The kids that study and apply themselves, I don't think it's so much that they can see they understand the benefits of linear algebra at the time, it's that their parents and the social network they're a part of sends them signals that this is what they should do to be successful and they're rewarded for doing well in school.
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.
In short, math is a powerhouse tool for carrying society forward.
Art, while cool to look at and experience, has a pretty low efficacy in terms of "motivating people to do work, or removing obstacles, to carry society forward"
In short, starving artists.
There is also the whole thing where art is an abstract concept with a subjective definition, and a solar cell sporting new tech with 33% efficiency objectively being better than one with 24% efficiency.
There were humans for tens of thousands of years before there was high technology. But there were hardly any humans around before there was art.
Idk, the soviets didn't invest in socialist realism propaganda for nothing.
Less sarcastically, art has had an outsized influence on society and culture. Take any social movement you want, and there was probably some novel or work of art that galvanized it.
10,000 artists in, one $20k work of art out.
Whereas something like the engineer is closer to
5 engineers in, $500k of work out (and even that is pretty conservative)
Also i'd point out the selection bias of not counting people who fail out of engineering school but still counting every unsuccessful artist.
As a first order approximation the "price" of art (as distinct from its value) is a function of branding not asthetics.
Secondly most artists get paid, not from doing fine art, but from adjacent careers that require good color, balance, composition, and so on. Industrial designers (think Jonny Ive), interior design, food presentation, magazine layout, web design, architecture and so on. Art skills are all around us. In the same way engineering is around us.
Put another way, engineers build ugly (think beige PC boxes). It took an artist to give us the iMac. And it was a marketing genius (yet another important skillset) to bring the artist and engineer together.
Teaching math goes far beyond creating mathematicians. Teaching art goes far beyond teaching artists. Societies that drop art because it is unproductive get ugliness permeating everywhere.
Applies to art, fashion, media.
Most practical (including engineering) successes are much less externally attractive but do make decent money for everybody involved.
Further, judging the value of art to society by how much it costs is ridiculous and an asinine comparison.
It grew out of a time where basic artistic skills were expensive to learn, and could be a real class differentiator (and had some employment benefits).
That's now a fair bit less true; but still continues to prevent these things becoming the sole domain of private schools.
Did do writing although a lot was extracurricular.
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.
An inability to understand compound interest is classic.
I think we're more talking about algebra or, really, anything "higher" in maths than arithmetic. Does a solid knowledge of, e,g, Set Theory, give any benefit later in life?
And also, if we think that basic financial management is a good thing for kids to learn, why don't we teach that?
If you bought 6 liters of soda for £3/2-liter bottle with 8% consumption tax, how much should it cost?
You have to shape that all into a series of operations for your calculator. The calculator can't do it by itself. Even basic arithmetic takes some education before the calculator can be useful.
I would disagree. How to minimize a function, how to calculate interest, first derrivative are all pretty useful in finance, and a bit beyond basic arithmatic.
> I think we're more talking about algebra
"Algebra" as a term covers a lot. Being able to solve for x is a very useful skill and often what people mean by algebra.
If you mean understanding groups, rings, fields, or whatever, then sure that is probably not very useful to the average person's day to day. However i dont think that is usually tought in high school.
> Does a solid knowledge of, e,g, Set Theory, give any benefit later in life?
Pretty sure nobody in high school is getting a solid understanding of set theory. That is more university level.
> And also, if we think that basic financial management is a good thing for kids to learn, why don't we teach that?
I guess it depends on where you live, but i had to take a class on that in high school.
These are college graduates.
> Does a solid knowledge of, e,g, Set Theory, give any benefit later in life?
Knowledge of statistics will help a person a lot.
Another example. I wanted to put an elliptical brick patio in my yard. The contractor gave a square footage and I signed a deal with the charge per square foot. He staked it out.
It looked a bit peculiar to me. So I measured the major and minor axes and computed the area of the ellipse. It was 1/3 smaller than the contracted amount. The pallet of bricks was sitting in the driveway. I multiplied xyz to get the square footage of the bricks, and walla, it matched the area staked out.
I.e. I was being cheated. The contractor evidently was used to math challenged customers, and discovered how much he could cheat before being noticed. I pointed out the "error" (hahahaha) and the contractor reduced the bill by a third.
> why don't we teach that?
Exactly!
Is there any benefit to being able to distinguish logical entailments from non sequiturs?
The things that are taught under the label "set theory" are taught elsewhere under the label "basic logic". The most primitive symbols are intentionally matched: in logic, "and" is ∧ and "or" is ∨, while in set theory, "and" is ⋂ and "or" is ⋃.
The symbols stop matching quite that well after that - compare logical ⟶ and ¬ to set-theoretic ⊆ and ᶜ - but they continue to consist of the same material.
Ha Ha Ha! Cute you think society cares about reading abilities!
I mean, OK, you are expected to be able to do basic level reading. But, say, reading something independently to learn something? Even when I was in university 20 years ago it was a struggle to get people to read.
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)".
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.
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).
'It's fun' is a pretty compelling reason for both kids and adults to learn certain things, but you can't just decide what's fun and what isn't. Maths rarely gets to have that reason (and when it does, it applies to people for whom this entire problem isn't relevant).
I taught at an English-immersion high school in Shanghai.
It's worth remarking that the boy at the top of the class in each grade was dating the girl at the top of the class.
I can believe it, but I don't know if it's true. Obviously not true in the US.
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.