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Hi, can you expand on this point? My position is that there's obviously marginal utility in increasing/decreasing schooling duration/homework, but then that's a very individual thing where some need more and some need less. This individuality expresses itself in extra tutoring (some people need more time than the average to get something) or special classes (some people need less time than the average to get something and is ready for the next thing). Since society most often rule in averages*, then yes an arbitrary fiat of extra 5 hours system-wide is probably going to be bad, probably just as bad if kids spend 5 hours digging. I suppose what I am trying to get at is do you have a different more clarifying example of your position?
* It's been said before but the dream for education is obviously personalized individual study plan suitable for the person. AI and tech seems to be 1 or 2 years from being able to offer this.
First homework is stupid. Even worse it is pointless. It takes the most valuable time of your life for some absolutely marginal advancement in academic performance. If someone can't grok quadratic equations - solving 200 more at home will help? Making them suffer trough war and peace or crime and punishment will make them appreciate literature? That somehow staring at the physics handbook will make them understand relativity?
We treat knowledge as goal not as a tool. Tell the little ones that at the end of the course they will know how to make total synthesis of cocaine and you will have the most attentive chemistry class in the history of the world. And they will do their homework without even being assigned.
Most work you perform during your working years will be stupid and pointless, but you still need to do it. Better that children are taught early to swallow their pride and get shit done even when they don't see the point in it.
You might as well put blinders on the kids to prepare them for the fact many of them will develop vision problems as they get older, and force them to wear fatsuits to get them ready for the obesity many of them will settle into as their metabolism slows, and steal their lunch money to train them for taxes, and...
"Adult life sucks, so we should make life for children suck to prepare them for it" is such an insanely negative-sum, anti-child view that I am filled with shock and outrage every time it comes up. It's like you don't remember what it was like to be a kid, because you don't treat children like people.
From "Book Review: The Cult Of Smart" by Scott Alexander:
And from "Chattel Childhood: and the way we treat children as property" by Aella:
For what it's worth, having seen homeschoolers extensively- the most impressive specimens homeschool through early highschool, but if male they switch to some sort of hybrid system after that(community college/homeschool hybrid is the best). Girls are approval motivated enough to keep themselves on track without a formal class structure. Boys are not. Not self motivated- approval motivated.
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We really need to stop talking about education like we're just educating ancient nobles' children.
Or as if the fact that a handful of related universities in one single country were based on an idea two hundred years ago somehow makes that idea The One True Fundamental Truth globally today.
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Going by the digging ditches comparison, it's also pointless and stupid, but for many kids it would be genuinely more fun and engaging. That's because it has the possibility of a positive reward signal: finishing the ditch. But the quadratic formula is something many genuinely are just not capable of: there is no final "get shit done" point for it.
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And better still that we work on removing the stupid and pointless work as much as possible.
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This sounds like a hack Michelle Pfeiffer would try to educate inner city children.
What would actually happen is that the kids would think you're cool but the minute they had to apply any of the things you said in a more boring, sterile environment (and of course they must) a bunch would get tired and move on to something significantly more stimulating. I don't know what schools you went to but plenty of kids are fucking lazy and need the tripwire of mandatory homework. Plenty of kids would be hooked on every word in one class and then not care about another.
You may have been particularly intelligent and conscientious, most aren't. Unless we're talking purely about schools that cut those people out, kids need to be forced to push through their boredom because work will be boring.
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@quiet_NaN this is interesting to me because I feel like high-school level homework (and to some extent college level) was actually helpful for me.
Doing the readings in history and typing up notes really helped me remember history better Doing problem sets in Calc I-III and professional exams helped me remember concepts better than I would've otherwise (though I still forgot most of them within a few years) Doing coding assignments in CS 101 really helped me be able to code.
Maybe it's more about elementary and middle school homework?
I absolutely agree. I had a math class at uni and the prof gave us hundreds of problems to solve with a promise, that one of them will be exact copy on the exam and that we are allowed to bring solved problems to it. This actually made me go through all the problems. Copying the one I solved from notes on exam helped, but I had perfect score on all the other problems as well. Solving them for a week or so definitely helped. I caught several deficiencies, I taught myself more efficient ways to do checks mid-problem, I even consulted theory as problem solving brought understanding that went beside me at the time, and I just rechecked the theory because it was cool to have more thorough understanding.
It was kind of grueling, but I did not regret it. It was probably better than yet another Netflix binge session.
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There is homework and then there is homework. On one end of the spectrum, you have problem sets designed to help you master algorithms. On the other end, you have things like projects, which Scott correctly defines as "take this subject you already understand, a few sheets of construction paper, scissors, and a computer program such as PowerPoint, and combine them in whatever random way you want as long as it takes a minimum of six hours of time". And there are plenty of those in high school.
In fact, Robin Hanson has a post about how only math homework helps. It probably generalizes to other math-like subjects, like physics and compsci. But it does not justify the three hours of homework a day that kids receive from all their subjects combined.
I've seen the justification that can be paraphrased as "most of them will be doing uninteresting and uninspiring work 9-5, uninteresting and uninspiring homework helps prepare them for the fact that not everything is gonna be exciting edifying self-directed projects all the time".
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Agreed. Doing the individual work is when learning happens. Sitting in lectures has its benefits but we probably do too much of it in high school. Cutting classroom instruction time by 66% with more time to do the work during the day would increase learning.
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I think that math class is probably the worst offender for pointless busywork.
Case in point: Polynomial long division. 100% "we make you learn an algorithm as a proxy for intelligence", 0% "something you will need to know as a prerequisite for understanding something else." The correct place for it would be "Having just discussed the properties of polynomial rings in general, here is as a curiosity a technique of dividing polynomials. You know that it will not be relevant for you exam because it involves just playing an algorithm (possibly even with concrete quantities)."
Instead you get tasks like "one of the factors of x^3+5x^2+7x-3 is (x+3). Factorize x".
People whose skill is to pass 'math' class in high school do not need to worry about being replaced by LLMs, because they were presumably replaced by WolframAlpha in 2011.
This is equivalent of doing multiplication and eventually memorizing the multiplication table during elementary school. With enough "busywork" you will be able to factorize from your head, which will enable you to solve some key problems much, much more quickly "look and see" style ,sifting through unproductive approaches before even trying them. This is cookie cutter thing in many engineering areas, basically anything that uses differential equations which is a really a lot of stuff.
Busywork is really important especially in early stages. You have to go through some shit like memorizing vocabulary when you are learning a new language, before you will be able to do some creative things like translating poetry or doing some Tolkien-like stuff with that language.
No, that is my whole point. Knowing the multiplication table up to 9*9 is a prerequisite for the following:
Anyone who is arguing that kids do not need to learn what 7*8 is denying the need for learning arithmetic at all. (There are probably people arguing that you do not need to know arithmetic because computers exist. I disagree. Knowing how to arrive at a result without a computer in principle, even if a million times slower and error prone, is useful in itself. Besides, with LLMs, this argument generalizes against anything you learn in high school.)
I am fine with busywork which is an instrumental goal for something worthier. I learned my multiplication table because I knew that it would enable me to do long multiplication in base 10. Then in fifth grade, they tried to make me learn 2..9 * 11..19, and I was not having it. If you are in base 10, the utility of knowing non-trivial products of integers takes a sharp dive after 99. I felt that if I gave in and learned what 137 was, they would come around in sixth grade and demand I learned by rot what 1315 or 237 was. (For factorization, the useful thing would be to quickly identify a prime factor in any integer in a given range, but even this obviously does not scale.)
A lot of the stuff kids learn in math class, painful as it may be, is actually useful in some fields. I don't think that youths should be forced to learn what a logarithm is, but they should be clearly told that any subject up to the softest social sciences will expect them to know, so that they can make an informed decision.
Other stuff has value because it teaches core concepts of math, such as proof by induction or the definition of real numbers. Sadly, people only learn what real numbers are when they go to university, and proof by induction in high school is turned into a mockery by turning it to just another pointless algorithm which can be used to prove increasingly pointless sum formulas by rote.
Wait - you value this, but not polynomial division? They're both things you can just ask the computer to do for you instead, but at least polynomial division requires you to hunt down a computer algebra system; long division capability come pre-installed on every phone.
Polynomial division is IMHO a curiosity.
Long division crops up every time you need want to split the bill.
Polynomial division might crop up in the wild if you want partial fraction decomposition, which I guess you might want if you are dealing with rational functions and want to numerically evaluate them or calculate their anti-derivatives. While I am sure that rational functions have their uses, my gut feeling is that they are both too narrow to pop up in physics a lot (where you will frequently have square roots placed so that your functions can not easily be transformed into rational functions) and too inconvenient to be preferred for empirical models.
Factorization of an integer is a hard but finite problem. Factorization of a polynomial is in general just not possible exactly. You can test if 7, 13, 17, 19, 23, ... etc happen to divide 3071 to factorize it. You can not test if x-1, x-1.1, x-sqrt(42+sqrt(42)) etc are factors of 5x5+4x4+7x**2-2x-2, because there are countably many algebraic numbers which could be a root.
I think that we learned both polynomial division and solving quadratic equations around grade eight. Solving quadratics in something which I would call bloody useful. Quadratic functions are the first non-trivial functions students can tackle, and quadratic equations pop up all the time in high school physics.
I strongly disagree with the sentiment that math skills which are less readily automated are more valuable. To grok (I'm reclaiming that word) how multiplication and division work doing long multiplication and division is definitely more useful than just using a calculator. Nobody needs the numeracy to be actually excellent at these operations any more. Anyone whose job actually requires them to multiply five-digit numbers will hopefully have the good sense not to try that by hand.
My more general point might be that I do not want students to be excellent at applying any algorithm. They will always suck very hard compared to the simplest of computers. Still, it is useful to demonstrate that you can apply an algorithm, even if it is just at toy-sized problems.
Also, applying a pre-learned algorithm is not math. Some algorithms (e.g. solving an equation for a variable) are genuinely useful in proofs, and thus are valid technical skills to learn to be able to engage in math, same as being able to write symbols with a pencil. And of course, 'can you apply an algorithm halfway reliably?' is also a good way to check if someone has a basic understanding of the algorithm in question (even if it does not probe if they understand why it works), which is why rotating trees by pencil is a staple in CS exams.
Still, for school math, I feel that 'can apply pre-learned algorithms' should earn a passing grade, not an actually good grade, which should require thinking.
This was an excellent explanation, thank you.
One side note:
Piecewise-rational functions are very popular for two big categories of empirical model: anything where the true behavior can have asymptotically-polynomial singularities, and CAD models. Being able to do sharp corners and spectral approximation refinement and exact conic sections all with the same backend is a very useful trick.
This is irrelevant to your points, though; even when working with NURBS, polynomial long division doesn't really come up.
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Where do you have proof by induction in high school?
IB does proof by induction in high school.
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In Finland in the mid 90s.
Of course that was by far the most useless thing they ever taught in high school math here (and in fact one of the few useless things).
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Any East Asian education system would touch upon proof by induction, and most certainly of any Math-specialized classes. Seems like AP Calculus briefly touches upon it. IB Math Higher Level and Further Level certainly does. The British A-Level Further Maths also does. India probably does.
Obviously teaching material quality varies and I'm not a math expert but proof by induction might not be accessible but definitely within reach for most high schoolers out there.
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