public school) instruction practices around it.
Many programs are at a much higher level of abstraction than mathematics. If you are implementing domain logic then you should definitely use names from the domain. But when implementing an algorithm often the most meaningful name is a single character. I find it odd when people try to force the "no single character" rule everywhere.
But I've got to say, the short names are not the problem. If you rewrote F=ma as "force is equal to mass multiplied by acceleration" this wouldn't suddenly make it more accessible to swathes of the population. People who are good at maths anyway have no problem with this.
imagining that alpha is what stops people from being good at math is a useless take. why pretend that such a low bar could prevent anyone from understanding? its some fake generosity towards "newcomers" that is completely unwarranted. math notation is by and for professional mathematicians.
are you really saying that "let function(argument has type RealNumber) has type RealNumber be a function from a real number argument to a real number" is somehow superior to "let f(x) : R->R"
> why pretend that such a low bar could prevent anyone from understanding?
I don't know why this is a startling take. If you encode your ideas in an unfamilar symbology, of course that's going to make it more difficult for someone who isn't familiar with the space.
I'm not arguing that we should teach real analysis this way, or any other high level math class. I'm only contesting GP's comment that there is NO value to be had in using more familiar language to explain a new concept to an unfamiliar audience.
This is the entire reasoning behind "word problems" at the elementary level; they're meant to ground the abstract modeling of a math problem (193 - 3 * 12 = ?) into something more intuitive for a child to understand (If you start with 193 eggs, and you take three dozen away to bake a cake, how many are left?)
> are you really saying that "let function(argument has type RealNumber) has type RealNumber be a function from a real number argument to a real number" is somehow superior to "let f(x) : R->R"
No, I'm saying the there's tradeoffs on either side, and our educators ought to be aware of this.
> math notation is by and for professional mathematicians.
I agree, but we teach math to plenty of people who aren't professional mathematicians. I wouldn't want to do formal abstract algebra proofs in a more verbose form, I'm perfectly happy using the domain notation, but my friends from biological sciences who have to take a calculus course now have to learn both a new symbology alongside the problem domain. I've watched enough of my (clearly intelligent) biology friends slam face first into calculus and spin out. They're not dumb, they can do circles around me when it comes to chemistry, yet they Just Can't wrap their heads around calculus-style math, which leads me to wonder what the difference is between how we teach complex chemistry vs complex math. Questioning the pedagogy is a fairly logical extension of that.
If there was some better notation that allowed biology people to understand calculus more easily, what do you imagine they'd do with it?
It's hard for me to imagine it without any special notation. It makes me think of the general relativity in words of four characters or less that was posted recently. Sure, it might be possible, but does it really make it easier to understand? Understanding is normally built up in layers. We learn things using big words because that makes it easier than learning with small words. And we learn maths with funny symbols because it makes it easier than learning it with words (or colours or mime or other things you already know).
For any given problem, you usually know what it is your studying, so writing out names doesn't have much benefit. On the other hand, a more visual language (which is what mathematical writing is) lets you easily look at specific portions of the picture and read off how it behaves, which is very useful. Basically, getting hung up on names means you're reading it wrong.
I don’t recall the exact age, but when I was doing math in primary school (somewhere around age 9/10) we were absolutely using symbols - “Paul has two apples, and the basket can hold 10 apples. How many more apples can Paul put in the basket” is the same as 2 + x = 10
We did these sorts of problems for a long time, with addition/multiplication/fractions, and even when we started doing actual algebra the problems were introduced the same way “let’s look at a problem we’ve solved already, and write it in a different way”.
This becomes even more true in higher level maths where programming language style functions would make everything vastly more clear, and easily typeable, than the traditional Greek symbols. sum(x+3, 1, 4) is just so much more clear (and consistent when generalized across other operations) and practically as concise as the mathematical way of expressing that which I cannot even type. Multiple variables would be a bit dirtier, but still much cleaner than the formal expression.
Interestingly mathematical symbols in the past also regularly evolved. Then at some point we just stopped doing that and get stuck in a time which is arguably no longer especially appropriate. So we're left with rather inconsistent symbols, oft reused in different contexts, and optimized for written communication.
The formal language of math is intensely optimized for rapidly communicating with yourself 90 seconds in the future, when doing a proof or calculation, turning paper into working memory. It does seem silly to use the same language for communicating with others across unkniwn but deep chasms of context. Its remarkable that it works at all
The strangest part about mathematics culture is that there is a culture of vibing the notation.
Nobody in school ever tells you that there are glossaries on Wikipedia that tell you the meaning of the symbols. You're supposed to figure it out yourself using vibes.
The way mathematic notation is taught is inherently unstructured. You're expected to just get it.
For the purposes of education, it is important to keep in mind that "optimized for performance of a highly trained person" and "optimized for understanding of a complete beginner" are two different things.
I often see people make the mistake of trying to teach inappropriately abstract things to small children, because that's what the pros do, and we want the little kids become pros as soon as possible. Problem is, trying to skip the fundamentals is only harmful in long term.
First kids need to learn what all that stuff means, and then we can proceed to teach them the shortcuts.
its silly. itd be like introducing first year programming students to advanced maps/filters/anonymous function syntax, instead of the easier to understand for loops and if/else statements. math's "no true scottsman" approach to teaching only hurts itself in the long run.
I'm not sure if it would be easier to explain a map / filter to a first year student vs implementing the patten manually using a for loop and if statement...
Seems like a pretty easy example to make practically, for map have a collection of things, say balls or black. Pick up each one and do a thing to them, paint them blue for example.
For filter do the same except have two different colour balls, if they are yellow they get thrown away, of they are blue they get put in a bucket.
A for loop doing exactly the same you would need to explain the topic at hand, as well as explain iterating an index etc...
Explaining loops is independent of the concepts of collections though. It's also more general, since map/filter/reduce use some kind of loops under the hood anyway, the fact that probably shouldn't be ignored in education process. Unless of course you go with pure functional recursive iterator, but good luck explaining that one.
Maps and filters also require understanding of higher order functions and the very idea of passing function around as a value. I would argue that implementing map/filter with a loop and then demonstrating how this pattern is generalized as .map()/.filter() functions is better and more accessible
I thought that was it too, but you're saying it's not..? I've been thinking about it for a few minutes now and I still can't figure out what other meaning it could have.
Edit: Oh wait, someone else mentions map/filter, did they mean this as a combination of range->map->sum and the latter two numbers are the range portion, like sum(map(x+3, 1..4)) ?
Edit2: And now I'm remembering sigma. I think it would have been more obvious to me if the order was flipped and your issue handled the way it is in that notation: sum(x=1, 4, x+3), though I'd still prefer the range notation: sum(x=1..4, x+3)
Yep. I agree and now we've basically reinvented sigma. Take the x=1 and put it below, take the 4 and put it above take the x+3 and put it to the right.
Granted I always found sigma a bit quirky for separating the range ends like that. Either x below and 1..4 above, or x=1..4 below/above would have been more intuitive.
But it's just a notation you learn once and then you know it.
Thanks for this comment. My secret shame as a programmer is that I haven't really learnt much maths, stopped at 16 in school. Writing out the sum function like you did makes perfect sense to me immediately.
What I should really do is create myself a cheat sheet of symbols to code...
It's hard to debate that mathematical notation has a lot of room for improvement. High level algebra is very cryptic and often looks like an arcane incantation rather than something comprehensible for an unknowing person.
That said, as a person who moderately enjoyed math in high school and university, this functional notation would make me hate math infinitely more. It's would look like Lisp, which, at high level, looks just as cryptic as algebra. The sheer amount of braces and mistakes that would be made when reading and writing them is nauseating.
Infix notation, for all its flaws, provides important visual aid for understanding the structure of the expression (the sum of two fractions looks very different from fraction of two sums for example). Whereas with functional notation it's like working on linear textual representation of abstract syntax tree. Trust me, nobody wants to read, write or transform one by hand
> People just want to know why it's x and not something else or how a letter can have value.
The way I was taught it and the way that worked now for my now 3 year old is just to say pirates buried a number under the X, and that we need to guess what they buried. If the concept of a number being hidden is a barrier to understanding for anyone they have seriously bad teachers.
The problem is, in many MANY MANY schools, teachers are more like social workers that have to compensate for utter horrifics outside of school. You got a ton of children so poor they didn't have breakfast which means their first (and all too often: only) meal will be the school-provided lunch (Covid showed that - a bunch of schools were open at least for lunches). You got children that are literally homeless and living with their parents in some car on a Walmart parking lot. You got children whose parents are in and out of jail. You got children living with their siblings in way too small, pest and mold ridden "apartments". You got children whose parents don't have money to pay for basic school supplies. You got children who are dealing with mental, physical and sexual abuse. You got children where the parents are constantly on drugs or seeking for drugs. You got children with a drug dependency on their own - if they're lucky it's just tobacco or weed, if not it's opioids. You got children with parents or siblings with serious mental or physical health issues. Or you got children with their own mental and physical health issues, or if you want it worse, children with these issues but without access to any kind of treatment. You got children that are being weaponized in nasty divorces. You got children that are being weaponized by street gangs. You got children committing crimes from petty theft to dealing drugs just to survive. You got children that have to literally work (and states like FL pushing to have more working children). You got children having their own children already (either from sexual abuse, from under-education about their own bodies, or intentionally because they fell for some stupid challenge/dare). You got children dealing with bullying, you got some who actually are bullies because they have no other way of dealing with their emotions or getting lunch money. You got children with parents with about zero interest in them. You got children who worry that they'll come home and find out their parents got snatched and disappeared by ICE. You got children who worry that ICE will storm their classroom and deport them. You got children who worry they might not survive the school day because someone will shoot at them. You got children who are constantly on the move because their parents' employment/deployment requires absolute mobility. You got children who are LGBT and have to deal with ever increasing hate against them (and LGBT youth already had significantly higher suicide rates than before the GQP made it a culture war issue).
The US doesn't have any kind of system to help these children but schools and libraries, both are horribly underfunded (there's some school districts where teachers gotta take up second jobs because the government can only afford paying them for 4 days a week), and all too often teachers have to pay with their own money for students' school supplies.
And on top of dealing with these kind of nightmares, they actually have to try and teach these children something - even if the children in question aren't anywhere near a headspace where they can actually learn.
I taught at a nice middle-class school, so most of the problems you mention were not relevant there. And yet, it seemed like half of the kids' families were either recently divorced or in the process of divorce. I couldn't really blame those kids for not paying attention to school. And this seemed like the best case, so probably at most places it gets much worse.
Education has a problem with scaling, especially at the elementary level. Sometimes people figure out a nice solution, but when you tell them "great, and now do this in every village" the problem becomes obvious. But there are kids in that village, too, and you want them to know reading and math and hopefully also something more.
> Education has a problem with scaling, especially at the elementary level.
Not if you actually provide the money. Europe gets this down decently well - although I'll admit, in rural areas in Germany we got some serious consolidation issues thanks to urban flight.
But at least our teachers are well paid government jobs and the job is decently attractive.
Scaling is not just about money. It's also about teachers. You can have hundreds of great teachers, but if the entire educational system requires tens of thousands of teachers, you will end up with many mediocre ones, because you simply don't have tens of thousands of great ones.
There's plenty of money thrown at schools in the US, but the issue is that the students that live in poor socioeconomic conditions tend to not do well. The "simple answer" that addresses the root cause would make individuals not subject to poverty and whatnot. But throwing money at institutions is already on the ropes in the US, let alone throwing money at the "undeserving".
(Yes, this is a political opinion. No, do not blame me for that. Politics does not come wrapped up neatly with a bow tie in a box. If you want to debate the veracity of my claim, go do that instead.)
> If you want to debate the veracity of my claim, go do that instead.
I'd do no such thing because you are completely correct - the only thing I'd add is that poverty, while being very dominant, isn't the only issue that desperately needs to be fixed.
I’ve always found that an indictment of math education — and spent many, many hours discussing it.
When teaching addition, workbooks commonly use a box, eg, “[ ] + 2 = 5” — and first graders have no conceptual problem with this. Somehow, we lose people by the time we’re trying to formalize the same concept in algebra. There’s been many times I’ve written a box around letters in a problem and asked students “what’s in the box labeled x?”
I agree. I think the actual problem is that the student is trying to comprehend what it means for anything to have mathematical value other than explicit numbers.
Numbers and letters are taught together, but not as symbols. Letters are taught with sounds and numbers are taught with counting. The notion of a symbol isn't really emphasized much.
I would explain it more like after
[ ] + 2 = 5
what happens if you need more than one box for a complicated problem? Teach the idea that saying box #3 is equivalent to assigning an arbitrary letter for whatever reason you want, but that people more familiar with math prefer letters because they stand in for words that describe what the number is for. You might want to use 'c' for the number of cats you're trying to figure out.
In a room of five animals two are dogs. How many cats?
a = 5, c = ?, d = 2
a = c + d
so... 5 = c + 2
what is c?
Light bulb goes off: "You can do that?" Yes, you can do whatever you want and it's not all about carrying the one or whatever other rote teaching they've been given. They can get creative and be engaged, and then you let them know that actually there are some conventions people like to use for what they're trying to do. They might even believe they've invented a new idea. At least they're having fun.
To me, a lot of pre-college math education could be summarized as "In this class I will show you a bunch of abstract problems, a bunch of ways to solve them, and I will test if you have learned them." Learning in these classes is often limited to memorizing a sequence of steps.
That's why I would frequently ask "You can do that?" myself when talking to those whom I considered mathematically gifted (math olympiad winners and such). I think they realized that as a problem-solving tool math could be used creatively. I saw it as a largely useless hammer that to work had to be held in a very specific way.
I remember connecting sets in, I think, Pascal to what I had learned in school and realizing that all that math was perhaps not as useless as I had thought : - )
You skipped a step. One of the problems is more obvious with a different operator we learn when in the "box" stage:
> Go from "[ ] x 2 = 10" to writing it "box x 2 = 10--what is box?". Then "b x 2 = 10--what is b?" then "x x 2 = 10--what is x?".
From memory, we didn't switch from "x" to dot for multiplication until at the exact same time we started using symbols. If we'd done it earlier (or even right from the start) it might not have been as much of a problem.
most likely this very unfortunate misnomer started with fortran, where it was deemed lucrative to point out "how much programs look like mathematic formulas!".
not only is this overloading a symbol (equality) with a completely different meaning (assignment), it is also a poor choice typographically, as it represents a directional operation with a directionless symbol.
using an arrow for assignment is much better.
it's also worth pointing out that unlike most others, logic programming languages (e.g. prolog) have actual variables, not references to mutable or immutable memory cells.
arrow for assignment is cool, but the backspace key is the only closest arrow-like key on the keyboard but it has a different purpose. plus the arrow key should be laid out such that u dont have to press a SHIFT/CTRL/ALT to produce it.
for this reason, i felt C a breath of fresh air cos u could just assign using = instead of what we was doing in pascal which was the horrible := where u had to press SHIFT for the :
There is a game called dragonbox algebra which I'm currently working through with my son and is an absolutely fantastic approach to this problem. Sadly its now part of a horrendous subscription service and is hard to access. I find it really sad that we've had computers for decades and there are so few good maths games like this.
One of my school math teacher had the same approach in another way: We were expected to use greek letters, not latin ones.
Same reasoning: It showed us kiddos that the letter was insignificant compared to the concept expressed by the letter.
So my take would be: Your friend taught the students for the first time what they were actually doing while handling equations with "a letter in it". That is no problem of algebra in itself. It just means their previous teachers sucked.
She loves it. It uses a ‘?’ for basic algebra style problems and after a few days of playing (if/when she wants to, we don’t make her play it), she was already much better and faster at those problems. It made me think that schools should be giving kids games like these.
There are two sides to this. The system or method might be bad but also a determined person can go all the way and perform at a decent level if they put in enough time.
Even if the system was better the person still has to be able to motivate themselves and put in the time.
I tell my kid that math is a language. You learn to speak it, just like you learn to speak any other language, slowly, by listening, understanding, speaking, intuitively recognizing patterns, rules and exceptions. When you start to become fluent you translate problems into math and solve them. At school they keep trying to make them memorize useful phrases, like a tourist that goes to Paris and learns how to say "where's the bathroom", "hello", "would you like to sleep with me", "thank you", "goodbye", etc.
If you are a physicist or an economist, you may be using mathematics as a language in the sense that you are using a mathematical description to convey an understanding of the natural world or the economy to your colleagues. But if you are a mathematician, you are interested in the mathematical objects for their own sake.
There is also a difference between the purpose of learning language and learning math. The goal of learning language is (often) to be fluent in it. In other words, the goal is to reach a level of proficiency which would allow you to not have to think about language and focus on the content of the conversation instead. On the other hand, the goal of learning mathematics is usually to be able to solve mathematical problems. Being able to do math without "thinking about it" is not usually a requirement.
"At school they keep trying to make them memorize useful phrases, like a tourist that goes to Paris…."
Like learning dozens of trig identities without any explanation about why one would need them. As I've mentioned elsewhere learning math for the sake of it isn't enough. For most of us math has to have relevance, and for that we have to link it to things in the real world.
I'm damed sure I'd be much worse at math if I'd not been pushed in a formal environment such as a school classroom.
I liked math—especially calculus as it made sense to me—but parts became a drudgery when I could see no reason for studying them.
Right, there's always the kid in class who excels at math like a mini Euler and gets bored because the rest can't keep up but the majority of us aren't like that—doing Bessel functions and Fourier stuff as abstract mathematics without any seeming purpose can seem pointless and our only interest in them was to pass exams. (Teaching may be better these days but my textbooks never discussed the value of learning these aspects of mathematics.)
Later whilst studying elec eng/electronics it became very obvious to me how important these aspects of mathematics were. If I'd been given some practical examples of why this math was useful then I'd have been much more enthusiastic.
Same goes for the history of mathematics, I'm old enough to have had a small textbook full of log and trig tables yet if someone had asked me at highschool who John Napier was I wouldn't have had a clue. In hindsight, that was terrible.
Mathematics is often taught as if the student was going to become a mathematician à la Hardy or Ramanujan and I'm firmly of the belief this is not the best approach for the average student let alone those with few math skills.
Mathematics ought to be taught with the real world in mind for ease of understanding. For example, it's dead easy to represent AC power as a sine wave and from there use that mathematical fact to solve power problems. (Perhaps maths and physics texts should be written in tandem and synced to show relevance.)
Teachers need to take time to explain that math isn't just abstract concepts but that it's very relevant to everyday life and that tying up mathematical functions to things in the real world is actually interesting and enjoyable.
> (Perhaps maths and physics texts should be written in tandem and synced to show relevance.)
I agree with most of what you wrote, but this part is tricky. Yes, it would be nice to have math and physics textbooks synced. Maybe other subjects, too.
But writing a textbook is a lot of work; it can take years. How do we get two textbooks synced, if they are written by different people? One writes their book first, then the other has to match it? What if the other disagrees with how the first book was organized? They both write together? Now there is a risk that one does a good job, another does a bad job, and the good textbook is connected to the bad one.
Or maybe write the common outline first, and then each author is trying to follow it independently? Plus, there could be multiple versions of each book, following the same outline, so each math textbook can be connected with each physics textbook based on the same outline. Here the problem is that people often disagree on the outline.
Also, not sure how important is this part, having things in sync could slow down the improvement in the future. For example, imagine that we figure out a better way to teach something in physics. But now everyone is used to having math and physics textbooks synced, so the new physics books would be rejected, until someone rewrites the math books too.
Compare learning math to learning to bicycle. There is some some sweat and struggle that needs to be put in, before one "gets it". After this it can become enjoyable. I encouraged my daughter with practice exercises from a young age, but tried to avoid making it a drudge. She built up confidence and did well with it. She is also very hands on creative. She decided to study engineering and is working towards her PhD.
Those aren't nearly comparable. Riding a bike is one simple skill and as long as you're not racing that's enough for most people. Meanwhile learning maths is a years-long effort at best. I learned how to ride a bike within an hour by myself when I finally had a good reason to learn it. I can't say the same about maths.
Bike is fabulous self-correcting vehicle in most operation conditions. The trick really is just to learn to trust it when it is moving. And then what to do when it stops.
Math is layers upon layers upon layers. And then it also branches. Never really had willpower to learn it myself alone.
It does depend on what one defines as "riding a bicycle." At a moderate pace from point A to point B, or simply a lap around the neighborhood is one thing. Technical single tracks, grueling climbs, steep and slippery downhills, racing, maintenance and tuning, trials, jumps, drafting...
Math is just splitting the bill with your friends, seeing if you have enough cash for a hotdog AND a coke, or counting how many months of savings in order to buy that 5000$ bicycle.
20" competition trials bike, mulleted DH racing machine, full-squish slope-style dirtjumps, Japanese keirin, multi-week bikepacking, ITT, freeride.... Obviously there is some overlap.
Math, for most people, is the same a bicycles, for most people. With a handful of simple concepts, you can get by daily life.
The key element here is nurturing curiosity.
Since then i and my 10yr old have been sitting through a virtual math circle led by Aylean McDonald on parallel.org.uk an organization run by Simon Singh
Forcing is kind of hopeless. So is logic, and reasoning.
How children learn (they can't rely on a fully formed prefrontal cortex like adults) is very different than how adults learn (no fully developed prefrontal cortex until 25-26), learning about this can help a lot.
Learning more about the Reggio Emelia approach might help parents curious about this, it has been quite surprising how much is possible naturally. One of the best things to do is to relentlessly read to and with your kids.
Showing kids the math in every day things, especially things they already love is a helpful way of making it approachable, or at least aware.
Also, linking a topic to their interest's radar, encouraging curiosity, play in general, and letting them potentially discover it can go a long away.
When they've got something they want, teaching math and savings is a great thing. Understanding life is a lot harder without knowing a basic bit of math, and can be made a bit easier when doing it younger.
I had a math teacher that once made it clear, some stuff can just click, others is just about doing a lot of examples to learn the patterns. Doing math is very different than being creative with being comfortable to find it.
Today, I'd probably setup a good prompt to find a way for the child to share their mine to discover how they like to learn, and how they might like to learn faster and easier by taking some shortcuts through math directly or on navigating an ontology/taxonomy perspective.
> One of the best things to do is to relentlessly read to and with your kids.
My mom would bring us into the clubhouse in the backyard and read to us, which I found really boring. Ended up not liking books because of it, and I'm pretty sure the same happened to both of my brothers. For years I'd only read the bare minimum required for school.
Years later I happened to see an neat book cover in the impulse-buy section of a store and begged for the book. That one book was what actually got me set on reading, and from then on I'd always have something with me.
She never realized this and still thinks I like reading because she read to us. I can't help but wonder how many of the anecdotes here are also parents not realizing what's actually going through their kids' minds.
When I was 8, I went to the library in our town a lot. My parents went there sometime to return their books. At some point I just stayed there when they would go home. First I was in the children/teenager section and soon in the general library, where I would read about programming and computers. I learned C by age of nine.
The "undeveloped PFC" argument is shallow, unspecific and usually just used to infantilize younger people. It may be useful if the child is under 6 years old, but at the time someone is 17 or older, it becomes essentially useless.
My learning process was always, and still is fueled by curiosity.
As a counterpoint, look at how the Polgar sisters were raised.
Yes, Lazlo and his wife were both education professionals, and spent an inordinate amount of time dedicated to developing the girls. But look how it turned out.
On a different note, I used to hate sport when my parents forced me to play it. I liked screwing around on the computer or playing video games. However, when I found tennis naturally around 12 or 13, I couldn't get enough of it, and vastly improved on my own because I had a lot more fun playing than most of my peers did, who were forced into it by their parents. Most of them don't even play for fun anymore with friends, and I'm in my mid 30s and still play frequently.
It's not about forcing your kids to "do math", but to excel at important skills far before the benefits of being good at that skill matter.
The amount of homework/study per day that maximizes math scores on tests is significant, 1+ hours/school day by the time they're in middle school, with it helping even more for those who are starting out poor at math[0]. You'll note the referenced study doesn't even max out progress for any group - meaning most could have studied more and improved more.
I don't know any kids that voluntarily did an hour or more of solely math study per day. I know plenty that were forced, and ended up loving math or other technical fields as adults.
As a parent of young kids, obviously I haven't gone through high school yet - but I don't think many children who reach their potential in math, english, music etc will have no pressure from their parents.
> As a parent of young kids, obviously I haven't gone through high school yet - but I don't think many children who reach their potential in math, english, music etc will have no pressure from their parents.
Well it depends. I had no pressure from my parents to learn about programming but still got really good at it. Could I have gotten even better had I been pressured to "practice"? Perhaps. But then I also wouldn't like it for the reasons I do (I like making stuff, but not solving riddles) and it would feel like the dad sport situation.
I also played the piano for 6 years, starting out because I liked it. My parents didn't suggest it, but a few years in they were pushing me to continue even when I didn't like it anymore. Finished the first level of music school (6 years where I live) and haven't touched it since. Just to clarify, they weren't using any directly abusive tactics to keep me going, but they did put a lot of pressure onto it.
There's a lot of nuance to all of this and I don't completely disagree that we should occasionally pressure our kids to push their limits. What we often fail to acknowledge is that kids easily change their minds after a while. Just because they liked something at a certain point doesn't mean they still do. The easiest way to get a kid to dislike something is to make it a chore. Additionally, I think we need to ask ourselves whether it's more important to us to have a kid that's average scoring but has a (mostly) stress free upbringing, or one that excels but is stressed out by the time they hit high school. Kids absorb stress differently than we (adults) do.
2. A love of subversives and cheating the system. Basically, the guys writing leetcode cheating software are saints in my book. All subversions of the attempt to turn society into a meritocracy (a term which was originally supposed to be a slur/negative connotation - https://en.m.wikipedia.org/wiki/The_Rise_of_the_Meritocracy) is extremely good.
3. An advanced knowledge of TI basic, so I could cheat hard on every single school assignment I could get away with. AP Chemistry? I’ve got a symbolic stoichometry solver app! Calculus? CAS system in the palm of my hand!
Play stupid games with children, win stupid prizes. Maybe don’t force them to work like little slaves in their early life, and they won’t strike back at your society systems.
Raising kids is hard. Sad. And what do I know about it? Regardless, parents do need to get involved in their children's education. For instance, they should help their children prepare for entry exams into secondary school. This shouldn't take their child 4 hours a day. Maybe 10 minutes on some days, and 1 hour on others.
Your experience sounds awful but surely there is a reasonable middle ground between forcing a kid to do any math and forcing them to do it in 4+ hour sessions.
I had similar conclusions, but the other way around: absolutely no guidance. Fortunately by the time I programmed and sold the basic ti math exam solvers to by classmates for 2 euros a pop I had everything memorized.
Nothing like cheating the system to know the system
You realize your experience can't be generalized to anybody else except for those who were abused in the same way you were? It also isn't what people in these comments are suggesting should be done.
As someone who just finished school, I’m trying to figure out how to get genuinely interested in mathematics. I’ve never been particularly strong at it, yet I’m planning to enter a university program that demands a high level of math. The problem is, it’s hard to motivate myself to study math for its own sake. For example, I loved learning programming because it’s hands‑on—I can build something and immediately see the results. In everyday life, though, I rarely need more than basic arithmetic or simple sin/cos/tan trigonometry.
How do you develop a lasting interest in math when it doesn’t feel immediately useful?
Make it practical! Graphics programming involves linear algebra. Databases involve relational algebra. Machine learning involves requires calculus. You’ll naturally encounter hands-on tasks with tangible goals that involve learning new math.
One of my undergrad degrees is in math. As you study it, you learn to identify your assumptions (axioms), find or build interesting abstractions, prove properties about them (theorems), and then map all sorts of other things into those abstractions by figuring out that they're really the same thing. It's even more interesting when you start to find things that are different or question things you always took for granted.
Math gives you the ability to leverage the very structure and relationships of pure abstraction. It's quite the super power.
None of the specific things you learn studying math will be nearly as useful as the ability to think mathematically.
N=1 datapoint here.
I studied physics in university and before I started I was not aware that physics is basically just math where the results sometimes relate to reality. The pure math courses I took were the most difficult and in the beginning I loathed them, because it felt so unattainable to get any intuition, let alone real proper comprehension for all the concepts they threw at us. For a long time I felt like I was just hanging on by threads and especially if I compared myself to those who had some innate interest in math or generally some really good intuition on the abstract concepts (or even prior knowledge) it was really demotivating. But I also felt like I had no choice but to continue and as time went on the I grew fond of it. And the feeling of being overwhelmed changed - that is to say I still was completely lost every time a new topic was breached and I could not understand even half of the proofs in class - but I did not feel so defeated about it. And I grew to like the feeling of actually completing the work sheets they gave us every week. The process of solving them was often excruciating but if you did the sense of accomplishment is real. I think for most people higher math is really difficult and that is part of why it is interesting. Another aspect I had to accept over time is that even though you can state a mathematical fact or conjecture in just a hand full of symbols or a plain sentence it does not mean that truly understand it, its implications or how you got there can be understood the same way that other prose can be. Sometimes you have to stare at, contemplate and scribble around one equation for days until you understand whats up.
If there was any advice I would give, then it's probably similar advice on how to stop procrastinating on anything that is difficult. Establish a routine first - find a spot that you will only use for studying this (like a spot in a library), start small, divide and conquer, accept that you will not understand most things easily, reward yourself for the small wins along the way, find an accountability partner or someone to study with if that's your thing, make a regular schedule with regular times where this is what you do - consistency is key, even if its just for 5 minutes, stack it onto other habits, see yourself as a scholar of math - it is what you do, lean into the discomfort, as enduring that is a valuable skill in itself.
Don't study it for usefulness, study it for beauty. Look for amazing insights.
Yes, you need some practical math as well. I did engineering, there's a lot of inelegant stuff there.
But that stuff actually tends to be right next to some very interesting things.
Here are three things you can find out.
First, there's more than one kind of infinity. You can't make a map from natural numbers like 1, 2, 3 etc to real numbers like e, 0.632268, sqrt(2) etc. Look for Cantor diagonalization.
Second, a random walk like a heads vs tails comes back to zero almost certainly. It also does so in two dimensions, like walking randomly in Manhattan. In three dimensions, it does not, and so for higher dimensions. Look for Polya.
Third. There is a way for you and me to communicate secretly, despite everyone in HN being able to see our entire exchange. Look for Diffie Helmann.
These days, there's a whole industry of people doing math videos with interesting stuff.
I didn't particularly find (at the time) calculus, multivariable calculus, physics, etc. interesting as I didn't find the applications interesting at the time. I find these subjects representative of what you traditionally learn at school.
When I entered uni I discovered my passion for discrete math, algebra (groups, rings, fields, etc.), number theory, cryptography, theory of computation, etc. as they have a lot of application in CS.
That's really what did it for me - and also I had great uni lecturers. I wish they would have taught the subjects I like in highschool - the difficulty level is about the same.
It's easier to appreciate math when you are disinterested in the results or applications, because the nature of academic topics near the core grouping of math/philosophy/empiricism is that they are discovered with a lot of meandering at first, and then sometime down the line they become repurposed into a direct application that can be learned by rote. School tends to instruct in some of the most directly applicable stuff first - the "three R"s" plus some civics and training aligned with national goals. And that means that school predominantly teaches associations between math and rote methods, to the disgruntlement of many mathematicians. The "meandering" part is left to self-selected professionals, so it doesn't get explored to much depth.
So I think a good motive for math study is really in games and puzzles, where the questions posed aren't about win/lose or right/wrong, but about exploring the scenario further and clarifying the constraints or finding an interesting new framing. Martin Gardner wrote a long-running column and a few books in this vein which are still highly regarded decades later.
> For example, I loved learning programming because it’s hands‑on—I can build something and immediately see the results. In everyday life, though, I rarely need more than basic arithmetic or simple sin/cos/tan trigonometry.
Consider doing something that actually needs it. You like computer programming - consider making a game engine. It might be easier to learn when you can actually see that it is useful.
Keep in mind though that math is a lot of things. People obsess over calculus but that is just one type. Math is just as much the different types of symmetry in wall paper patterns as it is finding the derrivative. Don't be afraid to try different areas. If you dont know where to start, consider picking up "A Concise Introduction to Pure Mathematics" by liebeck which introduces a bunch of different math concepts and see if any feel more interesting to you.
I'm going to share my anecdote, because it may help, but everyone is different and your mileage may vary.
I'm a MechE by classical training (professionally I actually work doing software/network stuff, don't ask, DNS (screams internally)), so here's where it stood out for me:
Internalize what this simple example represents, think about why that's mathematically interesting, and start looking for where it applies elsewhere. You too could be roped into doing systems engineering at scales you didn't think people haven't already figured out.
University is not a good place for learning mathematics as most of your math instructors there will be very good at math and very bad at teaching people that are not already very good at math.
For whatever reason, many University programs use high level math classes as a filter to weed out 1st year students from that program. If university instructors had a genuine passion, and ability, for teaching high level math then they wouldn't accept that as an outcome.
You are misrepresenting what's happening. Other departments use beginning math classes as a way of weeding out students they feel won't succeed in their fields because they can't pass basic mathematics classes. Most math departments would absolutely love to have more students in them.
The problem is that these students aren't prepared properly by K-12 mathematics courses and math builds upon itself. If you don't have a good grasp of algebra, you just won't succeed at calculus. We're sticking people in the equivalent of Spanish 4 without having learned Spanish 1 properly.
That is unfortunately true; not only in the US, but all around the world. The particulars do depend on the instructor, and many if not most instructors try to be motivational, but the syllabus is perfectly clear: "this is a weed out class". And when it comes to test time, the syllabus wins.
The only thing I disagree with in your comment is about the instructors: they want to be employed, and they have to accept the syllabus and testing standards. It is not about passion and ability to teach (most, especially younger ones, are full of those); it is about meeting the departmental requirements.
Except maybe not calculus. I remember my calc class kind of being terrible because it was a weed out for other majors. Every math class that wasnt required though was great.
If you love programming, there's quite a lot of programming where math is vital. Graphics, optimisation problems, cryptography, neural networks, figuring out if a hash works, projecting if an algorithm will scale...
The tricky bit is often that you need to learn some of the math before you can see how it's useful, but if you need stronger motivation, you might try diving into a slightly math heavy programming problem and learn the math as you go
Probability/Statistics is a good excuse to learn mathematics, because paying a little attention one finds lots of day-to-day situations where is possible to apply it. For example, see the secretary problem[1].
I wish I couldve excluded everything past basic algebra and hopped right to statistics at a young age - I *loved* everything about the practicality of it, how it explained tangible relationships and illuminated the world. Algebra and calculus were so un-engaging I had those teachers calling me everything but a stupid child.
I feel like a lot of platitudes are being said here.
If anyone had a guaranteed way to make people enjoy math, we'd already be applying that method.
Just read ahead to figure out what you'll need to learn, and do some advance reading. Anything thag make the courses easier will tend to make them more fun.
Perhaps think of them as solving logical puzzles. It's fun. Even though not always related to everyday tasks.
For me, it began many years ago when reading about Hilbert's hotel paradox. Turns out our laymen's understanding about infinity isn't as really refined.
I write mobile apps for living and indeed these stuffs are irrelevant for my work.
as someone who loved maths first but then do programming for a living, it's because solving puzzles is fun. I get the same dopamine hit whether it's a math problem, a coding task, or a video game level. but I think forcing yourself to like something is not the correct approach; you either like it naturally or you tolerate it for some other goals
Have you ever watched a video of a highly skilled tetris player? Where they fill the screen most of the way to the top and then suddenly they just combo the whole thing down and everything wraps up cleanly, and then they start fresh.
The feeling of "oh yeah, that was nice watching that mess turn into something clean and squared away" is where I get a lot of my joy from math.
But also, there are uses to math that you might be able to play with through every day, but you've never thought of those scenarios in a mathematical way.
I was walking today, and on the street there is a right angle turn. The inner portion of the turn is just a square right angle, but the outside of the turn is a radius. I started wondering to myself, if I want to be on the outside of the turn going into and exiting the turn, what would be different ways I could walk this, and what would the distance differences be.
Crossing directly across, to the inner corner and crossing directly across to the outer side again, would be 2w (for the width of the road w). Following the edge of the radius would (assuming perfectly circular), be 1/4 of a circle, so 1/42piw = 1/2 pi * w. The shortest route is a straight line, which would make a right triangle, so w^2 + w^2 = c^2, 2w^2 = c^2, sqrt(2) w = c
So crossing twice is 2w, following the edge is 1/2piw, and shortest path is sqrt(2)*w. Not super applicable, and I didn't need to do math to figure it out, but I was walking and bored, so I found joy in it. The fact that they all boil down to having w as a factor means I could figure out a nice ratio between all of them. And then I needed to mentally figure out what 1/2 pi was. 3.14/2 = 1.57... And I know that sqrt(2) is roughly 1.41 ish.
So now I know that crossing twice has a cost of 2, following the edge is 1.57, and direct line is 1.41. Following the edge is vaguely close enough to the ideal path to warrant not walking into the street to optimize the route, 1.57 / 1.41 is about ~110%. Whereas by defintion, a cost of 2 is going to be sqrt(2) times sqrt(2), so ~141% more than shortest path.
A few things to note here. First off, I'm aware that not everyone finds the same joy in doing simple mental math and thinking about problems mathematically even when there is no need to do it, but trying to think of things more minor trivial things mathematically may cause you to at least appreciate it more, which can grow into joy. And second, I wasn't doing any complicated math in my head. I just thought to myself "is it faster to cut to the inside corner and then cut back out... of course not, right?" and I was able to answer that definitively to myself. Did it matter? Was the answer probably obvious anyway? Probably, but I was able to _prove_ that. And I value facts. Finding joy in the simple things lets you build up more of a familiarity and view it more as a problem solving tool than a tedious thing to rote memorize.
A great way to build up math familiarity and see how other people find joy in mathematics would be to watch Numberphile videos on YouTube[0]. It's a bunch of mathematicians sharing things they find interesting about math. Some times are REAL hard to grasp, but some are just very interesting puzzles[1]. The puzzles don't always have clear immediate usefulness, but can often be described as "a mathematician wanted to know an answer, so they did some math to find out and prove something to themself."
Sorry, end of spiel.
tl;dr - find the joy in the simple things and use math as a tool to answer (even simple) questions to help highlight the usefulness.
> Kids are born explorers. They naturally want to discover new things, including math.
That's true only until their senses are not shut off and attention is not fixated on screens. Exploration happens only when you have unused attention, sensory capabilities and need for a bit of hard work and risk-taking. Curiosity is less of a biological feature. It is a product of the need and the available resources (senses etc). All of these are missing now.
There is no need or motivation. And there are no available resources (senses, attention). There is no justification for exploration and hard thinking.
When I was having trouble learning multiplication my father made up a payment system. He made flash cards and I got a payment for every one I mastered (I had to get it right some number of times, not just once). I ended up with maybe $25 or $50 which was a lot for a kid in the 1970s.
My mother tried to give me $5 for every book of the Bible I read. I never took her up on it even though I knew about the basically freebies like Jude. I wasn't opposed to it, but it felt like –on the one hand– I didn't want to half-ass it and read a few books –and on the other– I really didn't want to read the entire Bible. So I guess that a completionist attitude prevented me from getting $30!
For elementary school age kids, maybe even middle school, try getting them started with the app "Euclidea".
They won't think of it as math. It's gamified geometric constructions. Starts simple, "how do you bisect an angle" with a compass and a straight edge. It goes to a very high level that will challenge anyone.
Something I've been thinking a lot about is "stealth edutainment" games.
When I was a kid, I remember "edutainment" games that were basically like normal computer games, except every so often a homework problem pops up.
I think that doesn't work super well. Better is a game which has you learning naturally, in order to play the game more effectively. For example, I've been enjoying the computer game Slay the Spire recently, and there is a great deal of mental math which is inherent to the game. If I had a kid, I think I might give them that game as a method to motivate them to learn arithmetic.
30 minutes of play per 3 days is such a brutal reality to acknowledge. One of the most wonderful experiences in all of life so drastically limited by the society we’ve constructed.
> One of the most wonderful experiences in all of life so drastically limited by the society we’ve constructed.
I could understand if someone was forced to work two full-time jobs (as my grandfather was), but I find it much harder to blame ‘society’ when so many of these situations are self-imposed.
It’s possible that I’m jaded from hearing a subset of parents complain about not having enough time with their kids but then get stuck scrolling their phone while kids want to play. I also know some parents who insist on having a spotlessly clean house every day and then complain that there is enough time to spend with their kids.
I’ve gravitated toward peer parents who have similar priorities in life which has indirectly made me happier. Seeing all of the parents in my friend circles prioritize spending time with their kids and being honest with themselves about their priorities has been unexpectedly helpful for my own sanity.
Again, nothing against parents who are really forced to allocate time elsewhere, but I’m tired of seeing self-inflicted problems of prioritization and time management be externalized as blaming society.
In some ways yes, but men have always been the ones to go hunt/farm for long hours and provide for the family, leaving the children home under the care of the mother/village for days or weeks at a time.
I would go so far as to say modern society actually enables us to be more involved in our children’s lives, especially those for whom remote work and home schooling are options.
To clarify, for those who seem not to have RTFA but are downvoting (I can only assume based on perceived sexism since nobody has been brave enough to comment)—-the parent was quoting an article written by a working father, who said his internal KPI was, “If I haven’t spent 30 minutes playing with my kids in the last 3 days something is wrong.”
ChatGPT makes it so easy to build a lesson/workbook for something your kid is interested in. I've used it to build workbooks on special relativity, tsolkovsky's rocket equation (including euler integration to build a scratch program), triangulation, logic gates, probabilities of simple dice games, etc. My pro-tip is to tell the LLM to format the document in LaTeX, so you get beautiful math typesetting.
You don't even have to get through the workbook. Get to a part that they need to understand better and make a detailed workbook on that part (for example, triangulation -> solving a system of linear equations).
I guess these workbooks usually come in two different "shapes" - one, a guided workbook with a high-level goal that combines several concepts, and another would be a practice worksheet where we do a bunch of exercise of the same algorithm (say, long division, calculating summations, or matrix multiplication) over and over. For the "workbook" pattern, we first discuss with the LLM the final goal (e.g. a scratch program that can calculate a rocket's position using the rocket equation). Then we flesh out the steps towards the goal - is it reasonable to add the math for air resistance? air resistance that decreases with altitude? gravity turn? how do we integrate the velocity and position for each frame? How can we relate the integration by step size to the underlying integral, by showing that the result gets more precise (but slower to calculate) the smaller your delta-t is? Then, produce a Scratch code sample that implements the velocity and position calculation. Of course, there are things subtly wrong with the code sample (usually, if the math formulas are well-known, they're correct), which requires debugging - just another type of problem-solving.
The second shape, worksheets, is a lot more straightforward. Just define the type of problem you want to practice and have chatgpt make a bunch of problems. Then switch to one of the newer reasoning models and have it work the problems, and refine to get rid of any bogey problems (for example, for polynomial exercise, you could tell it to make sure the roots are integers)
The worksheets are more "hands off" - I run them through the algorithm once and check their work once or twice and then let them do the rest. The important thing is that the worksheets are connected to their high-level goal, and they understand that in order to solve the big, hairy problem that they're interested in, they need to build up certain specific skills.
Usually the worksheet goal is a pretty substantial conceptual stretch for my kids so they need to go through a series of fundamental worksheets. But the great thing about the LLM is, you can just tell it you're having a problem understanding some concept and to help build the scaffolding by listing all of the required skills to understand a concept, and picking the ones that needs improvement the most and practicing them.
My approach draws a little from "The MathAcademy Way" - https://www.justinmath.com/files/the-math-academy-way.pdf but instead of building fundamentals evenly in all topics before advancing (like expanding a sphere), we look only at the scaffolding required to support some higher-level goal - it's sort of like the masters/PhD process but guided through existing human knowledge: https://www.openculture.com/2017/06/the-illustrated-guide-to... . As a side note, I think it's really fun to include the history (mathematicians who contributed to the ideas) as well as the notation (using the greek letters, explaining why it's common to use them). When the kids notice the names like Pythagoras, Newton, and Euler reappearing frequently, and get a sense of the time scale these discoveries happened on, they treat the current state - and their ability to go learn thousands of years of math in months - with more reverence.
Maybe find an application of the subject that they might find interesting. I suppose if you can't find anything that interests them, then it's much harder to teach it.
For instance, perspective drawing might provide a nice application of 3D projective space, its subspaces, and perspectivities between those subspaces. Some of the theory of conic sections might be relevant too.
Computer graphics provides a nice application of coordinate geometry. This covers elementary algebra, Pythagoras's theorem, etc.
Even eating pizza can provide an application of differential geometry.
I tell my kids they can have letter cookies if they pick a word that starts with the letter, and can have 5 treats if they ask for 4 but know what "plus one means" or can have 4 if they recite "2 plus 2 equals ... ".
They're 3, so I don't expect that to scale, but I'm hoping it's normal reward-for-knowledge by the time we get report cards.
I'm not great at maths, my daughters good though, I think her binge watching number blocks when small helped a lot - felt my own arithmetic getting a bit better watching it, the songs were very catchy.
Something we don't pay enough attention to is that while calculators have solved everyday math to the point we downplay it as a required skill, people are not pulling out their calculator at the grocery store to make better purchase decisions, even though we all have one in our pocket now.
So we handwave the importance of being able to do everyday math in our heads, while also not taking advantage of the tool that's a substitute for it. We're less educated but also less effective than we would be if we'd never invented automated calculation and were forced to be sharp about it.
Is there a name for this phenomenon?
And what's it going to look like a decade after AI has caused people to stop using their brain for general thinking like it's stopped them from doing math?
(I'm sure you, the reader, are very good at math and are an exception to this still-apt generalization.)
But the reality is that's usually almost a false trade - I'm not buying one item in the grocery store I'm buying easily a dozen or more. The best way to do this would be toss the online inventory into a solver to calculate "best value" for me, but in reality it would be a waste of time because if they're out of something, or the quality looks suspect, then that blows that calculation completely. And then am I going to do this for every single item, where every minute in the store is multiplying through the rest of my day? How much is the time shopping trading off against extremely sparse leisure time?
And then there's intangibles - something being slightly cheaper doesn't necessarily mean I'm making a good trade off by buying it for my overall quality of life.
In Australia at least this whole problem was perfectly adequately solved by mandating bulk price labeling on all items in the supermarket. Products in comparable categories have per volume/weight prices listed alongside item prices.
> In Australia at least this whole problem was perfectly adequately solved by mandating bulk price labeling on all items in the supermarket. Products in comparable categories have per volume/weight prices listed alongside item prices.
Same in Europe. Mandatory labeling per volume/weight, pre-discount, after-VAT in addition to the discounted item prices. Then you glance at the shelves and make up your mind.
Learning to get to a best price per unit is a pretty useful skill that could make a lot of difference for a lot of future adults, just like financial literacy.
Some things aren't optional, and if they are seen as such, it's going to force the child to learn later in life what they couldn't earlier on.
I think most people don't care about optimizing an extra $10 out of their weekly grocery run.
Probably a better example is figuring out the cost of a loan. Just multiply the amortized monthly payment by the term and compare that to the loan amount. If the difference makes you balk, then go ahead and walk.
How many people even realize that loan interest is a significant cost and would bother to do that? Or know how to do that? Most people just try to minimize monthly payments to something they can bear and sign the paperwork.
> I think most people don't care about optimizing an extra $10 out of their weekly grocery run
I remember when this kind of "optimization" was done regularly by a great many shoppers on budgets. Back in the day some stores even used to put calculators on the shopping carts.
People used to know how to budget. Apparently the average American is affluent enough to not need to be able to do this any more. I worry that the atrophy of these kinds of practical skills will cause much pain for a great many people at some point down the road.
I worry too. American consumer credit card debt sounds like it's rising pretty quickly, and many people I talk to have a lack of free will and carry a sense of unfairness in the system they live in.
However, people can also adapt pretty quickly.
Those grocery shopping "optimization" skills are making a big come back (and have been since Covid). There are plenty of YouTube and TikTok videos popularizing how to get more out of their grocery hauls.
Lots of people are also learning how to budget, how to invest, etc. and sharing their excitement about it too. For some folks, they finally learn this stuff in their 40s and 50s, but there are also a lot of young adults learning these skills thanks to the Internet.
So I also have hope.
I just don't think the lack of basic math and budgeting skills displayed by average consumers are a problem so much as a symptom.
Oddly enough I found a great 'trick' for this. Kids hate doing math tests, but turn it into a competition and game and suddenly they love it. Print out a bunch of remedial problems, perhaps 50. And then give them 1 or 2 minutes to do as many as they can. It's just a contest to improve against your own scores over time, with prizes for the kids who score the highest after a month or whatever.
It's still literally just a math test/quiz, but somehow the context changes everything and even kids who really aren't into math were loving it, and also improving rapidly because the repetition helps instill intuition.
I imagine the part of a test people dislike is failing, and the consequences from failing. Framing it as a game without those emotional stakes fixes that.
If the teaching environment was set up to encourage learning rather than punish not having learnt yet we might not need these tricks, but that culture is slow to change
My claims are as follows:
- most math programs in the US schools are behind where children’s math abilities are
- most school math programs do an abysmal job connecting math with real life
- you can completely turn off a child to a subject/sport/activity by pushing it too hard
-being numerate is a real long term advantage in life
It’s balancing these things that’s hard, if your children are above “pace” math wise, see the value of math in their everyday life, and are on track to be numerate, yes don’t push, otherwise not pushing is the disservice
I think this isn't quite the same thing, never the less: I have dyscalculia on extreme mode (/dyslexia/autism), and I was forced to do math in the 90s in the UK, rote style. I don't know if they didn't know about dyscalculia, didn't care, or whatever, but holy hell I wish I'd never been forced to do that, it's still today a fairly painful memory and I'm in my 40s now. If you're gonna force kids into math, at least make sure they're not unable to process it correctly.
If you formulate the warnings just right, you wouldn’t need to “force” it, as kids will be willing to look both sides themselves. They like to be alive.
Forcing is kind of hopeless. So is logic, and reasoning.
How children learn (rely on the prefrontal cortex of their adults) is very different than how adults learn (no fully developed prefrontal cortex until 25-26), learning about this can help a lot.
Learning more about the Reggio Emelia approach might help parents curious about this, it has been quite surprising how much is possible naturally. One of the best things to do is to relentlessly read to and with your kids.
Also, linking a topic to their interest's radar, encouraging curiosity, play in general, and letting them potentially discover it can go a long away.
When they've got something they want, teaching math and savings is a great thing. Understanding life is a lot harder without knowing a basic bit of math, and can be made a bit easier when doing it younger.
I had a math teacher that once made it clear, some stuff can just click, others is just about doing a lot of examples to learn the patterns. Doing math is very different than being creative with being comfortable to find it.
Today, I'd probably setup a good prompt to find a way for the child to share their mine to discover how they like to learn, and how they might like to learn faster and easier by taking some shortcuts through math directly or on navigating an ontology/taxonomy perspective.
Must add i had struggles with mathematics. It can be interesting, but little did i understand as a pupil.
Later in life, i discovered it, i became a car mechanic, then it-guy, then non-destructive tester.
English is my first and only second language, its enough to lurk here, read books and serve customers on a professional level.
I think i dont need french, nobody around me speaks it, i am not interested going to france..at all.
All the math i was thaught, was do to the job and that filled my fridge.
Its okay to push kids to university so they can use that math knowledge, but who foresees what the kid wants to work?
School is not the end of the road, one can always attend courses, getting autodidactic knowledge later in life.
Today we dont need 10 architects while having only 1 roof tyler.....
I'm reminded of another HN comment on learning math, more pitched at advanced maths but probably still applicable
>...recommendation is a metaprinciple: enjoy mathematics. Benjamin Finegold said similarly that the secret to chess is to enjoy every move. https://news.ycombinator.com/item?id=42290996
Since then I've watched a few times Ben's beginners chess advice aimed at kids and feel it can apply to other things, math or in my case I'm trying to apply it to trading. It's been quite good. The basic idea, enjoy doing the thing and do it repeatedly so you build pattern recognition https://youtu.be/B5bCfwCyo18
I don't get why people take it so negatively when a parent mandating kids to do/learn things they don't like.
But the entire notion of public education is rested upon mandating that kids wake up and go to school, sit down and learn things they don't necessarily like. I am pretty sure there isnt a single student who loved/found joy in all the subjects all the time.
Yet when a parent does it, there is backlash?
Humans respond to carrot and stick, and so do kids. To excel at anything, requires healthy mix of enjoyment, love, discipline and motivation. Some of these come intrinsically, others extrinsic.
And then your kids and their same generation would be replaced by their peer kids from hard working boys and girls from India and China. Unfortunately curiosity only works with brilliant minds. Normal minds plus curiosity is useless.
I think the advice is good for younger children. The author is using 14+11 as an example. Very engaged parents can have a tendency to overdo it, so it's probably a good reminder.
As kids get older, they need to learn how to struggle and overcome struggles. (I would still caution against "forcing" math.) But yes, you need to start engaging hard work and determination.
Btw, the two are not mutually exclusive. Young children should be praised for struggling at things so they begin learning that skill, too.
A lot of people hope there is a magical way of making learning fun. The argument generally goes "young kids love exploring nature, experimenting, etc, so we are all inborn scientists. If only school did not extinguish the fire from us".
A huge problem is that giants of education such as Jean Piaget and Seymour Papert make a strong case for this. Unfortunately they generalized their own experience as kids to all others. They did not understand that they were exceptional cases, and what applies to them does not necessarily apply to 99.999% of the rest of the world.
But their message was so cool, somewhat similar to "we can all love each others", or "world peace", that it was embraced with abandon.
I was fortunate to have a great math educator in college (i.e. a guy who was teaching us, math majors, how to tech moth to kids). He told us bluntly "math is hard".
I think education would progress if one simply accepted this truth "math is hard". Stop the delusion that there is a way to make all math fun.
Still, once you accept that math is hard, you realize that the mission is the same: try to find ways so that learning math is less hard and more fun. But accept that the default state is that math is hard. There is no "royal road" to math. Aristotle was onto something.
And by the way, the fact that "math is hard" is not all bad news. The goal in school is not only to learn math, but also to learn how to work hard. There are kids for whom math feels like swimming for a dolphin. Up to a point. There will inevitably be a point where they will hit the phase of "math is hard". And it's going to come as a rude shock. It's better for this realization to come a bit early in life and a bit less shocking.
There is no template for how to raise kids. Expose them to as many things as you can, figure out what interests them and feed it. Keep doing this as they grow up because they change as they grow up.
The same can be said of music, art, sports and a zillion other things.
My daughter and loads of kids watched number blocks from around two or three up, I think it made quite a big difference- she's far ahead of where I was now, years later.
I believe that the most important thing I can show my kids is how I pursue the things I enjoy. That I make time for myself and that I handle setbacks and dips in motivation. So that they will know that when you do find something that interests you, that is how you pursue it in the long run. I show them how to not quit.
Know what, brother? I tell you that studying the humanities in high school is more important than mathematics — mathematics is too sharp an instrument, no good for kids.
Stephan Banach quoted by Steinhaus in Through a reporter’s eyes, Roman Kaluza, 1995
Kids do not understand the concept of "importance". At least no kid I've met. That part of their brain doesn't work. They'll trade effort for privileges or toys tho, and are little mimicry machines so they follow you if you use it.
yeah, I recoiled when the author of the post says "no bribing" - bribery is one of the most useful tools a parent has. I guess you could call it "incentive" or something, but really, it's quid pro quo.
Honestly it's so close to how the world works I can't believe 1. Avoiding loss of privilege and 2. Gaining new things as reward isn't the top two parenting tips.
But probably zeroth, most important, is modelling good behavior. Kids are mirrors.
We are torn but decided to keep books scarce, and scold them a little bit when they sneak books into bed. We know but they are much more likely to get their rebellion out reading now. Which I love.
We went the other way and have plentiful books, constant library trips etc. but have had to regulate sleep by setting a regular lights out time. Executive function and mood really suffers when sleep is insufficient.
I appreciate the idea of harnessing rebellion and I'll think more on how to apply that to my parenting :)
I do agree with the overall premise of encouraging children's creativity and the things that they enjoy doing. You don't want math to become a chore.
On the other hand, some things require study and practice to be really good at, and that is "work", and many kids don't want to do the work.
Our boy, who just turned 9, is very good at math (his school's standardized tests put him at 99th percentile in the US for his grade level, though 1) I don't put a lot of stock in those standardized tests, and 2) the US doesn't exactly rank high in math skills, so this is less impressive than it sounds). He's not a genius, but he grasps concepts quickly and fairly intuitively. He's curious about the world, asks lots of questions, and is capable of understanding and retaining many scientific concepts that kids older than him would struggle with. (Example: two days ago, he was asking me about quantum computers and I mentioned that they need to be kept very cold, he asked whether they use oxygen, because oxygen turns to liquid at -173C. I thought he just made that up, but when I checked (I didn't know myself), he was pretty close (the actual number is -183C.) So he has the innate talent to work with.
But despite his gifts, he still needs practice for the math concepts to take root, and without that he makes a fair share of basic mistakes; and he still needs to improve his logic reasoning skills. So he has daily math homework after school (because math instruction in elementary schools in the US is low). We use Singapore Math workbooks (I've tried various apps and online programs, and honestly, paper workbooks are just better--but that's another topic).
He knows he's good at math and wants to continue to excel at it. (Just like a talented basketball player doesn't reach his full potential without working at it, something I repeatedly emphasize to him.) BUT he still struggles every single day to do his homework, because he prefers to play video games, shoot hoops, etc. (loves basketball, football, soccer, but has a lifelong physical disability that will prevent him from ever playing a team sport, to his great chagrin). I have to push him every single day or he would simply not do it. He actually wants to do math, and when we talk about it, he'll confirm that, but when it comes time to actually do it, he just doesn't have the willpower. (I mean, what kid prefers to practice math problems instead of play video games?). Hopefully he'll get the willpower at some point when he's older. But that day has not yet come.
That was a long reply to say: it sometimes does take a lot of pushing.
Humans are more terrible at teaching math than any other concept. I remember being taught algebra by a teacher that had terrible idiosyncrasies. She would sometimes write numbers and variables differently, and this caused major problems trying to understand how and why the variable was to be written differently due to new context. But she would just go on writing it differently, just because she was weird. For example, she would sometimes write 'x' using two curves that didn't touch ')(' and expected you to continue with the algebra equation as if nothing was strange. My point is that teachers still don't understand how to correctly teach math to students. They reinforce using their old methods that are overall sloppy shorthand in a space where rigor, both visually and conceptually, must be maintained. When young minds are this fresh, you cannot have this slop and idiosyncrasy in your lessons and expect students to become enlightened. So no, forcing them to do some math is not harmful. Poor teaching in a very hard space definitely is harmful.
I would agree. Kumon wasn't my son's favorite thing and he eventually decided/asked to stop. But the repetition and discipline of working at it every day had an influence. It didn't manifest until undergraduate but he ended up switching majors to math and is now pursuing a math PhD. Probably not common, but like learning to play the piano, I think it gave him a comfort with the basics and an intuition that allowed him to explore his own interests.
I'm fortunate enough that my daughter has an admirable interest (and talent) for Math since very early age. She even won a medal at a renowned nationwide Math competition when she was in Grade 5... competing in the Grade 10 category.
The only thing better than telling a lie and people believing it, is telling the truth and no one believing it. Shows that her achievements are truly remarkable
Another article where someone thinks being a parent means they understand all children. I have 4 kids, and 2 of them definitely would never do math, even basic math, for fun, ever. Their brains lack whatever pathways most people utilize to learn math, so I now have a 15 year old who has to work nearly as hard at arithmetic as she did when she first learned it. No amount of drilling, change of curriculum, buckling down or backing off has had any impact. She has absolutely no interest in math. But the kid reads faster than I do, which is not slow at all.
The only thing I know about kids after having adopted 4 of them is that none of them are alike. The only time when you can really train them to do anything consistently is when they are babies. As a result all 4 have great sleep habits :)
I read it (as a non-child), and a lot of my certainties about what young brains are and are not capable of got joyfully exploded. I'm not linking it to you proscriptively, or with a specific suggestion or riposte in mind whatsoever - you just might be interested in it.
School is very successful at convincing kids (and former kids) of two things: firstly, that the academic subjects they purport to teach are actually delineated by the school textbooks and curricula. And secondly, that the reaction people have to specific subjects within these school structures are the actual unchangeable nature of the person's relationship with the subject.
I hope one day our societies move past these two egregious and immeasurably damaging beliefs.
I haven’t read the book, but we have 100% had the “you don’t have to graduate if you don’t want to” talk with this one haha. She doesn’t want to drop out, but definitely isn’t interested in college. We want to keep that door open for her if we can, so we just remind her that staying in school requires doing some things she doesn’t like.
But yeah, at 15 it gets a little hairy. You have a kid who wants to be an adult, but in a lot of ways they are not prepared to make adult decisions still. Eventually she will have to make them, ready or not. But we have a few years left to help her, so the focus becomes how to best do that.
> School is very successful at convincing kids (and former kids) of two things:
Well, and thirdly, that your worth as a person is determined by your results in graded examinations, and by extension, your salary or some other numerical rating decided by someone else.
I as a child, a teen, and a young adult thought I hated math, I got bad grades and it bored me. I dropped out of school. I later went to college and took remedial algebra twice.
Math in school was purposeless and rigid, a rote procedure to be followed by command because that's what kids have to do.
Now, I have grown older, and my curiosity drove me to learn because I wanted to make things, machines and software and probabilistic strategies. Things that necessitate math. If you can't rotate a vector, your guy walks faster diagonally. If you can't think mathematically and you want to lift a 2 jointed robot arm that weighs several tons, you're going to tip it over, and possibly die in the process. You can do it without trig but you can't do it without thinking about math.
Once I found purpose, I began to appreciate the beauty of the more elegant solutions. I kind of fell in love with math as an adult. Now I watch numberphile with my kids and make complicated machinery and software at work.
I think a lot more people love math than realize it, because they're conflating math itself and what school calls math, which is worksheets and demands, not beauty and creation.
With my kid in elementary school, I can see how math instruction is generally terrible: teachers rarely have any enthusiasm for teaching it. I only had one great math teacher (combining enthusiasm, skill and hard work) and I've been through special math programs (in high school and uni).
Again, it is a question of incentives: someone with enthusiasm for math would likely go with a higher paying job requiring higher level math.
Still, despite the crappy teachers, I was better than most to persevere at it until high school where I had the great teacher.
But this does not scale and we are losing kids to bad teachers: how can we fix this?
Yes. And it's the same when the kids come from the same parents too. We have one kid that's willing to go very deep on math. The only does what can be figured out in 3 seconds or less. Same genetic parents, same school system.
The original concept in the article of exploration is great. Some kids want to explore math, some science, some music, and some Starcraft.
I knew some who were bad at math. Asian immigrant test scores on math are ~1/2-1 standard deviation higher than white Americans. That’s noticeable comparing groups of people but still leaves a lot of Asian immigrants who are not good at math.
There is no royal road. If all your kids are biologically yours and you and all your family are good at math and you marry someone from a similar family, you can stack the deck maybe 95/5 in favor or your kid being good at math? But that option is already off the table if you lack that talent. And there are other things you should probably prioritize first!
I don’t personally see how one person’s experience with children other than my own has any connection to my own children. That was the point I was attempting to make, though. Just because you have anecdotes to share doesn’t mean you’ve stumbled upon some universal truth. They can be helpful to share but NOT if used to dismiss other people’s experience.
Very poor take. The author clearly has very limited experience with raising kids. Most kids won't do difficult things if you don't push them. Playing music, learning to spell correctly, doing mathematics, and so on. A very small minority of kids will do all of that easily and for the fun, but you can't rely on it. If you don't push your kid to do their 20 minutes of piano every day, they will half-ass it and will stop after 1 year and conclude they are not good at music. Same for sport. Same for reading books. Same for maths. And you know what? It's your fault. You chose to be lazy and complacent and didn't push them because it's hard to be a good parent. And now you expect me to validate your laziness? Nah.
The really important thing is to teach kids to find their joy.
At the end of my second year of piano lessons, my teacher took me into her living room, and we listened to Glen Miller records for most of the hour. And then we had a cup of tea, and she told me, "this is the music that I love. I play piano because I love that music, and I want to be able to play it myself. What kind of music do you like?" I didn't really have an answer. So she told me that we should stop doing lessons, but once I found music that I loved, she'd be happy to teach me how to play it.
In my early teens, I discovered Miles Davis. Once I had found my passion, all the hard work became play. I actually ended up learning to play jazz guitar, not piano. Even the heavy lifting was pure joy, because it had purpose and meaning.
I didn't become great at mathematics until I discovered the joy in mathematics (another brilliant teacher handed me a stack of old math contests, and said here, you might find these fun. I placed 4th among 20,000 students).
I didn't learn to write well until I discovered the joy in writings. (An absolutely brilliant English teacher who made us assign ourselves our own grades, but broke his promise in the end by upgrading all my papers to A+'s).
And I gave my kids the room to find their joy as well.
A counter argument is simply the observation that some stuff, it takes time (and effort) before you find the joy in it. Following your recepie, unless (as you say yourself) lucky teacher or wealthy parents, anything that doesn't incite immediate reward will be of low interest. A kid will probably pick up that general pattern too:
if joy can not be found in <T time, don't bother. And kids are not particularly known to be good at long horizon credit assignments, so that T is often hours, day, or maybe a week.
My brother (now an professional artist) told me at teenage years "some stuff you just won't understand the beauty and the joy until you've at least put 100 hours in it". And that's true in so many things in life.
I'm happy that one of my parent forced me to do some stuff (sports, music, language) even when I complained about it. Only 10 years later did I understand how valuable being able to speak another language fluently with minimal accent is, and how some of my fellow second generation migrants lost that ability, and regret it. (having to go to school on Saturday sucked as a kid)
> it takes time (and effort) before you find the joy in it.
And the right mentor.
I distinctly remember that for my master's thesis, I had initially chosen a topic that I loved deeply, but getting constantly rebuffed by my supervising professor who constantly berated me and insulted my intelligence led me to not only hate the dissertation topic (not to mention him also), but hate that field which I loved so much.
I later switched topics, to a very different field, under a professor who actually took stride in and complimented my achievements however meagre they were. Net result, we've collaborated on multiple papers together and even after 10 years or so, consider each other friends instead of a mere teacher-student relationship.
I could give multiple anecdotes in other completely unrelated fields, from painting and art to driving a stick. Guides and teachers matter in finding the joy in things, even more so than the time invested.
> "some stuff you just won't understand the beauty and the joy until you've at least put 100 hours in it"
Terrific quote and advice. 100 hours seems doable for a lot of things (even if it's not enough time.)
If you practice things, often you become better at them, at which point they become more enjoyable.
There's definitely a point of fun - the point where something challenging enough to be interesting, and where you can make progress, but not so punishing as to be discouraging. Games often target that fun point.
“Joy” is not found in a day. People enjoy doing things they are good at.
It takes a long time to get good at some things and those days suck.
>“Joy” is not found in a day. People enjoy doing things they are good at.
There's got to be more to it than your simplified breakdown.
My first exposure to computer programming was fun and instantly addictive. There was no struggle to learn coding. Same childhood experience for guitar. Nobody was around to push me. There was no need for "discipline to practice". It was simply practice-was-natural-thing-to-do because I enjoyed it. I wasn't a child prodigy. I was finding early joy in programming and guitar -- even though I was very bad at it.
On the other hand, I'm very skilled at cooking and Microsoft Excel. But I do not enjoy making any meals or fiddling with spreadsheets. Likewise, there are a lot of kids out there that hate farming but are actually very good at milking cows and running the tractor because their parents made them do the chores every day. Some kids then grow up to move to the city and leave behind the farm life for good. On the hand, some siblings will cherish farming and happily take over from the parents.
That said, I'm aware of the "No True Scotsman" argument about "joy" : If you _truly_ were skilled at cooking and MS Excel and farming, you'd actually enjoy it.
ok... so the meta question is ..... how does one tell the difference between "skill precedes joy" vs "The beatings will continue until morale improves!" ?
There was a popular "Tiger Mother" book where Amy Chua's daughter has a meltdown in public and didn't want to be forced to play the violin anymore. That finally convinced the mom to stop. On the other hand, the older sister seemed ok with piano lessons. Maybe children are just different.
TLDR of anecdotes above is any theories of optimal child-development has to account for _counterexamples_ to the skill-vs-joy connection : Kids can find joy in things they are bad at. Kids can hate doing things they are good at.
I find tremendous joy in playing the piano today. That mostly started when I was about 20, ~15 years after I started playing the piano.
It had its moments during the first 15 years of my life, but it was more of a competitive activity than an entertaining one. Conservatively, every fun hour had about 50 shitty hours when I was a serious piano student. Now it's 100% fun.
This is exactly the same for me—I grew up playing the piano for basically my entire childhood, but it was always a chore. I dropped it once I went to college and figured I'd never pick it up back up, but then I decided on a whim to learn a song I found online. But b/c now it's no longer just for the sake of lessons, it's become a hobby that I really enjoy in its own right (and indeed, all the forced practice growing up has greatly expanded the range of songs that I'm able to learn now).
Same for me, I've learned programming, reverse engineering, music production, cooking, etc. I learned all these things not because I'm intrinsically in love with doing them, I just love having done them. This quote fits it perfectly, "I hate writing, but I love having written."
> It takes a long time to get good at some things and those days suck.
If those days suck, chances are you won't get good at it. People like things that are engaging and develop their identity and understanding of themselves and the world, even more so than things they are good at.
> People enjoy doing things they are good at.
Sometimes. I still hate almost all things I'm good at.
i found joy in skiing the very first time i tried it in my mid 30s. been skiing every season since that day for 40+ days minimum.
same with coding. instantly loved it and choose it as my career. still enjoy it today.
But kids are going to have setbacks, they will reach a plateau in their craft (music, painting, art, sport, ...). You need also as a good parent to help your kids go through, to not give up, because even joy to do is not always enough. This is the hard part.
From my modest experience of being a ski/snowboard instructor and trying to raise 3 boys (now 12, 16 and 18).
why does a child need to break through a plateau at anything? Of my five sample size of five, expose them and support them, some things can’t even hook you until your brain grows enough .. The musical one is in a band now the nerdy one likes inhaling solder. I did force both boys to Hockey but just to have passable skills so that he can enjoy that all that comes with the sport as an adult
> why does a child need to break through a plateau at anything?
Learning that they can hit a plateau and move beyond it with concerted effort is super important. After you've done it once, you can look back on that experience for inspiration when there's a plateau that you want/need to move beyond.
Having experience with struggling with something that is easy for some others is important too. Some kids are just naturally good at a lot of things when they're younger; which is nice in some ways, but makes it hard to learn skills to deal with challenges... It's great when they find something that challenges them (even if it doesn't seem great to them in the moment). Other kids have a hard time with most things; you've got to look out for things they can be good at.
A child doesn't but a child carries it forward into adulthood.
The current trend, at least in Germany, is that as soon as a kid says "I do not want anymore.", this is normal to stop. With that, the kids do not have the experience that it can be hard, but going through can bring something.
Resilience, capacity to go through ups and downs, etc. are things you train by being exposed to it. If your life is only fun and joy as kid, the day you are hit hard as an adult, you have no training.
But, this is my very personal point of view, education is very personal and very context specific, every family is different (country, culture, education, etc.) and in every family education is difficult from one kid to another. I am not trying to tell you how to educate your kids.
> why does a child need to break through a plateau at anything?
If for no other reason than to teach them that some things are worth persevering for.
You can't teach kids to give up at the first sign of adversity...
This does need to be anchored in value though. They should be at least playing a part in deciding what those things are before they're pushed to persevere towards them.
Exactly
Then you have to be sure they really would like to succeed in wherever you're pushing them so they truly feel accomplished.
> why does a child need to break through a plateau at anything?
Exactly! Why? The few things I do better than most people are things I've stayed engaged with during those plateaus because I wanted to, not because someone else told me I should or that it was important. The people who respond positively to being forced into things generally end up not knowing who _they_ are, and end up generally unwell people.
I feel false dichotomy here - you assume helping child to go through plateau must be forced.
It doesn’t have to be and some people need a little bit of help - you didn’t and that’s great.
Conversely there will be kids that need to be forced or nothing good will come out of them - there will be kids that should be left alone because pushing them will just break whatever they should be doing.
It is delicate balance and difficult choices - but there is no white and black here that will be right for everyone.
Yeah I didn't mean to suggest this dichotomy. And I agree with you. Just not sure how much you can force people, even the ones who "need" to be forced. Or what "good" will come out of that. Good in my mind is a person who knows themselves, is functional, and is comfortable in their own skin. That is, a person who won't lead a life of total suffering, which seems pretty common!
You're using yourself as a refuting example, but at the end you disqualify yourself by being 4th out of 20000 in some undisclosed math ranking
his whole point was that once he found joy in it, he could excel. I'm confident there's loads of things I could be good at - I'm only good at the things that I enjoy putting effort into.
There are tens of thousands of people who love basketball playing right now and only 300 places in the NBA. Most people are average and never excel at anything, ever. Being 4th out of 20,000 is excelling and the proper response to someone using their own freakishly unrepresentative self as an example for normal people is to point out that they have no idea what it’s like to be normal.
and yet, without joy in the process, he could not have done it.
Yeah, but something vital happened: you learned the basics of music theory and how to sight read music - both prerequisites to jazz guitar (and something that most guitarists don’t know). Learning piano is a great way to step into other musical instruments.
Not forcing kids to learn mathematics and not becoming great at mathematics until you discovered the joy in them are not remotely the same thing.
Not learning to write and not learning to write well until... are not remotely the same thing.
Kids are inherently joyful, unless they are abused. One doesn't have to teach kids to find joy.
Whereas an admonishment to "teach kids to find joy", aka: "do what you feel like" according to the article, rings true as detached from reality self-talk meant to make adults feel good about themselves. Its almost a class signal, that is a privilege signal. With varying results across classes.
> The really important thing is to teach kids to find their joy.
As an adult, how can I find joy? I've been trying out various hobbies, but eventually, all of them became a chore. I really miss the feeling of fixating on something and getting lost in it, but it's not coming back. I'm so jealous of people who have a passion, because I just don't.
As a serial hobby-hopper myself, I have come to realize that anything worth doing is at times dull and tedious. Passion is not always intense joy, it's appreciating the highs and tolerating the lows. Don't get caught up chasing cheap thrills.
This is exactly it.
We fail at teaching a means with no end. Help them find an interesting end and they will achieve it by any means necessary.
Our job as parents is to expose our kids to a wide variety of disciplines so that they can find their interest.
I read that Elon Musk runs his private school this way. The kids narrow their focus quite early on. But of course there's tons of depth to study. So they actually get somewhere.
In your penultimate sentence, why did you put the period outside the parentheses instead of inside?
That was exactly my sentiment.
My parents pushed me hard to do piano when I was around 10-12. After a year that went pretty well I was starting to get lazy and put very little work and investment into preparing for the next lesson. They still had me play piano a full year until they eventually gave up and bitterly told me what a waste my resignation felt to them.
20 years later, I got back to playing piano, and I can't thank my parent enough for having me to continue playing in my teenage years. Because it only took me a few month to be able to play pretty advanced piano sheets compared to some of my relatives who are struggling with the basics starting it in their adulthood.
Same for maths. I feel that a lot of people like the author of this blog post are being extremely misdirected thinking math can and should be taught in a fun or amusing manner every time.
Sure, a lot of topics in Maths can be made more digestible by "gameification" to help younglings develop an intuition. But a very big part of Maths actually requires you to sit down and painstakingly crunch down the numbers/equations, memorize and learn when to apply the correct methods to solve some problems. And even though this part can feel fun and engaging after a while, you can't expect children to exhibit such interest right of the bat without having them first struggle with the classics.
Kids don't know better. Your role as a parent is to navigate along the fine line of forcing your kid to get good exposure to the (boring) activities we adults value and letting him enjoy what he enjoys. Only in doing that will your kid open up to the world and grow up into a functional human being.
"20 years later, I got back to playing piano, and I can't thank my parent enough for having me to continue playing in my teenage years."
One of the tragedies of being young is that few have the insight to realize that the 'boring' stuff parents and teachers are forcing us to learn will actually benefit us and that eventually we'll be very thankful that they did.
My parents nagged me all the time about studying and even though I did my fair share of it I never fully appreciated how important it was until much later.
It's a strange phenomenon, one cognitively understands the reasons but one is isolated from the reality so one is somewhat distant from it. For example, one can get upset watching war footage on TV but being there is on another level altogether (soldiers often do not talk of their experiences because they know those at home will never fully understand).
In the same way, wisdom gained through experience is almost impossible to impart to a younger generation who has no actual experience.
I upvoted all of the above posts because - all of them share some correct arguments.
> the 'boring' stuff parents and teachers are forcing us to learn will actually benefit us
My parents forced me to play the piano for more than 10 years because they were obsessed with the piano, and because they had a piano. I hated every second of doing that in order to please them, and I never got higher than beginner level because it was a torture for me. Being a beginner for 10 years should be considered as abuse and it messed me up big time, especially for my daily confidence.
30 years later, I still hate that fucking thing and I understand that they fucked up due to their delusion. They deny everything when we talk about it though.
Sometimes you have to listen to the kids and understand what they want do do, and accept it instead of feeding your Munchausen by proxy syndrome. All I wanted was a computer, even the cheapest computer ever would have been acceptable. Nowadays, I write C++ for a living and I still hate the piano. If only anyone listened to me back then... My hatred for that instrument is a mystery for some people, and some people think that "wisdom gained through experience is almost impossible."
Amen. And the surreal thing is to then hear the very same mentalities behind this uttered in this comment section.
It's like there's like a vehemence in people towards abuse. Reminds me of how Zweig said that people were in a state of jubilation in anticipation of WW1.
There's something dark in humans where they don't accept the absence of pain. They think to at least some extent, that hurting their kids is a good thing, perhaps under a twisted "toughen them up" mentality.
And the thing is, they get away with it. Maybe their kid gets a chip on their shoulder against them, or maybe even estranged from them. But they don't get hurt back.
In a moral world they absolutely would.
"Sometimes you have to listen to the kids and understand what they want do do, and accept it instead of feeding your Munchausen by proxy syndrome."
I agree, and it's more than 'sometimes', kids have a right to be heard and that hearing should be fair and reasonable. Clearly, in your case it wasn't.
What you experienced was unacceptable by any measure, and in my opinion the fact that your parents were oblivious to your predicament is a damning indictment on their parenting skills.
Your extreme situation isn't what I was referring to, so let me explain by briefly describing what I experienced.
I learned the piano because I wanted to, not because my parents forced me. In fact, whilst my parents were both musical we didn't have a piano when I was young—so I started late and that's been to my disadvantage. I mention that to let you know I understand what you went through.
Whilst I like the piano learning it was no bed of roses and it's difficult for all but the most talented (anyone not wishing to learn it would be an unmitigated drag). For me, those fucking Czerny scales used to drive me to distraction, I'd goof off and play whatever took my fancy whenever I could. Also, my teacher used to reprimand me regularly for not reading score timings as written, I'd play the tempo as I felt felt like it and that always casued a ruckus.
At no time did my parents force me to take subjects that I did not like. That said, gentle persuasion was used. I was never much good at languages and despite my ambivalence for the subject I took French not so much at my mother's insistence but rather her desire that I do so (her sister married a Frenchman and was living in France and she thought it would be useful). Learning French used to drive me crazy, it's not that I detested it (I understood its value), rather the problem was that I wasn't much good at the subject. I'd sit on my bed at home doing my French homework and bash my textbook up and down on the bedclothes whilst tying to learn those fucking French nouns with their damn random genders—why the fuck can't they all be 'la' or 'le' and not random? Having a single 'the' in English is immanently sensible.
Well, despite being not much good at the subject in hindsight learning French turned out to be a blessing when I was living in Europe. I could never have foreseen that situation when I was at school.
Another example, my father used to nag me about not taking Latin, my usual retort being why the hell would I want to learn a dead language (although that was more in jest at his persistence). I sort of had a paltry excuse as my school didn't teach Latin but there were arrangements to do certain subjects by correspondence under teacher supervision in the library. So I never took the subject at school, so nowadays my Latin is at best a mess.
That was a fucking mistake of the first order on my part for reasons too long to describe here. It's only the wisdom of hindsight that I now know I should have taken my father's advice.
BTW, I understand your frustration over not having access to a computer, I'm an IT professional and I managed an IT department for years (I was one of those nerds university security would regularly chuck out of the computer room at 10pm at night). If I'd been in your position, I'd have been mightily pissed off at your parents' miserable attitude.
> One of the tragedies of being young is that few have the insight to realize that the 'boring' stuff parents and teachers are forcing us to learn will actually benefit us and that eventually we'll be very thankful that they did.
I'm 40. I don't know, perhaps I'm still young.
I did not appreciate having to learn the boring parts. Learning things for the next exam so as to forget them in two weeks... I didn't see the point then and still don't.
I managed to get by with the minimum possible, fluked my CS education, then had a career earning an order of magnitude more than the average salary. Shrug.
Maybe I'm missing something else because of my lack of education? I don't know...
We’re all going to have different paths but I’m certain that flunking CS education and then getting 10x the average salary is not going to be the common case and was probably only possible for a given point in time.
I’m in my late 40s. I left grad school to get a job in VLSI because it was possible to do so in the job market of the 90s. In today’s job market we wouldn’t even pickup the resume of a new college graduate that didn’t have at least a masters. I would’ve been totally passed by today.
Assuming the benefit we’re looking is getting a high paying job of course.
You (and I and many others on HN) were lucky enough to join the tech industry while it was still growing explosively and got outsized salaries because of it. If you were to do the same thing today, you'd be telling a very different and much grimmer tale.
"…perhaps I'm still young."
Possibly so, wisdom often take years to gel and often only after life events force its notions to the fore.
I had way more than usual share of "life events". I threw my career out the window to care for my toddler and dying partner. Then my partner died and I'm left alone raising the kid. What else is going to happen to make me wiser?
My parents forced me to play piano, right up until I told them that I'll destroy our piano if they don't lay off, and any consequences they could think of would not stop me (I was normally an obedient child, but enough was enough).
That got their attention.
30 years later I picked up classical guitar and loved it! Do I thank my parents for forcing the piano on me? Hell no.
Like I commented in another post, piano gave you the foundation for learning classical guitar (and appreciating that genre of music). Very few guitar players can even recognize note names on a staff. You’re not going to get far with classical guitar without it.
Unless you plan to be a professional musician, why does it matter if you “get far”? Isn’t it supposed to be for fun?
That was ironic understatement. With classical guitar, you won’t really get anywhere without being able to read sheet music. It’s not like rock and pop guitar where you can just learn tabs and slightly develop your ear and that’s enough play along with all your favorite tunes.
If you’ve already picked up reading music for one instrument, it’s a ton easier for the next one.
You need to "get far" enough for it to be fun.
You want to have fun playing along to your favourite song. Or impromptu jam with a friend. Or sing for yourself because a song reminds you of a memory.
They all have a minimum skill requirement, without which it isn't as enjoyable. You need to know to play reasonably well by ear to have fun imo.
Sure, those are definitely fun things to be able to do, but it’s not some kind of essential life skill. If it’s not someone’s thing, why force it? There are plenty of other skills that are also fun to have.
I mean, fair enough. I had an aptitude for it. If you're able to figure out what skills they might have fun with in the future, that's excellent. If not - I'm not sure, you gotta shoot your shot I guess? Because the dislike might be for the process (practice) when they actually would like the end product (jamming)
I just had a kid so this is pretty real to me. How it will go is anybody's guess, but I hope it does go well :)
Congrats!!
I guess I believe more in the Montessori idea that kids are intrinsically motivated to learn and excel, and they will tend to be naturally drawn to work hard at the skills that they are best suited for.
I understand the idea that some skills have a hump to get over and it’s good to encourage that determination, but I’d also guess that for every person like you who is glad they were pushed to learn some particular skill, there is another person who it affected very negatively. So I suppose it’s a bit of a gamble in that sense.
Because eventually you plateau without proper foundations, and that's not fun.
> Because eventually you plateau without proper foundations, and that's not fun.
This is a completely alien perspective to most people. Most people never even really try to be good at anything. That you think this quirk of your own psychology is the norm shows a deep disconnect with the mass of mediocre people who don’t care about being competitive because they’re not trying to get highs up on some leaderboard. https://danluu.com/p95-skill/
Does it matter if you “plateau” at a hobby? I have lots of hobbies and skills I’ve learned then plateaued at. It doesn’t bother me in the least.
Yes, it’s been very frustrating because there’s things (songs, techniques) that are beyond my reach at the moment due to large gaps.
I get that. It’s satisfying to overcome those hurdles and frustrating to be blocked. Speaking for myself though, if I find I’m getting really frustrated by something that I’m supposedly doing for fun, it’s a sign that I might not be approaching it in the best way psychologically. I’m usually much happier when I try to have more of a zen ‘putting in the reps’ mindset. Then the periods of progress are like icing on the cake, not something I need to enjoy the thing.
It's not like learning to sight read is a "piano only" skill...
In fact, I never actually learned to sight read until I started on guitar. All I remembered from the old days was "all cows eat grass"
Learning sight reading is the most natural on piano like instruments. The notes are literally arranged in the same order. Stringed instruments are much more difficult to learn sight reading from scratch on.
That's an odd take. Sight reading is about associating the mark on the paper with the actual note, duration, style etc. How that note gets played on a particular instrument is a different matter.
Can learn the foundations when you give a shit.
Doesn't actually matter how good he gets at classical guitar either.
> piano gave you the foundation for learning classical guitar
Absolutely not. If you hate something and don't learn anything more that entry level, it won't give you any foundation, only hatred and bitterness. Also the piano and the guitar are very different beasts that you cannot compare at all.
The piano and the guitar are different in many ways, but they also have some similarities depending on how you play them.
Mechanically, sure, nothing transfers. Rhythm transfers pretty well. An ear for what sounds right would too.
If you're reading printed music, that transfers. A lot of guitar play comes from tabs though, which isn't really transferrable.
If you play chords on the piano and the guitar, and especially if you're thinking about chord progressions, that transfers. But you might play either instrument without a lot of chords.
Lead melody kinds of things can transfer a bit. Especially if you were thinking about how the notes in the melody fit with the chords, even if you didn't play the chords.
Even if you didn't think you were learning music fundamentals, you might have picked up something.
Your experience is the antithesis of mine, I wonder why people are so different.
I’m happy that there was overlap between what your parents put in front of you and what you found passion in later in life.
I think that story happens to many but I cannot accept a premise that it is somehow universal.
The passions I found later in life were unrelated to what my parents put in front of me. I suspect that it’s because the activities I eventually found (distance running, volleyball, cooking) were not activities that my parents enjoyed or thought much about.
Moreover, I was unable to develop healthy models of internal motivation until mid life. I didn’t have to when the “why” was covered by my parents.
Childhood should be the lowest risk time in life for people to learn to fail and find the path back to success. This is what I worry about as a parent when I try to set my kids up for future success. I want them to fail now.
I see my role as a parent as coaching them to care about how they spend their time and how to recover from disappointment and failure. If they get that, then learning piano later in life is just work. They won’t be afraid of that.
> I can't thank my parent enough for having me to continue playing in my teenage years.
Counter-example to anyone reading this and thinking about imposing this misery on their child - I absolutely hated piano lessons, and nowadays I absolutely hate that my parents forced me to do it. Total waste of time, even spending more time on Civilization or whatever instead would've been more valuable to me.
> "Because it only took me a few month to be able to play pretty advanced piano sheets compared to some of my relatives who are struggling with the basics starting it in their adulthood."
I don't get it. you'll be a beginner in something that you weren't pushed to in your childhood. so what?
are you planning to only do things you were pushed to as a child? I learnt skiing in mid 30s , never even saw snow as a child. Its my fav thing to do all winter and spent like 40 days a season on snow. Not sure if i would've enjoyed it the same if i was "pushed" skiing as a child and hated it.
I’m not a parent myself, but something I’ve seen happen with an American family I know, is that they push their kids way too much to learn and do as many things as possible. They have their music lessons, their many clubs at school, several physical activities such as soccer, tennis, taekwondo. At some point you have to stop and wonder whether you’re taking their childhood away.
These kids barely have any free time. School during weekdays, activities during the weekend… worse than a full time job.
I think there’s a balance to be struck. Your kids don’t need to be good at everything.
Every parent is fighting an uphill battle against the technology now.
You either structure the day in such a way that there is literally no time for anything outside of activities, or you just observe the kid gets sucked into the screens with less and less will to do anything else.
That is a false dichotomy.
If not at a club/activity, why does the child have unrestricted access to screens?
Have you personally tried to keep a teen away from a screen? If you did with a success, I would really like to hear your story and what has worked for you.
Looking at my kids friends / classmates, almost all of the parents just gave up, with the exception of a small group that is still trying with the discussed approach.
"Keeping teens away from screens"? And why are there screens?
Sugar is addictive. One would not necessarily expect a teen to healthily control their sugar intake; accordingly, we don't put bowls of candy around the house, and if we did we certainly wouldn't be shocked when they emptied themselves, and then thrown up our hands and said "can't keep kids from candy, what can you do?".
Our kids aren't teens yet, but the plan is for screen time to be whitelisted, that is, there are certain times and circumstances where screens are okay and the rest of the time they are not.
EDIT: To elaborate on parenting philosophy a bit, one can provide structure (good) without being authoritarian (bad). Rather than bouncing between "you have all the options available, including screens, hope you make a good choice!" and "you are doing this specific activity now", one can provide unstructured time with lots of options available- reading, board game, doing something outdoors, creating a craft, etc- while having none of those options be screens.
There are screens because their entire social circle has phones, sometimes from an early age. If your kids don’t have them then they are the odd ones out, and excluded socially, which has their own extremely negative consequences.
And if the parent cannot find a single way to prevent the constant use of the screens beyond simply packing the day with activities, that says more about the parent than the kid.
If the only way a teenager knows how to make good choices is through outright avoidance of situations where a poor choice might arise, then they don't know how to make good choices.
Do you have kids? Lots of assumptions from someone who doesn’t seem to be a parent.
I have three kids (19, 13, 11) and I agree with them completely.
My son at 19 is building websites for companies, still deep into manga and video games but is started to get out more with the gym. He still lives with us, but essentially has his own life and seems to be doing well.
My 13 year old daughter is the one who loves to try everything. She's in dance, show choir, volley ball, tennis, violin, clarinet, etc. She even signs up for college for kids classes over the summer. All self motivated. Just yesterday her and her friends walked about 5 miles around town to different stores. She has her own phone.
My 11 year old is the smartest of the bunch. She has an amazing vocabulary and reading has always seemed to be "natural" for her. She's straining my policy of buying my children any books they want. She's bored of the advanced learning classes she's been put in. She also plays tennis and flute and cello. She learns her own crafts and sciency projects to try at home from TikTok. She will likely get a phone this year, but has an iPad.
All of them have had practically unlimited screen time since they were double digit ages. They are on TikTok and YouTube and SnapChat. They just have many other interests as well and it doesn't consume their lives. They manage their own bedtimes (within reason) and are responsible for getting themselves up and ready in the morning.
The only times we've forced them into activities is when they were too young to make those sorts of decisions for themselves. So all of my kids played soccer while young until they could suggest an alternative activity they would rather do more. They all started in music, until they could find other creative alternatives. None of them are screen zombies that so many HN posters swear is inevitable without banning things. I'm not sure where the panic is coming from, but leave me and my children out of it.
I do, they are younger than teenaged, but still.
Good luck with that. Please report back on how it goes.
Happy to, how would you like me to contact you? I don't think HN allows replies after threads have been multiple years dead...
Went fine. Quite happy with how my children are turning out. We don't even limit screen time anymore. They seem to have developed healthy habits and boundaries.
> At some point you have to stop and wonder whether you’re taking their childhood away.
At some point you have to stop and wonder if a great childhood is doing - music lessons, many clubs at school, several physical activities such as soccer, tennis, taekwondo etc.
They are occupied, they are trying new things, learning new skills, running around outside, interacting with their peers.
Definitely agree though the alternative can quickly become all day spent on TikTok or YouTube shorts.
This. I have several people with kids similar age as mine in my circle, who seemingly gave up and now its all phone, pad or tv at all times. It is very easy to lose that kid to other distractions unless you provide enough of a structure for them.
Many kids will do difficult stuff, just not the stuff you'd have in mind. Sometimes parents are right in what the kids should be focusing on, but I'd guess more than not they are wrong. For example, all the parents who discouraged heavy computer use or video games, when this is how most millennials came into programming and IT. Then there's the thing where a kid who is interested, obsessed even, learns SO much faster. I recall a story of a parent who wanted their child checked for learning disabilities and the psychologist exclaimed "Your son has memorized 350 Pokemon! It's not a question of learning ability, it's a question of motivation".
In my view, if we let our children do what interests them, to some degree (of course anything taken to the extreme will likely fail, and it depends on the child), they are likely to cover way more territory, and probably more useful territory, than a child that is being forced and coerced. One of the many things my 7 year old has learned from Minecraft is an entire language (English), to a level which in the past (my generation) we didn't reach before perhaps 18 (and that was due to watching TV, not school). The other day I caught him taking notes on a piece of paper that said single = 1, double = 2, triple = 3, quadruple = 4, quintuple = 5, sextuple = 6. This is a child who should not be speaking English, but now he can write and spell it better than his native language, because we let him follow his passion. He's also learned a ton of engineering concepts and vocabulary, and has the ability to install mods, debug when they don't work, has a basic understanding of networking, IP addresses and on and on.
He has no interest in playing an instrument right now, why should we force him? If the time comes and he wants to, he will learn it so much faster because he wants to get better.
If the kid isn't enjoying the piano lessons, will forcing them to do it for 20 minutes every day really be beneficial? Sure, they will now be able to do something - something that they absolutely hate... (also, why is it always piano that parents try to force on children?)
"something they absolutely hate" is learning to read sheet music, training for skill, practicing for muscle memory.
The fruits are reaped when they (me!) get older. Like I mentioned in another comment, I can play along to a song I like, play a song that is a certain memory, jam with friends at a whim.
Those are not things I necessarily wanted to do when I was a kid. But the "forced" practice was required as a foundation to do what I want to today.
> I can play along to a song I like, play a song that is a certain memory, jam with friends at a whim
You can do any of those things without learning to read music. Ask me how I know
Let me guess, you self taught on some instrument?
That seems like a simplistic conclusion.
He could have learned to play from a teacher that doesn't teach reading music, for example.
> they will now be able to do something - something that they absolutely hate
A valuable life skill if you want to ever have a job or get paid.
Similarly, it teaches the value of putting forth the minimum effort to appear to be doing the work. Putting forth more effort rewards one with more work.
They already learn this by being in school, no need for more of such "learning opportunities" in their free time.
I agree wholeheartedly.
Honestly, I wish I had been taught that lesson early, so as to internalize it profoundly.
Even with a lot of discipline and self-control, going through each and every day without mind-altering substances at hand is pretty dang difficult.
Teaching them piano is probably the worse thing you can do if you want them to get paid lol. You should be teaching them plumbing instead.
You don't want to put them off plumbing for life!
That sucks man. I hope things get better for you.
The sweet is never as sweet without the sour.
That’s such a depressing way to see things. I’m sure most people do something they don’t utterly despise, is only because they select for their local optimum.
> I’m sure most people
If you live in the bubble where you experience this, congratulation you live a wonderfully privileged life, never interact with anyone or are totally oblivious to the experiences of all the people you interact with on a daily basis.
You're of course right, it's a privilege.
But also, many people choose to do something they hate so they earn more money. They could be just as privileged and choose not to, just so they can compete with the Joneses and consume more...
So your parenting advice is to teach your kids to do things they hate while suppressing their feelings so they can be like the average unhappy person?
I hate doing laundry and cleaning dishes. I still do it, though.
There are things in life that you won't enjoy but you need to do. Learning to do them anyway is in fact a life skill.
I've seen people follow their dreams into careers they chose because they wanted them, despite those careers not being paid well. They're all at least as miserable as the average person, because what they enjoyed is now work, and they don't have money for anything they now enjoy.
"Do whatever makes you happy" is a life plan for the financially independent. Most people simply don't have that luxury.
> I hate doing laundry and cleaning dishes. I still do it, though.
Sure, I see your point. I guess what it comes down to is: what percentage of your life do you spend doing that?
If you don't like doing laundry, then don't start a laundry service business.
Parenting, having and raising children, including but not limited to the act of giving birth is the ultimate example. There are many "piano lessons" along that journey.
Sometimes you have to eat a shit sandwich.
Sure, but you don’t have to accept that they’re the only thing on the menu.
Sure, you can take off at 2am and leave a screaming 2 month old child in a room and never come back, because you have been trying for hours to stop it from crying and it is just too fucking hard - just like you can walk out of your piano lesson and never go back.
Or you can reach for the sandwich.
If piano lessons is what trained you not to abandon a crying baby, I'm not sure to say.
Don't know about 'most' but I think many do exactly that in order to pay the bills.
Yep, 6 years of being forced to play the violin.
Sure, once I was playing it, I was fine, but I cannot explain to you the sheer dread I felt opening up the case.
Have not played in decades, despite all those lessons and concerts and orchestra sessions.
I felt the same. I didn't touch it for ~9 years.
But I'm glad for it, since it lets me jam or enjoy myself without having to put the practice in now from scratch. I do it for fun.
I live in the hope that one day I will pick it up and feel nothing but contentment of being in the moment, but I'm just not ready for that yet.
Even the smell of tree resin sometimes makes my stomach tighten with anxiety.
Executive function / demand avoidance. Not to the point of being pathological, but it is a learned emotional behavioral complex.
They don't hate it. They dislike being bad at it, they dislike working hard at things, and they like video games and scrolling on their phones.
And yes practicing will result in them getting better.
The primary design goal for most traditional instruments was making them as loud as possible.
I was briefly made to play violin as a child, and I definitely hated it (fortunately my parents recognized this and didn't push too hard). The reason is in retrospect obvious: violins are loud and piercing and played close to the ear. Nobody considered hearing protection back then. I learned recorder as an adult and the loud notes can exceed 100dB(A) measured at the ear (both alto and soprano recorders, and recorders have very limited dynamics). Violins seem to be at least as loud. I would hate to play without hearing protection no matter how skilled I become.
Even in instruments where you can more easily play softly like a piano, the design for loudness can cause suffering. Pianos are much bigger than they need to be now that we have amplification, with correspondingly wide and finger-straining keys. Steel string guitars are louder than nylon but hurt more to play (and even nylon can hurt depending on your individual hand size and shape). I expect there are many children suffering hand/finger pain from being forced to play various instruments and genuinely hating it regardless of their skill level.
When a child hates something, there's often a good reason for it that isn't obvious and that they don't have the communication skills to explain.
You have the worst case of Dunning-Kruger syndrome I have ever come across.
There are ages below which you are too young to play full-sized pianos, or play every interval an adult can play. That doesn't stop you playing it at all. What's more, your hands and fingers stretch. It isn't painful to play the piano.
The stuff about loudness is just rubbish. There is absolutely no need for hearing protection while playing the recorder (a very quiet instrument), the violin or the piano solo. You have no idea what you are talking about.
I never said it was painful for everybody to play instruments. I'm saying this is an underappreciated reason for children to hate playing. Maybe you are lucky enough that it doesn't affect you.
And I personally measured my recorders with an SPL meter and found them to reach over 100dB(A) at the ear (played indoors in an ordinary room with furniture but without acoustic treatment). The meter used does not have a traceable calibration but in all respects behaves as I would expect a correctly calibrated meter to behave. I have no reason to believe it is miscalibrated. Recorders are only quiet in the bass. The high notes require much higher air pressure and can be very loud. Perhaps you are fooled by the lack of distortion. I played without hearing protection at first, but I was disturbed by the prolonged discomfort this caused in my ears. I then recorded my playing and reproduced it with loudspeakers. I was shocked at how loud I had to turn the speakers up to reach a realistic level. I think it's easier to judge SPL from loudspeakers because they do have distortion which serves as a perceptual cue. Pure sounds can reach dangerous levels without sounding obviously loud. I also think the fact that I was playing the instrument myself and not just listening contributed to my misjudgement.
> I'm saying this is an underappreciated reason for children to hate playing.
I once shocked my mom by clearly hearing what she whispered from across a quiet room. And not like a room in a home, this room was about the width of a house. I think people massively underestimate how sensitive hearing can be for some people.
I think this is the crux. Nobody likes to fail, kids included. And their attention span is wonky too so they may not see much value in learning from failure/s since there are so many other attractive things asking for their attention and they would rather do them.
Insane you’re getting downvoted, this 100% and then some. There’s a clear difference in outcomes between kids taught self-discipline and those who are raised standard Anglo-American ADHD style once they become adults.
Different point of view: do you consider hunting in the wilderness to be difficult?
I do, it requires being still in miserable conditions for a long time, being cold, wet, mosquitos, and then usually still no success, but frustration.
But to my knowledge, no savage kid is in need of being forced to learn it.
"children sense your true passions and naturally want to join in"
And that is my experience as well. But if you stop childrens curiosity out of limited time and patience "Be quite now!" - stop them from helping, because they are not a help in the beginning and you are faster on your own - then of course they won't just start enthusiastically some years later doing with motivation whatever it is, you define as their arbitary target now.
There is a huge difference between pushing your kids to overcome their current limits and forcing them to do something they do not enjoy at all.
There is indeed a difference between giving a slight push and "forcing" which is what TFA is talking about.
Kids tend to want to partake of their own initiative in activities that are 1) physical, and 2) that they see adults themselves do.
Hunting in wilderness is a good example; so are sports, cooking, crafts, etc.
But unfortunately not all important activities that kids need to learn to become well adjusted adults in our modern societies fit those 2 criteria.
Point 2) can be hacked to an extent by modeling the behavior yourself - eg kids who see adults read books are more likely to want to read themselves.
Or staring to smartphone. Then, suddenly, we are surprised why our kids do same.
> But to my knowledge, no savage kid is in need of being forced to learn it
Uhh then your knowledge is very limited because that is rather well documented. Also, why are you saying "savage" like an 18th century racist? Is that in fashion again?
Oh, I am obviously a racist, by glorifying indigineous teaching methods.
But otherwise can you show, where this is documented? The natives tribes where I have some knowledge, don't force their kids to learn in the sense that is talked about here. No need to - the whole culture is about becoming a good hunter (for male individuals). So indeed lots of peer pressure, but no individual forcing.
> Oh, I am obviously a racist, by glorifying indigineous teaching methods.
No, by calling people "savages", a pejorative, based on their ethnicity.
Much like how it would be racist to call people "enslavers" based on their ethnicity, or "cotton pickers" based on their ethnicity.
Erm, english is not my first language, but I believe, savage stands for uncivilised person.
So exactly what I wanted to talk about, when referencing "natural education".
I did not talk about any ethnicity at all.
It's considered super racist but also awkwardly old fashioned anyway even if it weren't just the former.
Ok, seriously. I did not talk about any ethnicity at all. How exactly can I made a racist statement here?
Or were you simply trying to say, for you the term "savage" is strongly connected to racists and therefore inappropriate to use?
Calling indigenous people "savage" in English is almost universally considered racist.
Well, or just in your bubble?
Besides, I called arbitary savage people savage. No concrete person that might feel insulted. And savage .. is not an insult in my bubble anyway btw.
Like you said, you're not a native English speaker.
Talking about a specific ethnicity is not required to be racist in English. If a person were to use the word "Nazi" to describe any person who lives in an area that was Nazi-controlled in 1942, this would be roughly equivalent in terms of the connotation and in terms of the reasonable indignation the recipient might feel.
Furthermore, if you didn't have a specific ethnicity in mind, then when you're going off about "natural education", what you're really saying here is "all groups of people that are part of a group I consider 'uncivilized' are the same".
Or alternately, if ethnicity isn't what you're using as your basis for calling groups of people and their children "uncivilized", what is?
"Or alternately, if ethnicity isn't what you're using as your basis for calling groups of people and their children "uncivilized", what is?"
Culture.
And this debate is equally fascinating and frustrating.
I simply spoke of generic nomadic uncivilised hunters.
And not at all in a bad way, just to illustrate a point. Because to my knowledge yes, nomadic hunting cultures do have similarities. Education seems to be one of those.
Feel free to provide counter examples.
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This kind of forced practice can create the appearance of a certain level of competence, but it rarely produces a deep understanding or innate appreciation of any of those subjects.
Take music, for example. Many high schoolers play an instrument as part of the college admissions game. Almost none of those kids can play music with their friends and just enjoy it. To them music is this structured activity where they get paper with dots on it, and they have to play the right notes at the right time to pass the class. These kids never develop a true understanding or appreciation for music. They don't keep their instruments or practice as adults.
There's so many things to learn to be good at, why not find something that you actually like?
This is one of the reasons I'm really happy that my daughter found show choir. Choir sucks. My kids hated it. I hated going to watch it. Bunch of terrible old songs that no one knows. Now she's singing and dancing to pop songs and show tunes on the stage and it's far more engaging for her. I do think it also helps that show choir is a tryout based program so the floor for interest and talent is far higher than with the regular choir.
I don’t have kids.
The really important part of this is that kids mimic what they see adults they like and respect doing. If their role models spend 6+ hours in front of the television every night, that’s what they’ll do. If their role models are playing music or sport, that’s what they’ll want to do.
Yes, but one of the problems with our civilization is that we typically do the important stuff out of our children's sight, and then come home tired and try to relax. So they do not naturally get a correct idea of what we do.
Yes. Due to an unfortunate event, I'm a single father. My life improved dramatically when I started doing all the chores while the kid was awake:
- We do the chores together.
- Yes it takes ages, but I need to kill the time anyway.
- Then she falls asleep and I can relax.
This is literal heaven, compared to when I played with her the whole day and then did the chores when she slept...
I don’t disagree with you. Parenting is hard, and some of the job is being a role model. If you show your kids the only way to relax is to beg in front of Netflix that’s what they’ll see. One of the nicest things I see on a weekday evening bfis kids with their parents at the driving range - it’s clearly 0 break for the parent, but the kids are usually having a great time doing what mom/dad like doing.
You are incorrect, kids don’t necessarily mimic their parents’ interests..
Oh yeah let's turn otherwise fun hobbies into a forced chore, that will surely be great for the kid. Forcing kids to learn to spell when they have learning difficulties (eg dyslexia) doesn't usually go well either it's just causing suffering for the kid.
The problem in this discussion is that people here seem to miss that both an excessively authoritarian parenting style is bad but also going full liberal and just letting them run wild is not the solution. Sometimes children need guidance an a gentle push.
Even as a adult I sometimes need to get pushed. I sometimes take guided courses so I don't skip over the hard but important parts of learning a new thing.
Just don't push your children too hard or you do more harm than good. Accept that they are not you and have different interests and needs. Like make them practice an instrument but give them a choice which one. And if after a few years they still hate it, well you tried. Maybe it is not for them.
I think much can be learned from modern American kids sports vs the Soviet youth sports system.
Kids specialize almost immediately now in a sport that is most likely because the parent likes that sport and wants the kid to be good at it.
The Soviet system was the athlete as a kid should try as many different sports as possible until 12 or 13 because you don't know what the kid will have natural talent at for before then.
That is not pushing the kid to practice something they hate but it is also not letting the kid be free to not do anything besides play on the phone.
Kids ultimately like what they are good at. If I had a kid, I feel like my job would be to figure out what they have some talent at and then fan the flames so that talent turns into a passion. I think many parents though are trying to live out their own dreams through the kid, if the kid has talent for the activity or not.
The problem is that it’s extremely difficult for any activity like math, music, or drawing to compete with Minecraft and YouTube shorts.
Kinda yes, but there are some solutions.
I think the most important part is to start early. Make your kids interested in math, music, art, and sport, before they start school. Doesn't have to be anything sophisticated, simple addition and puzzles will do for math, etc. Then you have something you can later build on.
There are also ways to make things funny, including math. Most people say that they hate math, but then they do Sudoku. So, try to make more math like this. Not all math can be transformed to funny puzzles, but after a few the kids will get positive associations with the subject, and will be more willing to learn more.
Doesn’t seem to be an issue for Asian families or ones coming the from former Soviet block as well as Jewish ones. These groups as adults tend to outperform others. There’s a reason for that: early childhood discipline and consistency being built into their cultures.
> Forcing kids to learn to spell when they have learning difficulties (eg dyslexia) doesn't usually go well either it's just causing suffering for the kid.
I greatly valued the tutoring that I received for that (personally wish it had not been cut short). I was somewhat fortunate and received one-on-one tutoring in a secluded room.
They provided me with clearer definition of rules (instead of sayings like "i before e...", proper phonetics, and a history of where English came from.
That said, there's research into trying to determine which children with Dyslexia should receive specialized treatment as a segment just cannot learn to read at all.
Double-edged sword IMO. I was mandated to a half hour of piano practice early on, and I came to dread it. But in my experience that was less having to do with being pushed to practice, and more I loathed my parents overhearing my piano playing and thinking they'd come down and criticize me for not trying hard enough. This was an uncommon occurrence, but it occurred enough to plant the seeds of anxiety in my mind.
The nature of pushing needs to be considered in the sense of the overall parent-child relationship, and not just being handed a Mikrokosmos and an egg timer. If my parents were more proud of my ability to push forward and took interest in the piano and my playing beyond just performing good at recitals, I probably would have grown up to truly enjoy performing music. Today I'm left with a bit of a bad taste in my mouth that would require conceited effort to overcome. So I guess my parents weren't "lazy" in your terms but a bit too strict for me to conclude I would be "good at music" that early.
> A very small minority of kids will do all of that easily and for the fun, but you can't rely on it
This may be true, but explain to me what are the returns you get on forcing math (or anything) on kids? They won't like it, they won't learn it intimately, the won't internalize it, it'll be unusable knowledge and mostly a waste of time with lots of bad vibes and probably even a little trauma...
I spent a lot of time with math in high school and college but that was because I had a couple teachers who really elucidated why *I* might find math to be interesting (in my case, it was physics and computing). Forcing people to do anything generally leads to nothing worthwhile.
My take is Maths, Science and English push. Everything else let them decide what they like. Do parents push kids at every damn subject?
I think everything else like, drawing, singing, gardening, exercise, meditation could all use a bit more pushing...
I think there's also a significant cultural dimension to this discussion.
For example, in many Middle Eastern and Asian cultures (pardon my generalization here), there's an ingrained expectation that children should be pushed, often quite hard, especially in areas like mathematics, science, engineering, and law. Hence the old cliche: "You have three career options: doctor, lawyer, or engineer.".
I've seen this firsthand as a Middle Easterner (I was born in IRAN). My father is an engineer, and both my parents were relentless when it came to academic discipline. I ended up in computer science, and my brother became a pharmaceutical researcher after obtaining his PHD.. There's no question that this kind of structure and pressure produced tangible results. But I'd be lying if I said it was an easy or joyful process. It ended up costing me plenty of social anxieties and now I struggle with social dynamics.
That said, I have mixed feelings about it. While the rigor pays off in terms of career and technical competence, it often comes at the cost of creativity, intrinsic motivation, and the space to explore things like literature, music, and the arts. I sometimes wonder what paths we might have followed if exploration had been valued as highly as performance.
So I _partially_ agree with you that some degree of external motivation is necessary, especially with children who haven't yet developed discipline. But I also think we should be careful not to frame this solely as a matter of "lazy" vs. "good" parenting. Upon reflection, I think that there's a balance between encouragement, discipline, and allowing for the development of intrinsic interest. Different families, cultures, and even individual children may need to strike this in different ways.
But should the parent decide if the kid will become a musician? What if its not talented and pushing it with force to mechanically play Mozart? I later became interested in playing bass guitar, nobody forced me. I did it for leisure. Children are and will not be experts in all fields. Sure you are right that some discipline is needed to move forward and to keep up with something. Do you remember and use everything you ever learned in school, if its not needed for your current job? Kids nowadays spent half to 3/4 of the day in school or outside their own home. When should they be kids? I understand the pressure of parents to make sure they have good grades, some is necessary, but not really all of it. I never learned touch type in school. I did that on my own after work within half a year. I did it because i was interested in. Worked 20 years in IT. Now i am currently trying to get my amateur radio license, i use my knowledge that i collected so far, allthough i was bad at math in school. Life is a journey, i got three professions so far.
> Most kids won't do difficult things if you don't push them.
I guess it's true for adult humans, and other creatures as well. Instead of pushing, however, you should consider using other motivational methods (a simple prize for accomplishing something that you want from your kids works very well). Pushing can cause alienation and hate, which could affect their entire adult life.
I think many adults don't push themselves because they were always pushed by others their entire lives. It's a form of learned helplessness. You never have a say in what to do, so you just do what you're told, nothing more.
It’s amazing how far the promise of a sticker or special treat will go for young ones.
Every kid that I know who was forced to do their 20 minutes of piano a day now doesn't play piano and can only play with sheet music in front of them. They can't improvise, they seem to take no joy in the music.
I was the kid who wanted a keyboard and guitar but didn't get one until I could afford one in my twenties, then I learned just enough to be able to be creative. People say I'm good at piano but technically I suck, I'm just creative and expressive with limited tools.
It's an interesting phenomenon, the adults who are technically great at piano, but can't play anything without it being written in sheet music.
I agree. I got frustrated a lot being forced to practice the piano as a child. Not a long practice, just like you mentioned, about 20 minutes a few days a week and an hour lesson every other week or so with someone in the neighborhood.
I look back at the memories very fondly now. As a pre-teen I got invited to play at my cousin's wedding and everyone still talks about it. It gave me a good foundation and I performed well in highschool band and small ensembles. I now play my instruments for my kids and it brings us all a lot of joy.
Both of my parents weren't especially musical. I'm not amazing or anything, but I've got enough skill to hear a tune from a show or someplace and play it at home for my kids reasonably enough. But I wouldn't be able to if my mom didn't make me practice.
> The author clearly has very limited experience with raising kids. Most kids won't do difficult things if you don't push them.
Such a bold claim coming from some who does not share their credentials on the matter.
My kid will do everything as long as it is interesting. My sample of 1 contradicts your claim, but neither of us are experts on the matter.
Sample size 3 here and they are all adults and all STEM grads.
You have to push them, but push them right. That's a combination of coercion and encouragement and helping them avoid procrastination. There are hills to climb and they need helping over them to where the good stuff is.
I remember my eldest crying over ratios at the dining table. Then algebra at the kitchen table. Then crying again at real analysis in the pub with me. She graduated with a first in the end.
I'd be interested to hear what she has to say about the experience
> My kid will do everything as long as it is interesting
Difficult things aren't interesting locally, you have to practice boring things in order to do interesting things in difficult subjects. Some kids do practice boring things if you just ask them, but most do not.
I think you're very very wrong.
Especially in maths, there's not much to practice.
There's stuff to understand. And while this might be exhausting it's not boring and it's a very rewarding process in itself.
Or programming... What's there to practice?
Really. I'd like an example of something that's boring.
My impression is that if you follow the path of discovery and applying things in context, there's nothing that's really boring.
Do you do things because someone force you or beacuse you have self motivation?
As an adult, you develop the agency to force yourself to do things you don't like doing
I can tell you as someone who was never forced into any extracurricular activities and was forced to go to church-schools that you probably should force your kids to learn something well (and not send them to religious schools)
You are not forced. You do stuffs you dont like because you racionally evaluate consequences that could probably not worth it if you don't do it. Why cannot we approach same attitude when raising kids?
I spend at least 40 hr a week doing something I have no motivation for. Most people do. Even if you don't hate your job, would you actually do it if you weren't getting paid?
Do you find it healthy? Doing stuffs that you hate? Isn't that a consequence of forced education system?
> Most kids won't do difficult things if you don't push them.
I roughly classify parents in two groups: (1) like the author of the article, (2) like you. Based on my limited observation, neither can be claimed to give optimal results, and it more boils down to "see what actually works for your kid in the long term" which unfortunately far too often can only be definitely said in hindsight.
Just on this, do you factor in that maybe they don't practice the piano because they aren't interested in it, and that's fine because it has no practical utility? I.e. in contrast with things like spelling, which do.
Also in your opinion at what age should pushing start, and how much pushing per age group?
There is little practical utility in most subjects.
How do you know that the conclusion you’re drawing from your experience raising kids is correct? There are alternative conclusions that sound like they match your experience, such as “most kids won’t do difficult things that don’t interest them if you don’t push them.”
The world needs less Asian kids being forced to play piano since a very early age and it needs more kids (Asian and not only) that are left to explore the world.
Without that exploration the kids won't make the world their world, at best they'd only make it a bad approximation of what we, our (older) generation, best think that that world should be.
Any proof of why it is best?
I prefer to live among educated people, thank you. I prefer my peers to go through forced history lessons, forced math lessons so they don’t tank my government, and biology lessons so they don’t tank the health system. Yes they won’t be able to determine their gender, but that will give me grandkids, thank you very much.
Same goes for piano or sports. Yes we need to pull people upwards, otherwise we’ll all become fat americans.
I kind of get the both sides of the argument. It kinda feels wrong on one hand. Lots of people agree. The other hand, it kinda, just works. Great. Everyone's hit with down-trend TFR anyway so maybe not it.
> at best they'd only make it a bad approximation of what we, our (older) generation, best think that that world should be.
Also, this part in GP doesn't feel exactly right to me. The problem doesn't seem to be in education, but rather lack of systematic resistance in current systems of society against humans weaponizing the system as tools to hamper progress of humanity as means to win minor inner struggles which is stupid. But the world doesn't seem to be moving in a wrong direction, only slowly.
Asian kids in 80s dreamed of bunches of permanent artificial space habitats running on fusion reactors. Still do. We've only gotten ground based fission reactors and space motor homes since then. But at least we are moving in that direction, just slower than at the ideal rate.
China's just done a humanoid robot marathon event. The winner completed the race. They're definitely in the future. US is, in a state not in line with site guideline to describe. And the latter is supposed to be more correct state than the other? How is that possible?
Because "forced history lessons" doesn't help said kids understand what history really is about, it just helps them accumulate facts, if that.
I'd say the same thing applies to math, where one can't really start understanding math until said kid is already an adolescent (unless they're a young Euler or something), so it always baffles me when I see parents filling their young kids with (fancy) arithmetics, most probably making said kids future therapy patients, all the while lauding themselves (the parents do, that is) that they're teaching their kids "maths".
Related, one of the best maths teachers I've had (this was back in high-school, in the mid-90s) was very quick to point out that we should forget almost all "maths" we had learned in elementary school, and the he very soon started to explain to us the definition of the real numbers. Or maybe this is just an Eastern-European thing, who knows? Maybe further West they do confuse arithmetics with maths until the Uni' years.
You’ve got it backwards: the future therapy patients are kids who are not taught discipline and persistence. Those who aren’t struggle as adults as the real world is harsh on vibe based living. Also, all those “useless facts” eventually build up on each other. They are prerequisites of knowledge and mastery.
You mention Eastern Europe, are you by chance familiar with the Hejný method of math education in Czechia? Because that introduces some "math beyond mere arithmetics" concepts to the elementary school education.
Sometimes, it is possible to create a less abstract version of a more abstract thing, and thus introduce the seeds of the concept to children much younger. For example, "solve the equation 2x+1=7" is abstract, but "Peter decided to use a # symbol for a specific number, and he didn't tell us which one, but we found in his notes that # + # + 1 = 7; can you figure out which number is # ?" is simple to understand for a very young child, even if the child can only solve it by trial and error.
Forced history lessons are just indoctrination and propaganda, since what you learn is dictated by the government. I wonder if there’s a single country on Earth that teaches e.g. the history of Israel-Palestine conflict in a way that even tries to approach objectivity.
All history lessons are indoctrination at the very least. There's not some "objective history book" where people can just learn "objective history" without zero doubts. Even for things that are taught more or less "objectively", no one alive has firsthand experience of them, unless they are recent. The end result of teaching critical thinking is that you shouldn't trust anyone completely, not yourself, and not your teachers. It's just that adding the layer of government propaganda makes things worse.
> piano
This is such an arbitrary and random choice. I don't give a ** if your child can play piano. It's negligible if you compare it with other hobbies.
Teach them (and me) how to pay taxes, do community service, partake in social events instead. I also don't want to live in a world where robots go to work for 40 hours, go home wasted and repeat for 40 years as they do in so many East Asian country. Its a stereotype yes, but you can't deny its unhealthy.
> Yes they won’t be able to determine their gender, but that will give me grandkids, thank you very much.
All that praise for education and yet you've fallen for the tabloid-fueled conspiracy theory that transgender science is a hoax
What do you mean by "science" in this context? For example, both biology and anthropology are sciences, but biology can tell us that people evolved from apes, while anthropology can tell us that a specific tribe believes that they were created by a flying serpent. Both of them are sciences, both of them can talk about the same topic (the origin of humans), but they take a completely different perspective on the topic.
Is the "transgender science" you talk about more like biology, i.e. describing how things are, or more like anthropology, i.e. describing what some (sub)cultures believe? Those are not the same things.
Biological and cultural/historical. There is rather strong clinical evidence on the healthcare side of things, and an understanding of intersex biology (including how the the brain develops, not just the classically understood intersexes) shows a complex picture of where various components of gender may originate from on a biological level.
But yes, much of what Foucault taught us about the arbitrariness of being a human in a culture does still ring true. No, it doesn't discount the hard evidence from biology and psychology.
Except they are now, wealthy Chinese are one of the most rapidly growing segment of tourists. Wanna guess what the wealthy successful ones learned as kids? That’s right: piano and math.
Kids left to their own devices don't explore the world. They play video games and scroll on social media.
Not if access to those things are limited while providing opportunities for other things that people enjoy.
You don't replace enjoyable things with unenjoyable things and expect the child to become a well-adjusted adult. You give them alternative enjoyable things.
Managing a child's burgeoning dopamine regulation system is a primary function of a parent. Abdicating that function for quick fixes is a form of neglect, in my opinion, just like feeding kids sugary cereals.
If that is the world you are providing, that is the world they will explore.
It is not just me who "provides the world" to my children. Also their classmates, etc. And the internet: even when someone uses it to achieve a purpose, there are various ads and algorithms that try to turn you towards something else.
It appears that no sane parents will allow their kids to extensively explore the world that the modern society is currently providing.
Any patch of woods seem to cast an irresistible call to explore on kids.
what does it mean to "push" ?
they used to beat the living shit out of us india when were growing up. is that what you mean?
So now you have a kid that’s really good at playing piano but absolutely hates doing so. Mission accomplished?
Why not anxiety instead of laziness?
At first I am reluctant to agree. But I decided to take math and English every year. I sucked at math, and had to figure out how to get good on my own. Now I have a degree. Math and music go hand in hand. I hated the music I was learning, so I quit lessons, and got the music I wanted to learn and struggled to learn it and I got muh better. I am an avid reader.
I reluctantly admit that you are right, and I am the better for it because I overcame my lazyness and found joy, in math, English, reading, and music. I sing, play piano, guitar, and listen with appreciation.
Its not a good take because no alternative is provided, but the author does notice something important that 99% of other people don't notice today. They don't realize it explicitly, but the actions do recognize it implicitly.
The school system today uses elements, structures, and clusters, the same techniques used in real torture. Its embedded into the structure of by-rote pedagogy starting in the late 1970s, and it also goes by another name starting in the 90s, where Administrators, NEA representatives, and Teachers, call this "Lying to Children".
Most parents today seem to be simply too busy, treating school like daycare, or maybe they just don't love their children enough to put the time in to protect them and figure out what is actually happening to their kids.
Classic curricula followed the western philosophy of the greeks, you develop tools that let you reduce a working system to first principles (in guided manner), which are proven true, and then you use those principles to model the system accurate, and then predict the future parts of that system.
"Lying to Children" does the exact opposite in time. It starts with a flawed model that is useless teaching abstract concepts and includes other unrelated concepts that arise naturally from that flawed model. The student is then as mastery progresses forced to struggle to unlearn material that isn't correct, and then relearn the finer details with each new flawed model given in a progressive fashion, over, and over, and over, becoming more useful yes, but torturing themselves, and in a way destroying themselves in the process.
When questions or true insights occur, the flawed model breaks those insights requiring you to do things differently in earlier classes before you can use those, but not even this information is given so you can't leap frog the torture.
There are additional strategic structures that orchestrate failures to gatekeep technical fields like math. There is an Algebra->Geometry->Trigonometry sequence which uses a gimmick in undisclosed pass criteria between class 1 and class 3, so the student passes initially but then fails and has to go back to Algebra, but can't because its sequential. Its called burning the bridge.
Regardless, the student is blamed, no help is given (because there is no cure for torture). They are told, "maybe you're just not a math person, you should choose a career that doesn't use this if your having trouble.
This gatekeeper is orchestrated to induce PTSD towards math in general, and as all technical fields require math this prevents them from entering those fields. Some are able to pass and enter these professions, but never the best and brightest, only the most compliant with blinders.
The exception to this is if you bypassed the entire process through private boarding school, and Ivy league college straightaway. If your an elite, you get a decent education.
These structures follow a false ideology based in gnosis/gnosticism which is long refuted, but that hasn't stopped these things from being used for purpose, or allowed others to remove these.
There is an all out war that has been happening for years, a war on our children. Compare low attention spans and other things with the documented characteristics of torture from PoWs and you'll see there are parallels everywhere.
The thousand yard stare. Hollowed out feelings. Lashing out. These are often referenced in the material on torture.
The problem is unlike adults, once broken and distorted by torture children carry that forward their entire lives, unable to change because its not learning, its torture, and there are very few who ever recover.
Failing to see the reality of what is happening and calling it lazy and complacent without understanding is problematic and most definitely not the sign of a good parent if that means you let your children's minds be destroyed under a false belief that its just laziness.
For those parents that are unaware of what I mean by torture. You can read books on the subject matter by Joost Meerloo, or Robert Lifton. From the case studies you can derive the requirements and you would be shocked to find and recognize these things being used everywhere today without you knowing. Robert Cialdini touches on the psychological blindspots used which bypass your and your children's perception to the issue.
The elements are isolation, cognitive dissonance, coercion with real or perceived loss, and lack of agency to remove oneself from the situation. Some would argue this also includes time and exposure.
Structuring and Clustering, forces active engagement through specially designed circular trauma loops, forcing the psyche back on itself to destroy itself, and narco-synthesis and narco-analysis which in the 50s used barbituates to trigger dopamine are used today through associative priming through many ways including your phone (gamification uses many of these things learned from research on torture).
It is established that those who are drugged have less resistance to torture, and those with faith-based beliefs tend to resist torture better. One of the first things to go under torture is rational thought.
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The important part is to start as early as possible and absolutely not trust the school/teacher or kindergarden staff. They are badly programmed to reinforce kids in what comes easy to them and stop encouraging them after less than a handful of attempts.
If you have to restart later, no matter at which point, even up into 'the kids' 20s ( ultra late bloomers, slackers, kids disgusted by most people for reason Z, drug- or "condition X"-induced deadbeats, repressed kids with and without ADHD, failed or successful attempts by psycho-social environments ) understand three things:
1) you are not pushing, even if you are, you are demanding sth for the sake of your child AND yourself. YOU WANT THIS first and foremost. It's not a bad thing, fuck what the little fucker wants.
It's imperative for the kid to know that YOU WANT THIS no matter the obstacles. You want to see the process and result. It's a form of accountability, I guess. Kids pushing back is some dumb implicit way to check how important THEY and THE THING really are to you _or someone else_ (that counts for the ugly stuff, too). It's part of our evolutionary, hard-coded OODA loop.
2) just start at the very beginning, so that it's easy, almost effortless. The kid will be annoyed on most of the difficulty increases, it always depends on the sub-topic so don't back down. Even 20 year olds will catch up with their successful piers within some time. Neuro-genesis is awesome. Most 'grown up' stuff is child's play and a matter of baseline-human character anyway.
3) your stress level is what matters. Stay cool, be equanimous, serene, check your posture, voice, tone, the discussion won't last 5 min and will be worth it.
Absolutely force your kids to do math.
> Without realizing it, he was doing algebra.
A friend of mine taught remedial math at UW to incoming freshmen. She would write:
on the blackboard and ask a student "what is the value of x?" The student would see the x, and immediately respond with x means algebra, algebra is hard, I cannot do algebra.So she started writing:
and ask the student to fill in the blank. "Oh, it's 3!"The semantic meaning of a blank is much better understood to everyone than an arbitrary letter like 'x'.
People just want to know why it's x and not something else or how a letter can have value. They might even think how can 24 + 2 = 5? They just want something to grab onto and nobody is really teaching the concept of a symbol in a math class.
I will die on the hill that most of math would benefit from better naming, less short names and longer format. Yes, the crack math guys have no problems with terse symbols. But most people do. Good example is Greek letters for geometry. They are not really taught in school so an easy formula gets 'weird squiggly thing times another squiggly thing....' and that does not help understanding at all
This is like trying to change English or arguing that we should all speak Esperanto. Mathematical notation isn't the way it is to save ink or make it look difficult. It's that way because it works. Notation isn't set by committee, it's just a way of communication that works. If you read cutting edge research you'll find notations being invented all over the place. Most of them will never go anywhere, some will become standard in their field (like big-O) and others will become universally used (like dropping the multiplication symbol and using epsilon for a small number).
I think this is a very limited take for a hacker forum. We talk about how useful accurate names for variables are all the time, or generally how working to encode more natural/context-related semantics to code helps anyone reading it understand what the goal is better than an extremely terse symbology.
Yeah, lots of existing math texts will forever exist with greek alphabet soup, but we don't have to rely on those as our be-all-end-all teaching tools.
To operate at a high level in mathematics I would agree that having the skill of easily abstracting complex things into compact symbols is a necessary skill, just as I would agree to the same concept applied to software engineering or really any complex engineering system; by the same token, we don't have to START on hard mode with all of our students. Math is infamously difficult for some, largely (I think) because we make it unnecessarily opaque out of some misguided sense of traditionalism.
If we want to have lots of people who are good at math we should embrace whatever pedagogy is effective.
Math doesn't start on hard mode. Students spend years studying how numbers behave before doing symbolic math. That said, trying to cover the topics symbolic math does with a more verbose language would just make it into impossible mode. It'd be like trying to replace sheet music with words.
In fact the analogy to music notation is I think a fairly strong one. People's complaints always sound to me like asking why we don't write "C3 sixteenth note" for music instead of using dots and lines. After all, how are we meant to know what the dots mean and remember the difference between an eighth and sixteenth, or what flats/sharps do? And then the key signature can modify all of it!
The notation just isn't a barrier. Once you learn to read it, it's there because it's a clearer way to write the ideas. The hard part for people is they don't understand the ideas, and don't have the frameworks like key signatures, chord progressions, and meter to place them within. Longer words for variables won't help people understand e.g. inner and outer regular measures, or the open cover definition of compactness. That comes from a lot of work to understand what you're trying to say, the pitfalls of saying it wrong, and precisely how your slightly different way of saying it avoids those pitfalls (or selects the best set of pitfalls if you must pick some kind of degenerate behavior).
I hadn't thought of sheet music in this context before; that's a helpful counter-example, thanks.
Broadly I agree; the semantic density of domain-specific language is often required to operate well in that domain. I disagree some with the "Math doesn't start on hard mode," but I think that's just bikeshedding at some level.
The endemic "I just don't understand math" that my (American) peers have espoused, to me, points to a failure in our (American, public school) instruction practices around it.
Many programs are at a much higher level of abstraction than mathematics. If you are implementing domain logic then you should definitely use names from the domain. But when implementing an algorithm often the most meaningful name is a single character. I find it odd when people try to force the "no single character" rule everywhere.
But I've got to say, the short names are not the problem. If you rewrote F=ma as "force is equal to mass multiplied by acceleration" this wouldn't suddenly make it more accessible to swathes of the population. People who are good at maths anyway have no problem with this.
imagining that alpha is what stops people from being good at math is a useless take. why pretend that such a low bar could prevent anyone from understanding? its some fake generosity towards "newcomers" that is completely unwarranted. math notation is by and for professional mathematicians.
are you really saying that "let function(argument has type RealNumber) has type RealNumber be a function from a real number argument to a real number" is somehow superior to "let f(x) : R->R"
> why pretend that such a low bar could prevent anyone from understanding?
I don't know why this is a startling take. If you encode your ideas in an unfamilar symbology, of course that's going to make it more difficult for someone who isn't familiar with the space.
I'm not arguing that we should teach real analysis this way, or any other high level math class. I'm only contesting GP's comment that there is NO value to be had in using more familiar language to explain a new concept to an unfamiliar audience.
This is the entire reasoning behind "word problems" at the elementary level; they're meant to ground the abstract modeling of a math problem (193 - 3 * 12 = ?) into something more intuitive for a child to understand (If you start with 193 eggs, and you take three dozen away to bake a cake, how many are left?)
> are you really saying that "let function(argument has type RealNumber) has type RealNumber be a function from a real number argument to a real number" is somehow superior to "let f(x) : R->R"
No, I'm saying the there's tradeoffs on either side, and our educators ought to be aware of this.
> math notation is by and for professional mathematicians.
I agree, but we teach math to plenty of people who aren't professional mathematicians. I wouldn't want to do formal abstract algebra proofs in a more verbose form, I'm perfectly happy using the domain notation, but my friends from biological sciences who have to take a calculus course now have to learn both a new symbology alongside the problem domain. I've watched enough of my (clearly intelligent) biology friends slam face first into calculus and spin out. They're not dumb, they can do circles around me when it comes to chemistry, yet they Just Can't wrap their heads around calculus-style math, which leads me to wonder what the difference is between how we teach complex chemistry vs complex math. Questioning the pedagogy is a fairly logical extension of that.
If there was some better notation that allowed biology people to understand calculus more easily, what do you imagine they'd do with it?
It's hard for me to imagine it without any special notation. It makes me think of the general relativity in words of four characters or less that was posted recently. Sure, it might be possible, but does it really make it easier to understand? Understanding is normally built up in layers. We learn things using big words because that makes it easier than learning with small words. And we learn maths with funny symbols because it makes it easier than learning it with words (or colours or mime or other things you already know).
For any given problem, you usually know what it is your studying, so writing out names doesn't have much benefit. On the other hand, a more visual language (which is what mathematical writing is) lets you easily look at specific portions of the picture and read off how it behaves, which is very useful. Basically, getting hung up on names means you're reading it wrong.
I don’t recall the exact age, but when I was doing math in primary school (somewhere around age 9/10) we were absolutely using symbols - “Paul has two apples, and the basket can hold 10 apples. How many more apples can Paul put in the basket” is the same as 2 + x = 10
We did these sorts of problems for a long time, with addition/multiplication/fractions, and even when we started doing actual algebra the problems were introduced the same way “let’s look at a problem we’ve solved already, and write it in a different way”.
This becomes even more true in higher level maths where programming language style functions would make everything vastly more clear, and easily typeable, than the traditional Greek symbols. sum(x+3, 1, 4) is just so much more clear (and consistent when generalized across other operations) and practically as concise as the mathematical way of expressing that which I cannot even type. Multiple variables would be a bit dirtier, but still much cleaner than the formal expression.
Interestingly mathematical symbols in the past also regularly evolved. Then at some point we just stopped doing that and get stuck in a time which is arguably no longer especially appropriate. So we're left with rather inconsistent symbols, oft reused in different contexts, and optimized for written communication.
The formal language of math is intensely optimized for rapidly communicating with yourself 90 seconds in the future, when doing a proof or calculation, turning paper into working memory. It does seem silly to use the same language for communicating with others across unkniwn but deep chasms of context. Its remarkable that it works at all
The strangest part about mathematics culture is that there is a culture of vibing the notation.
Nobody in school ever tells you that there are glossaries on Wikipedia that tell you the meaning of the symbols. You're supposed to figure it out yourself using vibes.
The way mathematic notation is taught is inherently unstructured. You're expected to just get it.
For the purposes of education, it is important to keep in mind that "optimized for performance of a highly trained person" and "optimized for understanding of a complete beginner" are two different things.
I often see people make the mistake of trying to teach inappropriately abstract things to small children, because that's what the pros do, and we want the little kids become pros as soon as possible. Problem is, trying to skip the fundamentals is only harmful in long term.
First kids need to learn what all that stuff means, and then we can proceed to teach them the shortcuts.
its silly. itd be like introducing first year programming students to advanced maps/filters/anonymous function syntax, instead of the easier to understand for loops and if/else statements. math's "no true scottsman" approach to teaching only hurts itself in the long run.
I'm not sure if it would be easier to explain a map / filter to a first year student vs implementing the patten manually using a for loop and if statement...
Seems like a pretty easy example to make practically, for map have a collection of things, say balls or black. Pick up each one and do a thing to them, paint them blue for example.
For filter do the same except have two different colour balls, if they are yellow they get thrown away, of they are blue they get put in a bucket.
A for loop doing exactly the same you would need to explain the topic at hand, as well as explain iterating an index etc...
Explaining loops is independent of the concepts of collections though. It's also more general, since map/filter/reduce use some kind of loops under the hood anyway, the fact that probably shouldn't be ignored in education process. Unless of course you go with pure functional recursive iterator, but good luck explaining that one.
Maps and filters also require understanding of higher order functions and the very idea of passing function around as a value. I would argue that implementing map/filter with a loop and then demonstrating how this pattern is generalized as .map()/.filter() functions is better and more accessible
My first thought when I read sum(x+3, 1, 4) was x+3+1+4.
Also it should be sum(x+3, x, 1, 4) since you need to encode what the iterator variable is as well.
I thought that was it too, but you're saying it's not..? I've been thinking about it for a few minutes now and I still can't figure out what other meaning it could have.
Edit: Oh wait, someone else mentions map/filter, did they mean this as a combination of range->map->sum and the latter two numbers are the range portion, like sum(map(x+3, 1..4)) ?
Edit2: And now I'm remembering sigma. I think it would have been more obvious to me if the order was flipped and your issue handled the way it is in that notation: sum(x=1, 4, x+3), though I'd still prefer the range notation: sum(x=1..4, x+3)
Yep. I agree and now we've basically reinvented sigma. Take the x=1 and put it below, take the 4 and put it above take the x+3 and put it to the right.
Granted I always found sigma a bit quirky for separating the range ends like that. Either x below and 1..4 above, or x=1..4 below/above would have been more intuitive.
But it's just a notation you learn once and then you know it.
Thanks for this comment. My secret shame as a programmer is that I haven't really learnt much maths, stopped at 16 in school. Writing out the sum function like you did makes perfect sense to me immediately.
What I should really do is create myself a cheat sheet of symbols to code...
Just read this:
https://en.m.wikipedia.org/wiki/Glossary_of_mathematical_sym...
Thanks for this :)
It's hard to debate that mathematical notation has a lot of room for improvement. High level algebra is very cryptic and often looks like an arcane incantation rather than something comprehensible for an unknowing person.
That said, as a person who moderately enjoyed math in high school and university, this functional notation would make me hate math infinitely more. It's would look like Lisp, which, at high level, looks just as cryptic as algebra. The sheer amount of braces and mistakes that would be made when reading and writing them is nauseating.
Infix notation, for all its flaws, provides important visual aid for understanding the structure of the expression (the sum of two fractions looks very different from fraction of two sums for example). Whereas with functional notation it's like working on linear textual representation of abstract syntax tree. Trust me, nobody wants to read, write or transform one by hand
Might I introduce you to our lord and saviour APL? Infix notation and was originally created to be exactly that, a better math notation.
https://aplwiki.com/wiki/Comparison_with_traditional_mathema...
APL »» Linear A (Well almost!)
;-)
The notation as it is works very well. It looks unfamiliar to you because you aren't familiar with it.
> People just want to know why it's x and not something else or how a letter can have value.
The way I was taught it and the way that worked now for my now 3 year old is just to say pirates buried a number under the X, and that we need to guess what they buried. If the concept of a number being hidden is a barrier to understanding for anyone they have seriously bad teachers.
> nobody is really teaching the concept of a symbol in a math class.
This was what? 5th grade?
What kind of crap teachers never taught that
> What kind of crap teachers never taught that
It's rarely the fault of the teachers.
The problem is, in many MANY MANY schools, teachers are more like social workers that have to compensate for utter horrifics outside of school. You got a ton of children so poor they didn't have breakfast which means their first (and all too often: only) meal will be the school-provided lunch (Covid showed that - a bunch of schools were open at least for lunches). You got children that are literally homeless and living with their parents in some car on a Walmart parking lot. You got children whose parents are in and out of jail. You got children living with their siblings in way too small, pest and mold ridden "apartments". You got children whose parents don't have money to pay for basic school supplies. You got children who are dealing with mental, physical and sexual abuse. You got children where the parents are constantly on drugs or seeking for drugs. You got children with a drug dependency on their own - if they're lucky it's just tobacco or weed, if not it's opioids. You got children with parents or siblings with serious mental or physical health issues. Or you got children with their own mental and physical health issues, or if you want it worse, children with these issues but without access to any kind of treatment. You got children that are being weaponized in nasty divorces. You got children that are being weaponized by street gangs. You got children committing crimes from petty theft to dealing drugs just to survive. You got children that have to literally work (and states like FL pushing to have more working children). You got children having their own children already (either from sexual abuse, from under-education about their own bodies, or intentionally because they fell for some stupid challenge/dare). You got children dealing with bullying, you got some who actually are bullies because they have no other way of dealing with their emotions or getting lunch money. You got children with parents with about zero interest in them. You got children who worry that they'll come home and find out their parents got snatched and disappeared by ICE. You got children who worry that ICE will storm their classroom and deport them. You got children who worry they might not survive the school day because someone will shoot at them. You got children who are constantly on the move because their parents' employment/deployment requires absolute mobility. You got children who are LGBT and have to deal with ever increasing hate against them (and LGBT youth already had significantly higher suicide rates than before the GQP made it a culture war issue).
The US doesn't have any kind of system to help these children but schools and libraries, both are horribly underfunded (there's some school districts where teachers gotta take up second jobs because the government can only afford paying them for 4 days a week), and all too often teachers have to pay with their own money for students' school supplies.
And on top of dealing with these kind of nightmares, they actually have to try and teach these children something - even if the children in question aren't anywhere near a headspace where they can actually learn.
I taught at a nice middle-class school, so most of the problems you mention were not relevant there. And yet, it seemed like half of the kids' families were either recently divorced or in the process of divorce. I couldn't really blame those kids for not paying attention to school. And this seemed like the best case, so probably at most places it gets much worse.
Education has a problem with scaling, especially at the elementary level. Sometimes people figure out a nice solution, but when you tell them "great, and now do this in every village" the problem becomes obvious. But there are kids in that village, too, and you want them to know reading and math and hopefully also something more.
> Education has a problem with scaling, especially at the elementary level.
Not if you actually provide the money. Europe gets this down decently well - although I'll admit, in rural areas in Germany we got some serious consolidation issues thanks to urban flight.
But at least our teachers are well paid government jobs and the job is decently attractive.
Scaling is not just about money. It's also about teachers. You can have hundreds of great teachers, but if the entire educational system requires tens of thousands of teachers, you will end up with many mediocre ones, because you simply don't have tens of thousands of great ones.
There's plenty of money thrown at schools in the US, but the issue is that the students that live in poor socioeconomic conditions tend to not do well. The "simple answer" that addresses the root cause would make individuals not subject to poverty and whatnot. But throwing money at institutions is already on the ropes in the US, let alone throwing money at the "undeserving".
(Yes, this is a political opinion. No, do not blame me for that. Politics does not come wrapped up neatly with a bow tie in a box. If you want to debate the veracity of my claim, go do that instead.)
> If you want to debate the veracity of my claim, go do that instead.
I'd do no such thing because you are completely correct - the only thing I'd add is that poverty, while being very dominant, isn't the only issue that desperately needs to be fixed.
One answer: sometimes you need a name, especially because there’s more than one of them. Suppose you’re looking for one digit numbers like this:
Now try saying the answer: “7 and 3”. This gets vague quite quickly —- which blank is 7 and which is 3?Reminds me of how the Σ symbol in math is just a for-loop.
thank Descartes
I thank, therefore I am...
I’ve always found that an indictment of math education — and spent many, many hours discussing it.
When teaching addition, workbooks commonly use a box, eg, “[ ] + 2 = 5” — and first graders have no conceptual problem with this. Somehow, we lose people by the time we’re trying to formalize the same concept in algebra. There’s been many times I’ve written a box around letters in a problem and asked students “what’s in the box labeled x?”
Pedagogy is hard.
Go from "[ ] + 2 = 5" to writing it "box + 2 = 5--what is box?". Then "b + 2 = 5--what is b?" then "x + 2 = 5--what is x?".
I agree. I think the actual problem is that the student is trying to comprehend what it means for anything to have mathematical value other than explicit numbers.
Numbers and letters are taught together, but not as symbols. Letters are taught with sounds and numbers are taught with counting. The notion of a symbol isn't really emphasized much.
I would explain it more like after
[ ] + 2 = 5
what happens if you need more than one box for a complicated problem? Teach the idea that saying box #3 is equivalent to assigning an arbitrary letter for whatever reason you want, but that people more familiar with math prefer letters because they stand in for words that describe what the number is for. You might want to use 'c' for the number of cats you're trying to figure out.
In a room of five animals two are dogs. How many cats?
a = 5, c = ?, d = 2
a = c + d
so... 5 = c + 2
what is c?
Light bulb goes off: "You can do that?" Yes, you can do whatever you want and it's not all about carrying the one or whatever other rote teaching they've been given. They can get creative and be engaged, and then you let them know that actually there are some conventions people like to use for what they're trying to do. They might even believe they've invented a new idea. At least they're having fun.
I agree with you.
To me, a lot of pre-college math education could be summarized as "In this class I will show you a bunch of abstract problems, a bunch of ways to solve them, and I will test if you have learned them." Learning in these classes is often limited to memorizing a sequence of steps.
That's why I would frequently ask "You can do that?" myself when talking to those whom I considered mathematically gifted (math olympiad winners and such). I think they realized that as a problem-solving tool math could be used creatively. I saw it as a largely useless hammer that to work had to be held in a very specific way.
I remember connecting sets in, I think, Pascal to what I had learned in school and realizing that all that math was perhaps not as useless as I had thought : - )
You skipped a step. One of the problems is more obvious with a different operator we learn when in the "box" stage:
> Go from "[ ] x 2 = 10" to writing it "box x 2 = 10--what is box?". Then "b x 2 = 10--what is b?" then "x x 2 = 10--what is x?".
From memory, we didn't switch from "x" to dot for multiplication until at the exact same time we started using symbols. If we'd done it earlier (or even right from the start) it might not have been as much of a problem.
Basically, don't teach the new concept and the new syntax both at the same time. New things should be introduced one by one.
That is what math books already do.
Some of them do it better than others.
back when we was new in programming it was similarly difficult to grok
X = X + 1
once we got it, it was a like new world!
most likely this very unfortunate misnomer started with fortran, where it was deemed lucrative to point out "how much programs look like mathematic formulas!".
not only is this overloading a symbol (equality) with a completely different meaning (assignment), it is also a poor choice typographically, as it represents a directional operation with a directionless symbol.
using an arrow for assignment is much better.
it's also worth pointing out that unlike most others, logic programming languages (e.g. prolog) have actual variables, not references to mutable or immutable memory cells.
arrow for assignment is cool, but the backspace key is the only closest arrow-like key on the keyboard but it has a different purpose. plus the arrow key should be laid out such that u dont have to press a SHIFT/CTRL/ALT to produce it.
for this reason, i felt C a breath of fresh air cos u could just assign using = instead of what we was doing in pascal which was the horrible := where u had to press SHIFT for the :
things like this matter.
Right. If we went more in the direction of APL, we would have had way more symbols.
https://upload.wikimedia.org/wikipedia/commons/9/94/APL-keyb...
There is a game called dragonbox algebra which I'm currently working through with my son and is an absolutely fantastic approach to this problem. Sadly its now part of a horrendous subscription service and is hard to access. I find it really sad that we've had computers for decades and there are so few good maths games like this.
My kids all lived dragonbox games; the algebra and geometry one
edit: loved*
As we are sharing anecdotes:
One of my school math teacher had the same approach in another way: We were expected to use greek letters, not latin ones.
Same reasoning: It showed us kiddos that the letter was insignificant compared to the concept expressed by the letter.
So my take would be: Your friend taught the students for the first time what they were actually doing while handling equations with "a letter in it". That is no problem of algebra in itself. It just means their previous teachers sucked.
I saw a textbook that used a picture of a box in the equation. The number is hidden in the box, and you are supposed to figure out which number it is.
I got my daughter (just turned 6) this little hand held math game for her birthday: https://www.amazon.com/your-orders/pop?ref=ppx_yo2dv_mob_b_p...
She loves it. It uses a ‘?’ for basic algebra style problems and after a few days of playing (if/when she wants to, we don’t make her play it), she was already much better and faster at those problems. It made me think that schools should be giving kids games like these.
Is this the game? You linked to your order history.
https://www.amazon.com/Educational-Insights-Math-Electronic-...
Oops, yes that’s the one.
There are two sides to this. The system or method might be bad but also a determined person can go all the way and perform at a decent level if they put in enough time.
Even if the system was better the person still has to be able to motivate themselves and put in the time.
I tell my kid that math is a language. You learn to speak it, just like you learn to speak any other language, slowly, by listening, understanding, speaking, intuitively recognizing patterns, rules and exceptions. When you start to become fluent you translate problems into math and solve them. At school they keep trying to make them memorize useful phrases, like a tourist that goes to Paris and learns how to say "where's the bathroom", "hello", "would you like to sleep with me", "thank you", "goodbye", etc.
> and learns how to say "where's the bathroom", "hello", "would you like to sleep with me", "thank you", "goodbye"
Quite a story condensed into those five phrases.
https://en.wikipedia.org/wiki/Lady_Marmalade
For sale, condom, never worn
> math is a language
I think there are some differences
If you are a physicist or an economist, you may be using mathematics as a language in the sense that you are using a mathematical description to convey an understanding of the natural world or the economy to your colleagues. But if you are a mathematician, you are interested in the mathematical objects for their own sake.
There is also a difference between the purpose of learning language and learning math. The goal of learning language is (often) to be fluent in it. In other words, the goal is to reach a level of proficiency which would allow you to not have to think about language and focus on the content of the conversation instead. On the other hand, the goal of learning mathematics is usually to be able to solve mathematical problems. Being able to do math without "thinking about it" is not usually a requirement.
"At school they keep trying to make them memorize useful phrases, like a tourist that goes to Paris…."
Like learning dozens of trig identities without any explanation about why one would need them. As I've mentioned elsewhere learning math for the sake of it isn't enough. For most of us math has to have relevance, and for that we have to link it to things in the real world.
We can't even figure out that there are bottom up vs top down learners.
Instead we will just continue to slog along with the same poor system. Math wise, completely at the expense of the top down learners.
Right, you'd think by now we could do a little better.
I'm damed sure I'd be much worse at math if I'd not been pushed in a formal environment such as a school classroom.
I liked math—especially calculus as it made sense to me—but parts became a drudgery when I could see no reason for studying them.
Right, there's always the kid in class who excels at math like a mini Euler and gets bored because the rest can't keep up but the majority of us aren't like that—doing Bessel functions and Fourier stuff as abstract mathematics without any seeming purpose can seem pointless and our only interest in them was to pass exams. (Teaching may be better these days but my textbooks never discussed the value of learning these aspects of mathematics.)
Later whilst studying elec eng/electronics it became very obvious to me how important these aspects of mathematics were. If I'd been given some practical examples of why this math was useful then I'd have been much more enthusiastic.
Same goes for the history of mathematics, I'm old enough to have had a small textbook full of log and trig tables yet if someone had asked me at highschool who John Napier was I wouldn't have had a clue. In hindsight, that was terrible.
Mathematics is often taught as if the student was going to become a mathematician à la Hardy or Ramanujan and I'm firmly of the belief this is not the best approach for the average student let alone those with few math skills.
Mathematics ought to be taught with the real world in mind for ease of understanding. For example, it's dead easy to represent AC power as a sine wave and from there use that mathematical fact to solve power problems. (Perhaps maths and physics texts should be written in tandem and synced to show relevance.)
Teachers need to take time to explain that math isn't just abstract concepts but that it's very relevant to everyday life and that tying up mathematical functions to things in the real world is actually interesting and enjoyable.
> (Perhaps maths and physics texts should be written in tandem and synced to show relevance.)
I agree with most of what you wrote, but this part is tricky. Yes, it would be nice to have math and physics textbooks synced. Maybe other subjects, too.
But writing a textbook is a lot of work; it can take years. How do we get two textbooks synced, if they are written by different people? One writes their book first, then the other has to match it? What if the other disagrees with how the first book was organized? They both write together? Now there is a risk that one does a good job, another does a bad job, and the good textbook is connected to the bad one.
Or maybe write the common outline first, and then each author is trying to follow it independently? Plus, there could be multiple versions of each book, following the same outline, so each math textbook can be connected with each physics textbook based on the same outline. Here the problem is that people often disagree on the outline.
Also, not sure how important is this part, having things in sync could slow down the improvement in the future. For example, imagine that we figure out a better way to teach something in physics. But now everyone is used to having math and physics textbooks synced, so the new physics books would be rejected, until someone rewrites the math books too.
Compare learning math to learning to bicycle. There is some some sweat and struggle that needs to be put in, before one "gets it". After this it can become enjoyable. I encouraged my daughter with practice exercises from a young age, but tried to avoid making it a drudge. She built up confidence and did well with it. She is also very hands on creative. She decided to study engineering and is working towards her PhD.
Those aren't nearly comparable. Riding a bike is one simple skill and as long as you're not racing that's enough for most people. Meanwhile learning maths is a years-long effort at best. I learned how to ride a bike within an hour by myself when I finally had a good reason to learn it. I can't say the same about maths.
Bike is fabulous self-correcting vehicle in most operation conditions. The trick really is just to learn to trust it when it is moving. And then what to do when it stops.
Math is layers upon layers upon layers. And then it also branches. Never really had willpower to learn it myself alone.
It does depend on what one defines as "riding a bicycle." At a moderate pace from point A to point B, or simply a lap around the neighborhood is one thing. Technical single tracks, grueling climbs, steep and slippery downhills, racing, maintenance and tuning, trials, jumps, drafting...
Math is just splitting the bill with your friends, seeing if you have enough cash for a hotdog AND a coke, or counting how many months of savings in order to buy that 5000$ bicycle.
Learning math is equivalent to learning to cycling if you had to learn cycling from scratch with every bicycle.
20" competition trials bike, mulleted DH racing machine, full-squish slope-style dirtjumps, Japanese keirin, multi-week bikepacking, ITT, freeride.... Obviously there is some overlap.
Math, for most people, is the same a bicycles, for most people. With a handful of simple concepts, you can get by daily life.
About a year ago I came across the concept of ‘math circles’, here on HN. It was this longish but very interesting article: https://www.thepsmiths.com/p/review-math-from-three-to-seven...
The key element here is nurturing curiosity. Since then i and my 10yr old have been sitting through a virtual math circle led by Aylean McDonald on parallel.org.uk an organization run by Simon Singh
Forcing is kind of hopeless. So is logic, and reasoning.
How children learn (they can't rely on a fully formed prefrontal cortex like adults) is very different than how adults learn (no fully developed prefrontal cortex until 25-26), learning about this can help a lot.
Learning more about the Reggio Emelia approach might help parents curious about this, it has been quite surprising how much is possible naturally. One of the best things to do is to relentlessly read to and with your kids.
Showing kids the math in every day things, especially things they already love is a helpful way of making it approachable, or at least aware.
Also, linking a topic to their interest's radar, encouraging curiosity, play in general, and letting them potentially discover it can go a long away.
When they've got something they want, teaching math and savings is a great thing. Understanding life is a lot harder without knowing a basic bit of math, and can be made a bit easier when doing it younger.
I had a math teacher that once made it clear, some stuff can just click, others is just about doing a lot of examples to learn the patterns. Doing math is very different than being creative with being comfortable to find it.
Today, I'd probably setup a good prompt to find a way for the child to share their mine to discover how they like to learn, and how they might like to learn faster and easier by taking some shortcuts through math directly or on navigating an ontology/taxonomy perspective.
> One of the best things to do is to relentlessly read to and with your kids.
My mom would bring us into the clubhouse in the backyard and read to us, which I found really boring. Ended up not liking books because of it, and I'm pretty sure the same happened to both of my brothers. For years I'd only read the bare minimum required for school.
Years later I happened to see an neat book cover in the impulse-buy section of a store and begged for the book. That one book was what actually got me set on reading, and from then on I'd always have something with me.
She never realized this and still thinks I like reading because she read to us. I can't help but wonder how many of the anecdotes here are also parents not realizing what's actually going through their kids' minds.
When I was 8, I went to the library in our town a lot. My parents went there sometime to return their books. At some point I just stayed there when they would go home. First I was in the children/teenager section and soon in the general library, where I would read about programming and computers. I learned C by age of nine.
The "undeveloped PFC" argument is shallow, unspecific and usually just used to infantilize younger people. It may be useful if the child is under 6 years old, but at the time someone is 17 or older, it becomes essentially useless.
My learning process was always, and still is fueled by curiosity.
As a counterpoint, look at how the Polgar sisters were raised.
Yes, Lazlo and his wife were both education professionals, and spent an inordinate amount of time dedicated to developing the girls. But look how it turned out.
On a different note, I used to hate sport when my parents forced me to play it. I liked screwing around on the computer or playing video games. However, when I found tennis naturally around 12 or 13, I couldn't get enough of it, and vastly improved on my own because I had a lot more fun playing than most of my peers did, who were forced into it by their parents. Most of them don't even play for fun anymore with friends, and I'm in my mid 30s and still play frequently.
I think you might be like me. If I'm forced to do something I won't like it. But it's up to me I can find almost anything fun or interesting.
It's not about forcing your kids to "do math", but to excel at important skills far before the benefits of being good at that skill matter.
The amount of homework/study per day that maximizes math scores on tests is significant, 1+ hours/school day by the time they're in middle school, with it helping even more for those who are starting out poor at math[0]. You'll note the referenced study doesn't even max out progress for any group - meaning most could have studied more and improved more.
I don't know any kids that voluntarily did an hour or more of solely math study per day. I know plenty that were forced, and ended up loving math or other technical fields as adults.
As a parent of young kids, obviously I haven't gone through high school yet - but I don't think many children who reach their potential in math, english, music etc will have no pressure from their parents.
[0]: https://pmc.ncbi.nlm.nih.gov/articles/PMC8025066/
> As a parent of young kids, obviously I haven't gone through high school yet - but I don't think many children who reach their potential in math, english, music etc will have no pressure from their parents.
Well it depends. I had no pressure from my parents to learn about programming but still got really good at it. Could I have gotten even better had I been pressured to "practice"? Perhaps. But then I also wouldn't like it for the reasons I do (I like making stuff, but not solving riddles) and it would feel like the dad sport situation.
I also played the piano for 6 years, starting out because I liked it. My parents didn't suggest it, but a few years in they were pushing me to continue even when I didn't like it anymore. Finished the first level of music school (6 years where I live) and haven't touched it since. Just to clarify, they weren't using any directly abusive tactics to keep me going, but they did put a lot of pressure onto it.
There's a lot of nuance to all of this and I don't completely disagree that we should occasionally pressure our kids to push their limits. What we often fail to acknowledge is that kids easily change their minds after a while. Just because they liked something at a certain point doesn't mean they still do. The easiest way to get a kid to dislike something is to make it a chore. Additionally, I think we need to ask ourselves whether it's more important to us to have a kid that's average scoring but has a (mostly) stress free upbringing, or one that excels but is stressed out by the time they hit high school. Kids absorb stress differently than we (adults) do.
Me being forced to do tons of horrible math by my abusive grandfather at a young age for literally 4+ hours at a time gave me a few things.
1. A true hatred of work, make work, and a strong desire to defend laziness as a concept (note that Bertrand Russel agrees hard with me here!) -https://en.m.wikipedia.org/wiki/In_Praise_of_Idleness_and_Ot...
2. A love of subversives and cheating the system. Basically, the guys writing leetcode cheating software are saints in my book. All subversions of the attempt to turn society into a meritocracy (a term which was originally supposed to be a slur/negative connotation - https://en.m.wikipedia.org/wiki/The_Rise_of_the_Meritocracy) is extremely good.
3. An advanced knowledge of TI basic, so I could cheat hard on every single school assignment I could get away with. AP Chemistry? I’ve got a symbolic stoichometry solver app! Calculus? CAS system in the palm of my hand!
Play stupid games with children, win stupid prizes. Maybe don’t force them to work like little slaves in their early life, and they won’t strike back at your society systems.
Raising kids is hard. Sad. And what do I know about it? Regardless, parents do need to get involved in their children's education. For instance, they should help their children prepare for entry exams into secondary school. This shouldn't take their child 4 hours a day. Maybe 10 minutes on some days, and 1 hour on others.
Your experience sounds awful but surely there is a reasonable middle ground between forcing a kid to do any math and forcing them to do it in 4+ hour sessions.
Maybe it wasn't the math, but the abuse.
I had similar conclusions, but the other way around: absolutely no guidance. Fortunately by the time I programmed and sold the basic ti math exam solvers to by classmates for 2 euros a pop I had everything memorized.
Nothing like cheating the system to know the system
You realize your experience can't be generalized to anybody else except for those who were abused in the same way you were? It also isn't what people in these comments are suggesting should be done.
As someone who just finished school, I’m trying to figure out how to get genuinely interested in mathematics. I’ve never been particularly strong at it, yet I’m planning to enter a university program that demands a high level of math. The problem is, it’s hard to motivate myself to study math for its own sake. For example, I loved learning programming because it’s hands‑on—I can build something and immediately see the results. In everyday life, though, I rarely need more than basic arithmetic or simple sin/cos/tan trigonometry.
How do you develop a lasting interest in math when it doesn’t feel immediately useful?
Make it practical! Graphics programming involves linear algebra. Databases involve relational algebra. Machine learning involves requires calculus. You’ll naturally encounter hands-on tasks with tangible goals that involve learning new math.
One of my undergrad degrees is in math. As you study it, you learn to identify your assumptions (axioms), find or build interesting abstractions, prove properties about them (theorems), and then map all sorts of other things into those abstractions by figuring out that they're really the same thing. It's even more interesting when you start to find things that are different or question things you always took for granted.
Math gives you the ability to leverage the very structure and relationships of pure abstraction. It's quite the super power.
None of the specific things you learn studying math will be nearly as useful as the ability to think mathematically.
N=1 datapoint here. I studied physics in university and before I started I was not aware that physics is basically just math where the results sometimes relate to reality. The pure math courses I took were the most difficult and in the beginning I loathed them, because it felt so unattainable to get any intuition, let alone real proper comprehension for all the concepts they threw at us. For a long time I felt like I was just hanging on by threads and especially if I compared myself to those who had some innate interest in math or generally some really good intuition on the abstract concepts (or even prior knowledge) it was really demotivating. But I also felt like I had no choice but to continue and as time went on the I grew fond of it. And the feeling of being overwhelmed changed - that is to say I still was completely lost every time a new topic was breached and I could not understand even half of the proofs in class - but I did not feel so defeated about it. And I grew to like the feeling of actually completing the work sheets they gave us every week. The process of solving them was often excruciating but if you did the sense of accomplishment is real. I think for most people higher math is really difficult and that is part of why it is interesting. Another aspect I had to accept over time is that even though you can state a mathematical fact or conjecture in just a hand full of symbols or a plain sentence it does not mean that truly understand it, its implications or how you got there can be understood the same way that other prose can be. Sometimes you have to stare at, contemplate and scribble around one equation for days until you understand whats up.
If there was any advice I would give, then it's probably similar advice on how to stop procrastinating on anything that is difficult. Establish a routine first - find a spot that you will only use for studying this (like a spot in a library), start small, divide and conquer, accept that you will not understand most things easily, reward yourself for the small wins along the way, find an accountability partner or someone to study with if that's your thing, make a regular schedule with regular times where this is what you do - consistency is key, even if its just for 5 minutes, stack it onto other habits, see yourself as a scholar of math - it is what you do, lean into the discomfort, as enduring that is a valuable skill in itself.
Don't study it for usefulness, study it for beauty. Look for amazing insights.
Yes, you need some practical math as well. I did engineering, there's a lot of inelegant stuff there.
But that stuff actually tends to be right next to some very interesting things.
Here are three things you can find out.
First, there's more than one kind of infinity. You can't make a map from natural numbers like 1, 2, 3 etc to real numbers like e, 0.632268, sqrt(2) etc. Look for Cantor diagonalization.
Second, a random walk like a heads vs tails comes back to zero almost certainly. It also does so in two dimensions, like walking randomly in Manhattan. In three dimensions, it does not, and so for higher dimensions. Look for Polya.
Third. There is a way for you and me to communicate secretly, despite everyone in HN being able to see our entire exchange. Look for Diffie Helmann.
These days, there's a whole industry of people doing math videos with interesting stuff.
Find math that interests you!
I didn't particularly find (at the time) calculus, multivariable calculus, physics, etc. interesting as I didn't find the applications interesting at the time. I find these subjects representative of what you traditionally learn at school.
When I entered uni I discovered my passion for discrete math, algebra (groups, rings, fields, etc.), number theory, cryptography, theory of computation, etc. as they have a lot of application in CS.
That's really what did it for me - and also I had great uni lecturers. I wish they would have taught the subjects I like in highschool - the difficulty level is about the same.
It's easier to appreciate math when you are disinterested in the results or applications, because the nature of academic topics near the core grouping of math/philosophy/empiricism is that they are discovered with a lot of meandering at first, and then sometime down the line they become repurposed into a direct application that can be learned by rote. School tends to instruct in some of the most directly applicable stuff first - the "three R"s" plus some civics and training aligned with national goals. And that means that school predominantly teaches associations between math and rote methods, to the disgruntlement of many mathematicians. The "meandering" part is left to self-selected professionals, so it doesn't get explored to much depth.
So I think a good motive for math study is really in games and puzzles, where the questions posed aren't about win/lose or right/wrong, but about exploring the scenario further and clarifying the constraints or finding an interesting new framing. Martin Gardner wrote a long-running column and a few books in this vein which are still highly regarded decades later.
> For example, I loved learning programming because it’s hands‑on—I can build something and immediately see the results. In everyday life, though, I rarely need more than basic arithmetic or simple sin/cos/tan trigonometry.
Consider doing something that actually needs it. You like computer programming - consider making a game engine. It might be easier to learn when you can actually see that it is useful.
Keep in mind though that math is a lot of things. People obsess over calculus but that is just one type. Math is just as much the different types of symmetry in wall paper patterns as it is finding the derrivative. Don't be afraid to try different areas. If you dont know where to start, consider picking up "A Concise Introduction to Pure Mathematics" by liebeck which introduces a bunch of different math concepts and see if any feel more interesting to you.
I'm going to share my anecdote, because it may help, but everyone is different and your mileage may vary.
I'm a MechE by classical training (professionally I actually work doing software/network stuff, don't ask, DNS (screams internally)), so here's where it stood out for me:
https://en.wikipedia.org/wiki/Hydraulic_analogy
Internalize what this simple example represents, think about why that's mathematically interesting, and start looking for where it applies elsewhere. You too could be roped into doing systems engineering at scales you didn't think people haven't already figured out.
University is not a good place for learning mathematics as most of your math instructors there will be very good at math and very bad at teaching people that are not already very good at math.
Sorry, no. Universities are great places to learn math. You’re misrepresenting the genuine passion for teaching that many university instructors have.
Sorry, no.
For whatever reason, many University programs use high level math classes as a filter to weed out 1st year students from that program. If university instructors had a genuine passion, and ability, for teaching high level math then they wouldn't accept that as an outcome.
Sorry no.
You are misrepresenting what's happening. Other departments use beginning math classes as a way of weeding out students they feel won't succeed in their fields because they can't pass basic mathematics classes. Most math departments would absolutely love to have more students in them.
The problem is that these students aren't prepared properly by K-12 mathematics courses and math builds upon itself. If you don't have a good grasp of algebra, you just won't succeed at calculus. We're sticking people in the equivalent of Spanish 4 without having learned Spanish 1 properly.
That is unfortunately true; not only in the US, but all around the world. The particulars do depend on the instructor, and many if not most instructors try to be motivational, but the syllabus is perfectly clear: "this is a weed out class". And when it comes to test time, the syllabus wins.
The only thing I disagree with in your comment is about the instructors: they want to be employed, and they have to accept the syllabus and testing standards. It is not about passion and ability to teach (most, especially younger ones, are full of those); it is about meeting the departmental requirements.
Except maybe not calculus. I remember my calc class kind of being terrible because it was a weed out for other majors. Every math class that wasnt required though was great.
If you love programming, there's quite a lot of programming where math is vital. Graphics, optimisation problems, cryptography, neural networks, figuring out if a hash works, projecting if an algorithm will scale...
The tricky bit is often that you need to learn some of the math before you can see how it's useful, but if you need stronger motivation, you might try diving into a slightly math heavy programming problem and learn the math as you go
Probability/Statistics is a good excuse to learn mathematics, because paying a little attention one finds lots of day-to-day situations where is possible to apply it. For example, see the secretary problem[1].
[1] https://en.m.wikipedia.org/wiki/Secretary_problem
I wish I couldve excluded everything past basic algebra and hopped right to statistics at a young age - I *loved* everything about the practicality of it, how it explained tangible relationships and illuminated the world. Algebra and calculus were so un-engaging I had those teachers calling me everything but a stupid child.
Except you can't really understand statistics without calculus.
*statistical theory notice I had a heavy emphasis on my love of practicality…which theory, to me, is not.
I feel like a lot of platitudes are being said here.
If anyone had a guaranteed way to make people enjoy math, we'd already be applying that method.
Just read ahead to figure out what you'll need to learn, and do some advance reading. Anything thag make the courses easier will tend to make them more fun.
Perhaps think of them as solving logical puzzles. It's fun. Even though not always related to everyday tasks.
For me, it began many years ago when reading about Hilbert's hotel paradox. Turns out our laymen's understanding about infinity isn't as really refined.
I write mobile apps for living and indeed these stuffs are irrelevant for my work.
Haigh's Mathematics in Everyday Life [0] provides modern examples.
[0] https://plus.maths.org/content/john-haigh
as someone who loved maths first but then do programming for a living, it's because solving puzzles is fun. I get the same dopamine hit whether it's a math problem, a coding task, or a video game level. but I think forcing yourself to like something is not the correct approach; you either like it naturally or you tolerate it for some other goals
https://betterexplained.com might prove helpul?
Get a good teacher. They make it fun, or interesting.
Have you ever watched a video of a highly skilled tetris player? Where they fill the screen most of the way to the top and then suddenly they just combo the whole thing down and everything wraps up cleanly, and then they start fresh.
The feeling of "oh yeah, that was nice watching that mess turn into something clean and squared away" is where I get a lot of my joy from math.
But also, there are uses to math that you might be able to play with through every day, but you've never thought of those scenarios in a mathematical way.
I was walking today, and on the street there is a right angle turn. The inner portion of the turn is just a square right angle, but the outside of the turn is a radius. I started wondering to myself, if I want to be on the outside of the turn going into and exiting the turn, what would be different ways I could walk this, and what would the distance differences be.
Crossing directly across, to the inner corner and crossing directly across to the outer side again, would be 2w (for the width of the road w). Following the edge of the radius would (assuming perfectly circular), be 1/4 of a circle, so 1/42piw = 1/2 pi * w. The shortest route is a straight line, which would make a right triangle, so w^2 + w^2 = c^2, 2w^2 = c^2, sqrt(2) w = c
So crossing twice is 2w, following the edge is 1/2piw, and shortest path is sqrt(2)*w. Not super applicable, and I didn't need to do math to figure it out, but I was walking and bored, so I found joy in it. The fact that they all boil down to having w as a factor means I could figure out a nice ratio between all of them. And then I needed to mentally figure out what 1/2 pi was. 3.14/2 = 1.57... And I know that sqrt(2) is roughly 1.41 ish.
So now I know that crossing twice has a cost of 2, following the edge is 1.57, and direct line is 1.41. Following the edge is vaguely close enough to the ideal path to warrant not walking into the street to optimize the route, 1.57 / 1.41 is about ~110%. Whereas by defintion, a cost of 2 is going to be sqrt(2) times sqrt(2), so ~141% more than shortest path.
A few things to note here. First off, I'm aware that not everyone finds the same joy in doing simple mental math and thinking about problems mathematically even when there is no need to do it, but trying to think of things more minor trivial things mathematically may cause you to at least appreciate it more, which can grow into joy. And second, I wasn't doing any complicated math in my head. I just thought to myself "is it faster to cut to the inside corner and then cut back out... of course not, right?" and I was able to answer that definitively to myself. Did it matter? Was the answer probably obvious anyway? Probably, but I was able to _prove_ that. And I value facts. Finding joy in the simple things lets you build up more of a familiarity and view it more as a problem solving tool than a tedious thing to rote memorize.
A great way to build up math familiarity and see how other people find joy in mathematics would be to watch Numberphile videos on YouTube[0]. It's a bunch of mathematicians sharing things they find interesting about math. Some times are REAL hard to grasp, but some are just very interesting puzzles[1]. The puzzles don't always have clear immediate usefulness, but can often be described as "a mathematician wanted to know an answer, so they did some math to find out and prove something to themself."
Sorry, end of spiel.
tl;dr - find the joy in the simple things and use math as a tool to answer (even simple) questions to help highlight the usefulness.
0: https://www.youtube.com/channel/UCoxcjq-8xIDTYp3uz647V5A 1: https://youtu.be/ONdgXYEBihA
> Kids are born explorers. They naturally want to discover new things, including math.
That's true only until their senses are not shut off and attention is not fixated on screens. Exploration happens only when you have unused attention, sensory capabilities and need for a bit of hard work and risk-taking. Curiosity is less of a biological feature. It is a product of the need and the available resources (senses etc). All of these are missing now.
There is no need or motivation. And there are no available resources (senses, attention). There is no justification for exploration and hard thinking.
When I was having trouble learning multiplication my father made up a payment system. He made flash cards and I got a payment for every one I mastered (I had to get it right some number of times, not just once). I ended up with maybe $25 or $50 which was a lot for a kid in the 1970s.
My mother tried to give me $5 for every book of the Bible I read. I never took her up on it even though I knew about the basically freebies like Jude. I wasn't opposed to it, but it felt like –on the one hand– I didn't want to half-ass it and read a few books –and on the other– I really didn't want to read the entire Bible. So I guess that a completionist attitude prevented me from getting $30!
For elementary school age kids, maybe even middle school, try getting them started with the app "Euclidea".
They won't think of it as math. It's gamified geometric constructions. Starts simple, "how do you bisect an angle" with a compass and a straight edge. It goes to a very high level that will challenge anyone.
I adored this post right up until:
> I have an internal KPI: if in the last three days I haven’t spent at least 30 minutes playing with my kid, there’s something seriously wrong
I think I'm interpreting this ungenerously, because my knee-jerk reaction was to wonder about who is handling the other 12+ waking hours a day.
I read this as remembering to set aside time specifically for play and not just for day-to-day parenting and discipline
Something I've been thinking a lot about is "stealth edutainment" games.
When I was a kid, I remember "edutainment" games that were basically like normal computer games, except every so often a homework problem pops up.
I think that doesn't work super well. Better is a game which has you learning naturally, in order to play the game more effectively. For example, I've been enjoying the computer game Slay the Spire recently, and there is a great deal of mental math which is inherent to the game. If I had a kid, I think I might give them that game as a method to motivate them to learn arithmetic.
30 minutes of play per 3 days is such a brutal reality to acknowledge. One of the most wonderful experiences in all of life so drastically limited by the society we’ve constructed.
> One of the most wonderful experiences in all of life so drastically limited by the society we’ve constructed.
I could understand if someone was forced to work two full-time jobs (as my grandfather was), but I find it much harder to blame ‘society’ when so many of these situations are self-imposed.
It’s possible that I’m jaded from hearing a subset of parents complain about not having enough time with their kids but then get stuck scrolling their phone while kids want to play. I also know some parents who insist on having a spotlessly clean house every day and then complain that there is enough time to spend with their kids.
I’ve gravitated toward peer parents who have similar priorities in life which has indirectly made me happier. Seeing all of the parents in my friend circles prioritize spending time with their kids and being honest with themselves about their priorities has been unexpectedly helpful for my own sanity.
Again, nothing against parents who are really forced to allocate time elsewhere, but I’m tired of seeing self-inflicted problems of prioritization and time management be externalized as blaming society.
In some ways yes, but men have always been the ones to go hunt/farm for long hours and provide for the family, leaving the children home under the care of the mother/village for days or weeks at a time.
I would go so far as to say modern society actually enables us to be more involved in our children’s lives, especially those for whom remote work and home schooling are options.
To clarify, for those who seem not to have RTFA but are downvoting (I can only assume based on perceived sexism since nobody has been brave enough to comment)—-the parent was quoting an article written by a working father, who said his internal KPI was, “If I haven’t spent 30 minutes playing with my kids in the last 3 days something is wrong.”
ChatGPT makes it so easy to build a lesson/workbook for something your kid is interested in. I've used it to build workbooks on special relativity, tsolkovsky's rocket equation (including euler integration to build a scratch program), triangulation, logic gates, probabilities of simple dice games, etc. My pro-tip is to tell the LLM to format the document in LaTeX, so you get beautiful math typesetting.
You don't even have to get through the workbook. Get to a part that they need to understand better and make a detailed workbook on that part (for example, triangulation -> solving a system of linear equations).
Where can one learn more about this? I want to get some activities for my kids this summer…
Me too.
I guess these workbooks usually come in two different "shapes" - one, a guided workbook with a high-level goal that combines several concepts, and another would be a practice worksheet where we do a bunch of exercise of the same algorithm (say, long division, calculating summations, or matrix multiplication) over and over. For the "workbook" pattern, we first discuss with the LLM the final goal (e.g. a scratch program that can calculate a rocket's position using the rocket equation). Then we flesh out the steps towards the goal - is it reasonable to add the math for air resistance? air resistance that decreases with altitude? gravity turn? how do we integrate the velocity and position for each frame? How can we relate the integration by step size to the underlying integral, by showing that the result gets more precise (but slower to calculate) the smaller your delta-t is? Then, produce a Scratch code sample that implements the velocity and position calculation. Of course, there are things subtly wrong with the code sample (usually, if the math formulas are well-known, they're correct), which requires debugging - just another type of problem-solving.
The second shape, worksheets, is a lot more straightforward. Just define the type of problem you want to practice and have chatgpt make a bunch of problems. Then switch to one of the newer reasoning models and have it work the problems, and refine to get rid of any bogey problems (for example, for polynomial exercise, you could tell it to make sure the roots are integers)
The worksheets are more "hands off" - I run them through the algorithm once and check their work once or twice and then let them do the rest. The important thing is that the worksheets are connected to their high-level goal, and they understand that in order to solve the big, hairy problem that they're interested in, they need to build up certain specific skills.
Usually the worksheet goal is a pretty substantial conceptual stretch for my kids so they need to go through a series of fundamental worksheets. But the great thing about the LLM is, you can just tell it you're having a problem understanding some concept and to help build the scaffolding by listing all of the required skills to understand a concept, and picking the ones that needs improvement the most and practicing them.
My approach draws a little from "The MathAcademy Way" - https://www.justinmath.com/files/the-math-academy-way.pdf but instead of building fundamentals evenly in all topics before advancing (like expanding a sphere), we look only at the scaffolding required to support some higher-level goal - it's sort of like the masters/PhD process but guided through existing human knowledge: https://www.openculture.com/2017/06/the-illustrated-guide-to... . As a side note, I think it's really fun to include the history (mathematicians who contributed to the ideas) as well as the notation (using the greek letters, explaining why it's common to use them). When the kids notice the names like Pythagoras, Newton, and Euler reappearing frequently, and get a sense of the time scale these discoveries happened on, they treat the current state - and their ability to go learn thousands of years of math in months - with more reverence.
Thanks.
Maybe find an application of the subject that they might find interesting. I suppose if you can't find anything that interests them, then it's much harder to teach it.
For instance, perspective drawing might provide a nice application of 3D projective space, its subspaces, and perspectivities between those subspaces. Some of the theory of conic sections might be relevant too.
Computer graphics provides a nice application of coordinate geometry. This covers elementary algebra, Pythagoras's theorem, etc.
Even eating pizza can provide an application of differential geometry.
I tell my kids they can have letter cookies if they pick a word that starts with the letter, and can have 5 treats if they ask for 4 but know what "plus one means" or can have 4 if they recite "2 plus 2 equals ... ".
They're 3, so I don't expect that to scale, but I'm hoping it's normal reward-for-knowledge by the time we get report cards.
Something that might work for getting your kids interested in modular arithmetic: The Chicken McNugget Theorem.
I'm not great at maths, my daughters good though, I think her binge watching number blocks when small helped a lot - felt my own arithmetic getting a bit better watching it, the songs were very catchy.
Something we don't pay enough attention to is that while calculators have solved everyday math to the point we downplay it as a required skill, people are not pulling out their calculator at the grocery store to make better purchase decisions, even though we all have one in our pocket now.
So we handwave the importance of being able to do everyday math in our heads, while also not taking advantage of the tool that's a substitute for it. We're less educated but also less effective than we would be if we'd never invented automated calculation and were forced to be sharp about it.
Is there a name for this phenomenon?
And what's it going to look like a decade after AI has caused people to stop using their brain for general thinking like it's stopped them from doing math?
(I'm sure you, the reader, are very good at math and are an exception to this still-apt generalization.)
But the reality is that's usually almost a false trade - I'm not buying one item in the grocery store I'm buying easily a dozen or more. The best way to do this would be toss the online inventory into a solver to calculate "best value" for me, but in reality it would be a waste of time because if they're out of something, or the quality looks suspect, then that blows that calculation completely. And then am I going to do this for every single item, where every minute in the store is multiplying through the rest of my day? How much is the time shopping trading off against extremely sparse leisure time?
And then there's intangibles - something being slightly cheaper doesn't necessarily mean I'm making a good trade off by buying it for my overall quality of life.
In Australia at least this whole problem was perfectly adequately solved by mandating bulk price labeling on all items in the supermarket. Products in comparable categories have per volume/weight prices listed alongside item prices.
> In Australia at least this whole problem was perfectly adequately solved by mandating bulk price labeling on all items in the supermarket. Products in comparable categories have per volume/weight prices listed alongside item prices.
Same in Europe. Mandatory labeling per volume/weight, pre-discount, after-VAT in addition to the discounted item prices. Then you glance at the shelves and make up your mind.
Learning to get to a best price per unit is a pretty useful skill that could make a lot of difference for a lot of future adults, just like financial literacy.
Some things aren't optional, and if they are seen as such, it's going to force the child to learn later in life what they couldn't earlier on.
I think most people don't care about optimizing an extra $10 out of their weekly grocery run.
Probably a better example is figuring out the cost of a loan. Just multiply the amortized monthly payment by the term and compare that to the loan amount. If the difference makes you balk, then go ahead and walk.
How many people even realize that loan interest is a significant cost and would bother to do that? Or know how to do that? Most people just try to minimize monthly payments to something they can bear and sign the paperwork.
> I think most people don't care about optimizing an extra $10 out of their weekly grocery run
I remember when this kind of "optimization" was done regularly by a great many shoppers on budgets. Back in the day some stores even used to put calculators on the shopping carts.
People used to know how to budget. Apparently the average American is affluent enough to not need to be able to do this any more. I worry that the atrophy of these kinds of practical skills will cause much pain for a great many people at some point down the road.
I worry too. American consumer credit card debt sounds like it's rising pretty quickly, and many people I talk to have a lack of free will and carry a sense of unfairness in the system they live in.
However, people can also adapt pretty quickly.
Those grocery shopping "optimization" skills are making a big come back (and have been since Covid). There are plenty of YouTube and TikTok videos popularizing how to get more out of their grocery hauls.
Lots of people are also learning how to budget, how to invest, etc. and sharing their excitement about it too. For some folks, they finally learn this stuff in their 40s and 50s, but there are also a lot of young adults learning these skills thanks to the Internet.
So I also have hope.
I just don't think the lack of basic math and budgeting skills displayed by average consumers are a problem so much as a symptom.
Oddly enough I found a great 'trick' for this. Kids hate doing math tests, but turn it into a competition and game and suddenly they love it. Print out a bunch of remedial problems, perhaps 50. And then give them 1 or 2 minutes to do as many as they can. It's just a contest to improve against your own scores over time, with prizes for the kids who score the highest after a month or whatever.
It's still literally just a math test/quiz, but somehow the context changes everything and even kids who really aren't into math were loving it, and also improving rapidly because the repetition helps instill intuition.
There’s a fine line between chores and games.
Imagine having to move a round thing around some other people to get that thing into a square frame. Then, imagine that you can only use your feet!
clever!
I imagine the part of a test people dislike is failing, and the consequences from failing. Framing it as a game without those emotional stakes fixes that.
If the teaching environment was set up to encourage learning rather than punish not having learnt yet we might not need these tricks, but that culture is slow to change
My claims are as follows: - most math programs in the US schools are behind where children’s math abilities are - most school math programs do an abysmal job connecting math with real life - you can completely turn off a child to a subject/sport/activity by pushing it too hard -being numerate is a real long term advantage in life
It’s balancing these things that’s hard, if your children are above “pace” math wise, see the value of math in their everyday life, and are on track to be numerate, yes don’t push, otherwise not pushing is the disservice
I think this isn't quite the same thing, never the less: I have dyscalculia on extreme mode (/dyslexia/autism), and I was forced to do math in the 90s in the UK, rote style. I don't know if they didn't know about dyscalculia, didn't care, or whatever, but holy hell I wish I'd never been forced to do that, it's still today a fairly painful memory and I'm in my 40s now. If you're gonna force kids into math, at least make sure they're not unable to process it correctly.
Related to what the article mentions, about playing cards, I tried to get my kids into doing basic arithmetic by playing "scopa"[0] with them.
Turns out, the one who didn't like math didn't like the game either, and the one who did like math liked the game too.
So I'm not totally convinced you can just "trick" kids into liking maths, tho for sure it's a way to get them to exercise.
[0] Scopa: https://en.m.wikipedia.org/wiki/Scopa
Is there any knowledge that is recommended to be forced to kids?
Probably safety behaviors, e.g,, “let’s look both ways before we cross the street, regardless of whether you want to”
If you formulate the warnings just right, you wouldn’t need to “force” it, as kids will be willing to look both sides themselves. They like to be alive.
Forcing is kind of hopeless. So is logic, and reasoning.
How children learn (rely on the prefrontal cortex of their adults) is very different than how adults learn (no fully developed prefrontal cortex until 25-26), learning about this can help a lot.
Learning more about the Reggio Emelia approach might help parents curious about this, it has been quite surprising how much is possible naturally. One of the best things to do is to relentlessly read to and with your kids.
Also, linking a topic to their interest's radar, encouraging curiosity, play in general, and letting them potentially discover it can go a long away.
When they've got something they want, teaching math and savings is a great thing. Understanding life is a lot harder without knowing a basic bit of math, and can be made a bit easier when doing it younger.
I had a math teacher that once made it clear, some stuff can just click, others is just about doing a lot of examples to learn the patterns. Doing math is very different than being creative with being comfortable to find it.
Today, I'd probably setup a good prompt to find a way for the child to share their mine to discover how they like to learn, and how they might like to learn faster and easier by taking some shortcuts through math directly or on navigating an ontology/taxonomy perspective.
Must add i had struggles with mathematics. It can be interesting, but little did i understand as a pupil. Later in life, i discovered it, i became a car mechanic, then it-guy, then non-destructive tester. English is my first and only second language, its enough to lurk here, read books and serve customers on a professional level. I think i dont need french, nobody around me speaks it, i am not interested going to france..at all. All the math i was thaught, was do to the job and that filled my fridge. Its okay to push kids to university so they can use that math knowledge, but who foresees what the kid wants to work? School is not the end of the road, one can always attend courses, getting autodidactic knowledge later in life. Today we dont need 10 architects while having only 1 roof tyler.....
I'm reminded of another HN comment on learning math, more pitched at advanced maths but probably still applicable
>...recommendation is a metaprinciple: enjoy mathematics. Benjamin Finegold said similarly that the secret to chess is to enjoy every move. https://news.ycombinator.com/item?id=42290996
Since then I've watched a few times Ben's beginners chess advice aimed at kids and feel it can apply to other things, math or in my case I'm trying to apply it to trading. It's been quite good. The basic idea, enjoy doing the thing and do it repeatedly so you build pattern recognition https://youtu.be/B5bCfwCyo18
I don't get why people take it so negatively when a parent mandating kids to do/learn things they don't like.
But the entire notion of public education is rested upon mandating that kids wake up and go to school, sit down and learn things they don't necessarily like. I am pretty sure there isnt a single student who loved/found joy in all the subjects all the time.
Yet when a parent does it, there is backlash?
Humans respond to carrot and stick, and so do kids. To excel at anything, requires healthy mix of enjoyment, love, discipline and motivation. Some of these come intrinsically, others extrinsic.
taps the Case Against Algebra II sign
https://harpers.org/archive/2013/09/wrong-answer/
And then your kids and their same generation would be replaced by their peer kids from hard working boys and girls from India and China. Unfortunately curiosity only works with brilliant minds. Normal minds plus curiosity is useless.
I think the advice is good for younger children. The author is using 14+11 as an example. Very engaged parents can have a tendency to overdo it, so it's probably a good reminder.
As kids get older, they need to learn how to struggle and overcome struggles. (I would still caution against "forcing" math.) But yes, you need to start engaging hard work and determination.
Btw, the two are not mutually exclusive. Young children should be praised for struggling at things so they begin learning that skill, too.
> Repetition is key
Even with a "normal" mind. Train consistently to gain excellence!
A lot of people hope there is a magical way of making learning fun. The argument generally goes "young kids love exploring nature, experimenting, etc, so we are all inborn scientists. If only school did not extinguish the fire from us".
A huge problem is that giants of education such as Jean Piaget and Seymour Papert make a strong case for this. Unfortunately they generalized their own experience as kids to all others. They did not understand that they were exceptional cases, and what applies to them does not necessarily apply to 99.999% of the rest of the world.
But their message was so cool, somewhat similar to "we can all love each others", or "world peace", that it was embraced with abandon.
I was fortunate to have a great math educator in college (i.e. a guy who was teaching us, math majors, how to tech moth to kids). He told us bluntly "math is hard".
I think education would progress if one simply accepted this truth "math is hard". Stop the delusion that there is a way to make all math fun.
Still, once you accept that math is hard, you realize that the mission is the same: try to find ways so that learning math is less hard and more fun. But accept that the default state is that math is hard. There is no "royal road" to math. Aristotle was onto something.
And by the way, the fact that "math is hard" is not all bad news. The goal in school is not only to learn math, but also to learn how to work hard. There are kids for whom math feels like swimming for a dolphin. Up to a point. There will inevitably be a point where they will hit the phase of "math is hard". And it's going to come as a rude shock. It's better for this realization to come a bit early in life and a bit less shocking.
Teach kids to do math by have them make mods for their favourite games.
There is no template for how to raise kids. Expose them to as many things as you can, figure out what interests them and feed it. Keep doing this as they grow up because they change as they grow up.
The same can be said of music, art, sports and a zillion other things.
My daughter and loads of kids watched number blocks from around two or three up, I think it made quite a big difference- she's far ahead of where I was now, years later.
I believe that the most important thing I can show my kids is how I pursue the things I enjoy. That I make time for myself and that I handle setbacks and dips in motivation. So that they will know that when you do find something that interests you, that is how you pursue it in the long run. I show them how to not quit.
Everybody is different. Some should be forced to learn and others not. Quit trying to measure fish on a tree climbing test.
Know what, brother? I tell you that studying the humanities in high school is more important than mathematics — mathematics is too sharp an instrument, no good for kids.
Stephan Banach quoted by Steinhaus in Through a reporter’s eyes, Roman Kaluza, 1995
Perhaps make them aware how important it is with examples from nature? https://duckduckgo.com/?t=lm&q=fibonacci+in+nature+examples&...
Kids do not understand the concept of "importance". At least no kid I've met. That part of their brain doesn't work. They'll trade effort for privileges or toys tho, and are little mimicry machines so they follow you if you use it.
yeah, I recoiled when the author of the post says "no bribing" - bribery is one of the most useful tools a parent has. I guess you could call it "incentive" or something, but really, it's quid pro quo.
Honestly it's so close to how the world works I can't believe 1. Avoiding loss of privilege and 2. Gaining new things as reward isn't the top two parenting tips.
But probably zeroth, most important, is modelling good behavior. Kids are mirrors.
You can definitely make things better or worse for kids by choosing the rewards you give them.
My parents would reward me by letting me pick out a book at the book store. I'd be excited the whole week.
I may feel differently about reading it I had been forced to read and rewarded with something else, like junk food.
We are torn but decided to keep books scarce, and scold them a little bit when they sneak books into bed. We know but they are much more likely to get their rebellion out reading now. Which I love.
We went the other way and have plentiful books, constant library trips etc. but have had to regulate sleep by setting a regular lights out time. Executive function and mood really suffers when sleep is insufficient.
I appreciate the idea of harnessing rebellion and I'll think more on how to apply that to my parenting :)
Something occurring in nature doesn’t necessarily make it important to their lives.
I do agree with the overall premise of encouraging children's creativity and the things that they enjoy doing. You don't want math to become a chore.
On the other hand, some things require study and practice to be really good at, and that is "work", and many kids don't want to do the work.
Our boy, who just turned 9, is very good at math (his school's standardized tests put him at 99th percentile in the US for his grade level, though 1) I don't put a lot of stock in those standardized tests, and 2) the US doesn't exactly rank high in math skills, so this is less impressive than it sounds). He's not a genius, but he grasps concepts quickly and fairly intuitively. He's curious about the world, asks lots of questions, and is capable of understanding and retaining many scientific concepts that kids older than him would struggle with. (Example: two days ago, he was asking me about quantum computers and I mentioned that they need to be kept very cold, he asked whether they use oxygen, because oxygen turns to liquid at -173C. I thought he just made that up, but when I checked (I didn't know myself), he was pretty close (the actual number is -183C.) So he has the innate talent to work with.
But despite his gifts, he still needs practice for the math concepts to take root, and without that he makes a fair share of basic mistakes; and he still needs to improve his logic reasoning skills. So he has daily math homework after school (because math instruction in elementary schools in the US is low). We use Singapore Math workbooks (I've tried various apps and online programs, and honestly, paper workbooks are just better--but that's another topic).
He knows he's good at math and wants to continue to excel at it. (Just like a talented basketball player doesn't reach his full potential without working at it, something I repeatedly emphasize to him.) BUT he still struggles every single day to do his homework, because he prefers to play video games, shoot hoops, etc. (loves basketball, football, soccer, but has a lifelong physical disability that will prevent him from ever playing a team sport, to his great chagrin). I have to push him every single day or he would simply not do it. He actually wants to do math, and when we talk about it, he'll confirm that, but when it comes time to actually do it, he just doesn't have the willpower. (I mean, what kid prefers to practice math problems instead of play video games?). Hopefully he'll get the willpower at some point when he's older. But that day has not yet come.
That was a long reply to say: it sometimes does take a lot of pushing.
Have them play a game like math maze 2!
They will force themselves to play... and do math in the process.
Just spent 10 minutes playing it, looks pretty fun!
This article has all the tells of being AI generated with random bolding and constant emdashes.
This is all fun and games until your kid has school assignments with deadlines
In the Netherlands we didn't get homework until 12 and lots of play time. Curious how that stacks up to other places.
I expected way more than a personal opinion coated in some moralization.
Humans are more terrible at teaching math than any other concept. I remember being taught algebra by a teacher that had terrible idiosyncrasies. She would sometimes write numbers and variables differently, and this caused major problems trying to understand how and why the variable was to be written differently due to new context. But she would just go on writing it differently, just because she was weird. For example, she would sometimes write 'x' using two curves that didn't touch ')(' and expected you to continue with the algebra equation as if nothing was strange. My point is that teachers still don't understand how to correctly teach math to students. They reinforce using their old methods that are overall sloppy shorthand in a space where rigor, both visually and conceptually, must be maintained. When young minds are this fresh, you cannot have this slop and idiosyncrasy in your lessons and expect students to become enlightened. So no, forcing them to do some math is not harmful. Poor teaching in a very hard space definitely is harmful.
Every kid is different. We can’t generalize the approach.
Surprised no one here has mentioned Kumon. Hated it but it works
I would agree. Kumon wasn't my son's favorite thing and he eventually decided/asked to stop. But the repetition and discipline of working at it every day had an influence. It didn't manifest until undergraduate but he ended up switching majors to math and is now pursuing a math PhD. Probably not common, but like learning to play the piano, I think it gave him a comfort with the basics and an intuition that allowed him to explore his own interests.
I'm fortunate enough that my daughter has an admirable interest (and talent) for Math since very early age. She even won a medal at a renowned nationwide Math competition when she was in Grade 5... competing in the Grade 10 category.
That kid's name? Alberta Einstein.
The only thing better than telling a lie and people believing it, is telling the truth and no one believing it. Shows that her achievements are truly remarkable
Get a set of dominoes. Make up games with them.
Learning is pain, knowing is pleasure...
Learning can be fun.
math circles are good for this. i’d suggest it if there is one nearby
Another article where someone thinks being a parent means they understand all children. I have 4 kids, and 2 of them definitely would never do math, even basic math, for fun, ever. Their brains lack whatever pathways most people utilize to learn math, so I now have a 15 year old who has to work nearly as hard at arithmetic as she did when she first learned it. No amount of drilling, change of curriculum, buckling down or backing off has had any impact. She has absolutely no interest in math. But the kid reads faster than I do, which is not slow at all.
The only thing I know about kids after having adopted 4 of them is that none of them are alike. The only time when you can really train them to do anything consistently is when they are babies. As a result all 4 have great sleep habits :)
Have you come across https://en.wikipedia.org/wiki/The_Teenage_Liberation_Handboo...
I read it (as a non-child), and a lot of my certainties about what young brains are and are not capable of got joyfully exploded. I'm not linking it to you proscriptively, or with a specific suggestion or riposte in mind whatsoever - you just might be interested in it.
School is very successful at convincing kids (and former kids) of two things: firstly, that the academic subjects they purport to teach are actually delineated by the school textbooks and curricula. And secondly, that the reaction people have to specific subjects within these school structures are the actual unchangeable nature of the person's relationship with the subject.
I hope one day our societies move past these two egregious and immeasurably damaging beliefs.
I haven’t read the book, but we have 100% had the “you don’t have to graduate if you don’t want to” talk with this one haha. She doesn’t want to drop out, but definitely isn’t interested in college. We want to keep that door open for her if we can, so we just remind her that staying in school requires doing some things she doesn’t like.
But yeah, at 15 it gets a little hairy. You have a kid who wants to be an adult, but in a lot of ways they are not prepared to make adult decisions still. Eventually she will have to make them, ready or not. But we have a few years left to help her, so the focus becomes how to best do that.
> School is very successful at convincing kids (and former kids) of two things:
Well, and thirdly, that your worth as a person is determined by your results in graded examinations, and by extension, your salary or some other numerical rating decided by someone else.
Absolutely, I think that's the other huge one. Thanks for chiming in to complete the thought!
Best advice I ever received is: You have to parent the kid you have - not the kid you want
I have 5 and can say that this is the way.
This 100%
I as a child, a teen, and a young adult thought I hated math, I got bad grades and it bored me. I dropped out of school. I later went to college and took remedial algebra twice.
Math in school was purposeless and rigid, a rote procedure to be followed by command because that's what kids have to do.
Now, I have grown older, and my curiosity drove me to learn because I wanted to make things, machines and software and probabilistic strategies. Things that necessitate math. If you can't rotate a vector, your guy walks faster diagonally. If you can't think mathematically and you want to lift a 2 jointed robot arm that weighs several tons, you're going to tip it over, and possibly die in the process. You can do it without trig but you can't do it without thinking about math.
Once I found purpose, I began to appreciate the beauty of the more elegant solutions. I kind of fell in love with math as an adult. Now I watch numberphile with my kids and make complicated machinery and software at work.
I think a lot more people love math than realize it, because they're conflating math itself and what school calls math, which is worksheets and demands, not beauty and creation.
With my kid in elementary school, I can see how math instruction is generally terrible: teachers rarely have any enthusiasm for teaching it. I only had one great math teacher (combining enthusiasm, skill and hard work) and I've been through special math programs (in high school and uni).
Again, it is a question of incentives: someone with enthusiasm for math would likely go with a higher paying job requiring higher level math.
Still, despite the crappy teachers, I was better than most to persevere at it until high school where I had the great teacher.
But this does not scale and we are losing kids to bad teachers: how can we fix this?
Yes. And it's the same when the kids come from the same parents too. We have one kid that's willing to go very deep on math. The only does what can be figured out in 3 seconds or less. Same genetic parents, same school system.
The original concept in the article of exploration is great. Some kids want to explore math, some science, some music, and some Starcraft.
> The only time when you can really train them to do anything consistently is when they are babies.
This is really stupid.
If you can’t recognize a little tongue-in-cheek humor then maybe you’re the stupid one ;)
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I knew some who were bad at math. Asian immigrant test scores on math are ~1/2-1 standard deviation higher than white Americans. That’s noticeable comparing groups of people but still leaves a lot of Asian immigrants who are not good at math.
There is no royal road. If all your kids are biologically yours and you and all your family are good at math and you marry someone from a similar family, you can stack the deck maybe 95/5 in favor or your kid being good at math? But that option is already off the table if you lack that talent. And there are other things you should probably prioritize first!
I don’t personally see how one person’s experience with children other than my own has any connection to my own children. That was the point I was attempting to make, though. Just because you have anecdotes to share doesn’t mean you’ve stumbled upon some universal truth. They can be helpful to share but NOT if used to dismiss other people’s experience.
At some point you have to force them for the sake of homework, just saying.
But yeah, you're better off in math if you can make it make sense on a philosophical level. That I agree with.
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