Perhaps the most damning thing about math education is its focus on the what, not the why. For example, the quadratic formula: it is introduced and students are told that if you have an equation "of the form" ax^2+bx+c=0, you can "find x" by plugging in the numbers. Never are you given an explanation of where the quadratic formula comes from, never are you given an explanation of why you would want to solve a quadratic.
This is not entirely the education's fault.
When I was taking algebra in 7th grade, the teacher did derive the quadratic formula for us. We studied completing the square first, and then he did it with generic symbols for A, B, and C. I thought it was WAY cool. I never memorized it; instead, for the next two years, any time I needed it, I simply re-derived it. You could find the derivation on the back of just about every math test I took in high school.
None of my classmates took that route, though. Every last one of them memorized the thing.
I was the sort of person who automatically thought the why of something was much cooler than the what, but I don't think most people are that way. I don't doubt math education could inspire an interest in the why, but I'm not optimistic that it will inspire everyone. At the very least, I think that would take more than merely presenting it.
I don't know. Maybe tests have pounded the natural curiosity out of kids, maybe it's just cynicism. But it's certainly my perception that the vast majority of them care more about the what.
>Never are you given an explanation of where the quadratic formula comes from //
That's not [exclusively] how I was taught the quadratic equation and it's solutions, in high school in the UK, either.
I wish people would remember to provide geographical context on HN. The article is about Australian middle school so should I assume that's what everyone is referring to with their generalised statements of "this is what 'math' is like"?
>I simply re-derived it //
This is why I did well at maths. Practically no memorisation required; you can start with something you know and derive what you need to answer the question.
No memorization? To do those derivations, you must have memorized derivation steps and be able to recognize when it makes sense to apply them.
That, IMO, is the big thing: students that are relatively poor at abstraction cannot see commonalities between problems that those with more talent find trivial.
Certainly later on, like with QFT, I was left to grope in the dark recesses of memory for the next step in a proof of some corollary or other but I found that understanding how a proof works means that the steps make sense in the same way as having to pull down your trousers before pulling down your underwear. Yes there is memorisation involved but nothing like that required to establish who was the King of France in 1492.
I did say "practically", perhaps "comparatively" would have been more to the point.
This is not entirely the education's fault.
When I was taking algebra in 7th grade, the teacher did derive the quadratic formula for us. We studied completing the square first, and then he did it with generic symbols for A, B, and C. I thought it was WAY cool. I never memorized it; instead, for the next two years, any time I needed it, I simply re-derived it. You could find the derivation on the back of just about every math test I took in high school.
None of my classmates took that route, though. Every last one of them memorized the thing.
I was the sort of person who automatically thought the why of something was much cooler than the what, but I don't think most people are that way. I don't doubt math education could inspire an interest in the why, but I'm not optimistic that it will inspire everyone. At the very least, I think that would take more than merely presenting it.
I don't know. Maybe tests have pounded the natural curiosity out of kids, maybe it's just cynicism. But it's certainly my perception that the vast majority of them care more about the what.