I will bet that the number of adults who ever engage in coloring or painting as adults is extremely small. Probably less than the number of full time scientists, engineers, finance professionals etc. Yet no one complains that we are forcing students to do art in school, even when many students don't particularly like doing art. Why? Because we recognize that developing general artistic ability in humans is important, so we need art classes.

The other argument about teaching "advanced math" is the same as why Cristiano Ronaldo spends a significant part of his training in the gym lifting weights? Ever seen Ronaldo take out a barbell and start doing squats during a game? One should reflect on this.

re: not teaching math to kids is a pet peeve of mine.

the number of adults i've met who cannot add two fractions together is depressing.

at some point each of them had decided "i'm just bad with numbers, hahaha" and they gave themselves permission to stop trying math. worse, society gives you a pass at not knowing math. we need to apply the same constant social pressure to mathematics skills that we do for learning to read.

> kids why they should learn advanced abstract math

Could you clarify what do you mean by 'kids' and 'advanced math' here?

I personally believe we should stop believing advanced math is meaningful for everyone. Especially stop trying to push them down to high school curriculum.

When I say advanced math I mean anything involved with "what exactly is a ___ (vector space, real number, group, set, etc)".

Motivation to learn has nothing to do with practicality. That was definitely that way for me, especially when I was young.

I know full well that languages are necessary and useful ... and were. I still found learning languages the most boring thing in the world. I liked abstract math despite thinking it is not necessary useful - I did not cared. I could go on, but relation between interesting and useful was never all that straight forward.

> It's hard to convince kids why they should learn advanced abstract math, beyond what is necessary to calculate the tip on a restaurant bill.

When I was just a bit younger, I detested what I'm about to say, but now know as the "reality".

Your argument is focused on rationalism. You're trying to give kids/teenagers real world reasons to learn something.

People are rarely motivated by reason. They are motivated by emotions.

If you look, you'll find plenty of examples of very "rational" adults (college professors included) who clearly know something to be true, will admit to it, but will still go the emotional route.

As a parent, I looked into the research on changing/shaping children's behavior. And the key things that stood out:

1. If you know enough adults who do equivalently bad things even while they know the harm in it, don't expect kids to behave based on reason.

2. Focus on (positive) emotions. Give kids incentives. They shouldn't clean up the table because it will keep the house clean. They should clean it up because they'll get a (short term) positive reward.

3. Focus on building the ritual as a habit, and separate it from any semblance of morality. The brain needs to get accustomed to the actual behavior. The rationale can be added (now or when older), but if you focus too much on rationale without the habit, you'll get someone like me, who realizes a lot of behaviors are good for me, but won't do them because "my brain isn't wired for it".

Getting back to kids learning algebra, or whatever: Their lack of incentive isn't because they can't connect to practical skills in life.[1] The reason they don't want to do it is because it is not a valued skill amongst their peers. And it's also not a valued skill in American society.

That's why high school kids in Eastern Europe or East Asia tend to know this a lot better. If you can't multiply two numbers on paper, you're an idiot. Everyone will know you're an idiot. As much an idiot as not being able to read properly. So you learn it because you know that it's just a baseline intelligence marker you should have by a certain age. You don't whine about it any more than you'd whine about how to properly eat food without spilling it. Sure, once they're older and reflect back, they may say "I never needed algebra", but it doesn't bother them. Knowing it is merely part of being cultured.[2]

Now being motivated by shame is really not a great way to get people to do something, and that's not what I'm encouraging. The point is that it's a broader societal problem. Why should they learn it if they see no one else values it?

I wrote more about this about a month ago: https://news.ycombinator.com/item?id=48065640

[1] Think about all the useless things kids can be good at. Did they have to rationalize why they should learn them?

[2] This is why California, in particular, had a strong push back regarding calculus not being taught in high schools. There's a strong and relatively wealthy Asian/immigrant community in those places, and they've tried to maintain the value of being decent at math. (All the stuff about impacting university education is fluff. I used to work at a university, and they had remedial programs for incoming students who didn't know algebra/pre-calculus. It adds to the time to graduate, but by and large is successful - it's OK if you go into engineering without being exposed to calculus).

Here's my take: school math past the basic arithmetic will be useless in life for the majority of people. Any non-trivial school-level-related math question can be easily solved within 10-20 seconds by a Google search.

That's also why all the examples of math's usefulness become ridiculous stories like: "imagine yourself getting stuck on an uninhabited island and having to calculate the triple integral to find the volume of a barrel of water".

No. The real use of school-level math/physics/chemistry/language is in laying the _foundation_ and training the brain.

And it doesn't really matter what exactly you want to use for mental training. Every structured activity is fine, as long as it engages the brain.

Even pointless tasks like memorizing scriptures help. There are studies that show that religious students who spent a lot of time on rote memorization, and later switch to other disciplines, in the end do quite well with their studies.