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.
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)
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.
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.
It takes a long time to get good at some things and those days suck.
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.
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.
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.
Sometimes. I still hate almost all things I'm good at.
same with coding. instantly loved it and choose it as my career. still enjoy it today.
From my modest experience of being a ski/snowboard instructor and trying to raise 3 boys (now 12, 16 and 18).
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.
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.
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...
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.
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.
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.
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.
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.
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.
* 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.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."
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.
Hurting a kid and proper discipline are two separate matters. Good discipline and training doesn't hurt kids (in fact many enjoy them). If you find that your actions are hurting a kid then you are doing things wrong.
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.
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...
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.
Possibly so, wisdom often take years to gel and often only after life events force its notions to the fore.
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.
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.
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.
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/
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"
Doesn't actually matter how good he gets at classical guitar either.
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.
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 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.
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.
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.
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.
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.
If not at a club/activity, why does the child have unrestricted access to screens?
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.
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.
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.
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.
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.
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.
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.
You can do any of those things without learning to read music. Ask me how I know
A valuable life skill if you want to ever have a job or get paid.
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.
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...
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.
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.
Sometimes you have to eat a shit sandwich.
Or you can reach for the sandwich.
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.
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.
Even the smell of tree resin sometimes makes my stomach tighten with anxiety.
And yes practicing will result in them getting better.
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.
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 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 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.
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.
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?
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.
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.
So exactly what I wanted to talk about, when referencing "natural education".
I did not talk about any ethnicity at all.
Or were you simply trying to say, for you the term "savage" is strongly connected to racists and therefore inappropriate to use?
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?
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.
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?
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.
- 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...
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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 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)
Nobody's forcing me to work. I could quit today if I wanted. But I doubt that would be beneficial to my overall health, given I do not have the wealth required to support myself and my family for very long.
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.
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.
> 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?
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.
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.
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.
All that praise for education and yet you've fallen for the tabloid-fueled conspiracy theory that transgender science is a hoax
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.
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.
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.
Also in your opinion at what age should pushing start, and how much pushing per age group?
they used to beat the living shit out of us india when were growing up. is that what you mean?
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.
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.
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.
A friend of mine taught remedial math at UW to incoming freshmen. She would write:
x + 2 = 5
So she started writing:
_ + 2 = 5
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.
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.
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).
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.
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.
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"
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.
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).
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”.
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.
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.
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.
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...
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
Also it should be sum(x+3, x, 1, 4) since you need to encode what the iterator variable is as well.
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)
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.
What I should really do is create myself a cheat sheet of symbols to code...
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
https://aplwiki.com/wiki/Comparison_with_traditional_mathema...
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.
This was what? 5th grade?
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.
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.
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.
(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.)
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.
10•_ + _ = 73
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.
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 : - )
> 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.
X = X + 1
once we got it, it was a like new world!
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.
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.
https://upload.wikimedia.org/wikipedia/commons/9/94/APL-keyb...
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.
https://www.amazon.com/Educational-Insights-Math-Electronic-...
Even if the system was better the person still has to be able to motivate themselves and put in the time.
Quite a story condensed into those five phrases.
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.
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 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.
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.
Math is layers upon layers upon layers. And then it also branches. Never really had willpower to learn it myself alone.
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.
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
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.
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.
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.
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.
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.
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.
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.
Nothing like cheating the system to know the system
How do you develop a lasting interest in math when it doesn’t feel immediately useful?
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.
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.
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.
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.
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 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.
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.
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.
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
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.
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.
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
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.
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 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 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.
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.
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.
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).
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.
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.
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.
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.)
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.
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.
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.
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 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.
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.
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.
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!
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
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
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
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.
>...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
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.
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.
Even with a "normal" mind. Train consistently to gain excellence!
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.
The same can be said of music, art, sports and a zillion other things.
But probably zeroth, most important, is modelling good behavior. Kids are mirrors.
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.
I appreciate the idea of harnessing rebellion and I'll think more on how to apply that to my parenting :)
Stephan Banach quoted by Steinhaus in Through a reporter’s eyes, Roman Kaluza, 1995
They will force themselves to play... and do math in the process.
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.
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.
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.
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.
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.
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?
The original concept in the article of exploration is great. Some kids want to explore math, some science, some music, and some Starcraft.
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!
But yeah, you're better off in math if you can make it make sense on a philosophical level. That I agree with.
