It seems obvious to me that the answer should be yes. So the follow ups should be figuring out how to move a student from an unwilling participant to a willing participant.
I think about three strata of students. The stubbornly unwilling, the coaxable, and the eager. It is pretty easy to design education for the eager. And discussing how to optimize that is a completely different discipline than the discussion about how to coax. The discussion about moving the unwilling to the coaxable is another topic on its own.
Having a mixed class of unwilling, coaxable, and eager in a classroom with a mantra of "no child left behind" is a huge mistake in the same way it would be a mistake to have one teacher in a mixed classroom for Geometry, Alphabet, and Orchestra.
I have a real issue dividing kids up along these lines. I've found that virtually all young kids love to explore and learn things, and if anything schooling can extinguish this innate desire when it becomes a source of stress.
This is a very bold claim. I don't think most kids are curious about the multiplication tables
https://news.ycombinator.com/item?id=48395840
and ultimately this about a successful experiment in other approaches to maths:
Kids will learn anything that gives them social standing or self-worth in another way, whatever it takes to be a cool kid.
Which is exactly why they stopped teaching them in US curriculum under No Child Left Behind.
When rubber hits the road with a learning objective, I think the two most important axis are: how much does the student want to learn (this), and how easy is it for the student to learn (this)?
Both can depend on a variety of factors... For example a masters student paying their own way mid career maybe really wants to learn as much as they can, but a specific research report assigned during a busy work week, and some family emergency, etc. may mean they treat the assignment as "I just need to get this done" instead of "I want to get as much as I can out of this", and one way that can show up is how much they depend on an LLM to do the work for them...
In any case, people who wanted to learn were easy to deal with. The other two motivations could be used to coax the person to learn, but they required different approaches.
There is no stress, they just don’t want to “explore” things they see as non-urgent.. basically everything you need like writing, reading and calculating properly.
No amount of coaxing, gamification or whatever works consistently. The only thing that got my smartest kid through anything is by force. Not too much, but still, they need some amount of coercion no question about it. Anyone that denies this I find very, very hard to take seriously.
Interestingly the slightly less cerebral one is easier to guide through gamification. I guess the smarter you are the easier you see through BS. It’s easier to just learn to suck it up and Do The Thing instead of “learning is fun”. It isn’t and it doesn’t matter.
I've found that the people who are more optimistic about kids tend to live in a particular category of socioneconomic bubble.
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.
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)
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.
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.
Arithmetic, Algebra, and Statistics are different classes should be taught separately.
"Please wake up and take your headphones off and answer my question even though you don't plan on passing any of your classes" and History are different classes with different types of students. Trying to conduct both classes at the same time using the same teacher is folly. You will be forced to abandon one or both of the students. You might argue that you should abandon them it turns every other day so they both get something out of the class. But that means they will each get half or less out of the class than they would have if you separated the classes. It is highly likely that you will frustrate both students to the point of impediment.
It shouldn't be. The research overwhelming says its a good practice. The type of people who say this type of thing are the exact type of ideologically motivated people who are destroying school systems in blue districts. Ironically this group both hates private schools and creates the environment that pushes parents to pay for private schools. I've personally seen the bad consequences of schools that do this and I know people who aren't here anymore because of it. So please, for the love of god, stop talking about topics you know nothing about.
The upshot for this is that the benefit is as much for the student doing the teaching as the one doing the learning. Teaching has a much greater effect on _retention_ than listening reading or even doing, which is the majority determinant underlying the primary school curriculum.
There are a whole host of secondary benefits to this (as well as lots of logistical challenges): the students are doing something useful, teaching, and we pay teachers if you wanted to expend budget there I suspect it would have great effect, as would any other form of ~~bribery~~, I mean, incentivisation; socialising, especially if you have the teaching being done across different classes (which you would want to do because you want the teacher to know more than the student).
Let's say that you have some curriculum C that you think is vital for children to learn, and you want as many children as possible to learn C.
Even ignoring ethics, it's not obvious to me that attempting to coerce all children into learning C is the best way to accomplish your goal!
Why is it obvious that an educator should do their best to teach a student something even when they don't want to learn? Well for one, it's their job, and two... Children especially are not good judges of which knowledge and skills will benefit them later in life.
And you need to do that. It trains your brain. If you simply rely on calculators, LLMs, and Google Search, then you likely can forget about doing advanced science.
It doesn't mean that you have to _master_ everything. Far from it. But you need to apply real effort to various subjects to train yourself.
Thus to be ethical in your society, usually means you must follow the rules determined by a collective group of your nations ancestors or you will be shunned/jailed/harmed/etc. Which is essentially coercion. "Act this way or be punished."