Don't force your kids to do math

The really important thing is to teach kids to find their joy.

At the end of my second year of piano lessons, my teacher took me into her living room, and we listened to Glen Miller records for most of the hour. And then we had a cup of tea, and she told me, "this is the music that I love. I play piano because I love that music, and I want to be able to play it myself. What kind of music do you like?" I didn't really have an answer. So she told me that we should stop doing lessons, but once I found music that I loved, she'd be happy to teach me how to play it.

In my early teens, I discovered Miles Davis. Once I had found my passion, all the hard work became play. I actually ended up learning to play jazz guitar, not piano. Even the heavy lifting was pure joy, because it had purpose and meaning.

I didn't become great at mathematics until I discovered the joy in mathematics (another brilliant teacher handed me a stack of old math contests, and said here, you might find these fun. I placed 4th among 20,000 students).

I didn't learn to write well until I discovered the joy in writings. (An absolutely brilliant English teacher who made us assign ourselves our own grades, but broke his promise in the end by upgrading all my papers to A+'s).

And I gave my kids the room to find their joy as well.

That was exactly my sentiment.

My parents pushed me hard to do piano when I was around 10-12. After a year that went pretty well I was starting to get lazy and put very little work and investment into preparing for the next lesson. They still had me play piano a full year until they eventually gave up and bitterly told me what a waste my resignation felt to them.

20 years later, I got back to playing piano, and I can't thank my parent enough for having me to continue playing in my teenage years. Because it only took me a few month to be able to play pretty advanced piano sheets compared to some of my relatives who are struggling with the basics starting it in their adulthood.

Same for maths. I feel that a lot of people like the author of this blog post are being extremely misdirected thinking math can and should be taught in a fun or amusing manner every time.

Sure, a lot of topics in Maths can be made more digestible by "gameification" to help younglings develop an intuition. But a very big part of Maths actually requires you to sit down and painstakingly crunch down the numbers/equations, memorize and learn when to apply the correct methods to solve some problems. And even though this part can feel fun and engaging after a while, you can't expect children to exhibit such interest right of the bat without having them first struggle with the classics.

Kids don't know better. Your role as a parent is to navigate along the fine line of forcing your kid to get good exposure to the (boring) activities we adults value and letting him enjoy what he enjoys. Only in doing that will your kid open up to the world and grow up into a functional human being.

If the kid isn't enjoying the piano lessons, will forcing them to do it for 20 minutes every day really be beneficial? Sure, they will now be able to do something - something that they absolutely hate... (also, why is it always piano that parents try to force on children?)

Different point of view: do you consider hunting in the wilderness to be difficult?

I do, it requires being still in miserable conditions for a long time, being cold, wet, mosquitos, and then usually still no success, but frustration.

But to my knowledge, no savage kid is in need of being forced to learn it.

"children sense your true passions and naturally want to join in"

And that is my experience as well. But if you stop childrens curiosity out of limited time and patience "Be quite now!" - stop them from helping, because they are not a help in the beginning and you are faster on your own - then of course they won't just start enthusiastically some years later doing with motivation whatever it is, you define as their arbitary target now.

Do you do things because someone force you or beacuse you have self motivation?

I don’t have kids.

The really important part of this is that kids mimic what they see adults they like and respect doing. If their role models spend 6+ hours in front of the television every night, that’s what they’ll do. If their role models are playing music or sport, that’s what they’ll want to do.

My take is Maths, Science and English push. Everything else let them decide what they like. Do parents push kids at every damn subject?

Oh yeah let's turn otherwise fun hobbies into a forced chore, that will surely be great for the kid. Forcing kids to learn to spell when they have learning difficulties (eg dyslexia) doesn't usually go well either it's just causing suffering for the kid.

The semantic meaning of a blank is much better understood to everyone than an arbitrary letter like 'x'.

People just want to know why it's x and not something else or how a letter can have value. They might even think how can 24 + 2 = 5? They just want something to grab onto and nobody is really teaching the concept of a symbol in a math class.

As we are sharing anecdotes:

One of my school math teacher had the same approach in another way: We were expected to use greek letters, not latin ones.

Same reasoning: It showed us kiddos that the letter was insignificant compared to the concept expressed by the letter.

So my take would be: Your friend taught the students for the first time what they were actually doing while handling equations with "a letter in it". That is no problem of algebra in itself. It just means their previous teachers sucked.

There is a game called dragonbox algebra which I'm currently working through with my son and is an absolutely fantastic approach to this problem. Sadly its now part of a horrendous subscription service and is hard to access. I find it really sad that we've had computers for decades and there are so few good maths games like this.

There are two sides to this. The system or method might be bad but also a determined person can go all the way and perform at a decent level if they put in enough time.

Even if the system was better the person still has to be able to motivate themselves and put in the time.

I’ve always found that an indictment of math education — and spent many, many hours discussing it.

When teaching addition, workbooks commonly use a box, eg, “[ ] + 2 = 5” — and first graders have no conceptual problem with this. Somehow, we lose people by the time we’re trying to formalize the same concept in algebra. There’s been many times I’ve written a box around letters in a problem and asked students “what’s in the box labeled x?”

Pedagogy is hard.

> and learns how to say "where's the bathroom", "hello", "would you like to sleep with me", "thank you", "goodbye"

Quite a story condensed into those five phrases.

> math is a language

I think there are some differences

If you are a physicist or an economist, you may be using mathematics as a language in the sense that you are using a mathematical description to convey an understanding of the natural world or the economy to your colleagues. But if you are a mathematician, you are interested in the mathematical objects for their own sake.

There is also a difference between the purpose of learning language and learning math. The goal of learning language is (often) to be fluent in it. In other words, the goal is to reach a level of proficiency which would allow you to not have to think about language and focus on the content of the conversation instead. On the other hand, the goal of learning mathematics is usually to be able to solve mathematical problems. Being able to do math without "thinking about it" is not usually a requirement.

"At school they keep trying to make them memorize useful phrases, like a tourist that goes to Paris…."

Like learning dozens of trig identities without any explanation about why one would need them. As I've mentioned elsewhere learning math for the sake of it isn't enough. For most of us math has to have relevance, and for that we have to link it to things in the real world.

Those aren't nearly comparable. Riding a bike is one simple skill and as long as you're not racing that's enough for most people. Meanwhile learning maths is a years-long effort at best. I learned how to ride a bike within an hour by myself when I finally had a good reason to learn it. I can't say the same about maths.

Learning math is equivalent to learning to cycling if you had to learn cycling from scratch with every bicycle.

Make it practical! Graphics programming involves linear algebra. Databases involve relational algebra. Machine learning involves requires calculus. You’ll naturally encounter hands-on tasks with tangible goals that involve learning new math.

Don't study it for usefulness, study it for beauty. Look for amazing insights.

Yes, you need some practical math as well. I did engineering, there's a lot of inelegant stuff there.

But that stuff actually tends to be right next to some very interesting things.

Here are three things you can find out.

First, there's more than one kind of infinity. You can't make a map from natural numbers like 1, 2, 3 etc to real numbers like e, 0.632268, sqrt(2) etc. Look for Cantor diagonalization.

Second, a random walk like a heads vs tails comes back to zero almost certainly. It also does so in two dimensions, like walking randomly in Manhattan. In three dimensions, it does not, and so for higher dimensions. Look for Polya.

Third. There is a way for you and me to communicate secretly, despite everyone in HN being able to see our entire exchange. Look for Diffie Helmann.

These days, there's a whole industry of people doing math videos with interesting stuff.

It's easier to appreciate math when you are disinterested in the results or applications, because the nature of academic topics near the core grouping of math/philosophy/empiricism is that they are discovered with a lot of meandering at first, and then sometime down the line they become repurposed into a direct application that can be learned by rote. School tends to instruct in some of the most directly applicable stuff first - the "three R"s" plus some civics and training aligned with national goals. And that means that school predominantly teaches associations between math and rote methods, to the disgruntlement of many mathematicians. The "meandering" part is left to self-selected professionals, so it doesn't get explored to much depth.

So I think a good motive for math study is really in games and puzzles, where the questions posed aren't about win/lose or right/wrong, but about exploring the scenario further and clarifying the constraints or finding an interesting new framing. Martin Gardner wrote a long-running column and a few books in this vein which are still highly regarded decades later.

One of my undergrad degrees is in math. As you study it, you learn to identify your assumptions (axioms), find or build interesting abstractions, prove properties about them (theorems), and then map all sorts of other things into those abstractions by figuring out that they're really the same thing. It's even more interesting when you start to find things that are different or question things you always took for granted.

Math gives you the ability to leverage the very structure and relationships of pure abstraction. It's quite the super power.

None of the specific things you learn studying math will be nearly as useful as the ability to think mathematically.

> For example, I loved learning programming because it’s hands‑on—I can build something and immediately see the results. In everyday life, though, I rarely need more than basic arithmetic or simple sin/cos/tan trigonometry.

Consider doing something that actually needs it. You like computer programming - consider making a game engine. It might be easier to learn when you can actually see that it is useful.

Keep in mind though that math is a lot of things. People obsess over calculus but that is just one type. Math is just as much the different types of symmetry in wall paper patterns as it is finding the derrivative. Don't be afraid to try different areas. If you dont know where to start, consider picking up "A Concise Introduction to Pure Mathematics" by liebeck which introduces a bunch of different math concepts and see if any feel more interesting to you.

Find math that interests you!

I didn't particularly find (at the time) calculus, multivariable calculus, physics, etc. interesting as I didn't find the applications interesting at the time. I find these subjects representative of what you traditionally learn at school.

When I entered uni I discovered my passion for discrete math, algebra (groups, rings, fields, etc.), number theory, cryptography, theory of computation, etc. as they have a lot of application in CS.

That's really what did it for me - and also I had great uni lecturers. I wish they would have taught the subjects I like in highschool - the difficulty level is about the same.

N=1 datapoint here. I studied physics in university and before I started I was not aware that physics is basically just math where the results sometimes relate to reality. The pure math courses I took were the most difficult and in the beginning I loathed them, because it felt so unattainable to get any intuition, let alone real proper comprehension for all the concepts they threw at us. For a long time I felt like I was just hanging on by threads and especially if I compared myself to those who had some innate interest in math or generally some really good intuition on the abstract concepts (or even prior knowledge) it was really demotivating. But I also felt like I had no choice but to continue and as time went on the I grew fond of it. And the feeling of being overwhelmed changed - that is to say I still was completely lost every time a new topic was breached and I could not understand even half of the proofs in class - but I did not feel so defeated about it. And I grew to like the feeling of actually completing the work sheets they gave us every week. The process of solving them was often excruciating but if you did the sense of accomplishment is real. I think for most people higher math is really difficult and that is part of why it is interesting. Another aspect I had to accept over time is that even though you can state a mathematical fact or conjecture in just a hand full of symbols or a plain sentence it does not mean that truly understand it, its implications or how you got there can be understood the same way that other prose can be. Sometimes you have to stare at, contemplate and scribble around one equation for days until you understand whats up.

If there was any advice I would give, then it's probably similar advice on how to stop procrastinating on anything that is difficult. Establish a routine first - find a spot that you will only use for studying this (like a spot in a library), start small, divide and conquer, accept that you will not understand most things easily, reward yourself for the small wins along the way, find an accountability partner or someone to study with if that's your thing, make a regular schedule with regular times where this is what you do - consistency is key, even if its just for 5 minutes, stack it onto other habits, see yourself as a scholar of math - it is what you do, lean into the discomfort, as enduring that is a valuable skill in itself.

If you love programming, there's quite a lot of programming where math is vital. Graphics, optimisation problems, cryptography, neural networks, figuring out if a hash works, projecting if an algorithm will scale...

The tricky bit is often that you need to learn some of the math before you can see how it's useful, but if you need stronger motivation, you might try diving into a slightly math heavy programming problem and learn the math as you go

I read this as remembering to set aside time specifically for play and not just for day-to-day parenting and discipline

> As a parent of young kids, obviously I haven't gone through high school yet - but I don't think many children who reach their potential in math, english, music etc will have no pressure from their parents.

Well it depends. I had no pressure from my parents to learn about programming but still got really good at it. Could I have gotten even better had I been pressured to "practice"? Perhaps. But then I also wouldn't like it for the reasons I do (I like making stuff, but not solving riddles) and it would feel like the dad sport situation.

I also played the piano for 6 years, starting out because I liked it. My parents didn't suggest it, but a few years in they were pushing me to continue even when I didn't like it anymore. Finished the first level of music school (6 years where I live) and haven't touched it since. Just to clarify, they weren't using any directly abusive tactics to keep me going, but they did put a lot of pressure onto it.

There's a lot of nuance to all of this and I don't completely disagree that we should occasionally pressure our kids to push their limits. What we often fail to acknowledge is that kids easily change their minds after a while. Just because they liked something at a certain point doesn't mean they still do. The easiest way to get a kid to dislike something is to make it a chore. Additionally, I think we need to ask ourselves whether it's more important to us to have a kid that's average scoring but has a (mostly) stress free upbringing, or one that excels but is stressed out by the time they hit high school. Kids absorb stress differently than we (adults) do.

Me being forced to do tons of horrible math by my abusive grandfather at a young age for literally 4+ hours at a time gave me a few things.

1. A true hatred of work, make work, and a strong desire to defend laziness as a concept (note that Bertrand Russel agrees hard with me here!) -https://en.m.wikipedia.org/wiki/In_Praise_of_Idleness_and_Ot...

2. A love of subversives and cheating the system. Basically, the guys writing leetcode cheating software are saints in my book. All subversions of the attempt to turn society into a meritocracy (a term which was originally supposed to be a slur/negative connotation - https://en.m.wikipedia.org/wiki/The_Rise_of_the_Meritocracy) is extremely good.

3. An advanced knowledge of TI basic, so I could cheat hard on every single school assignment I could get away with. AP Chemistry? I’ve got a symbolic stoichometry solver app! Calculus? CAS system in the palm of my hand!

Play stupid games with children, win stupid prizes. Maybe don’t force them to work like little slaves in their early life, and they won’t strike back at your society systems.