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The real problem is the disconnect between math and "math". "math" is the game of rote memorization that kids play in school where they try to memorize arcane

The real problem is the disconnect between math and "math". "math" is the game of rote memorization that kids play in school where they try to memorize arcane rules that seemed to have been pulled from some greek dudes ass with no explanation. Math is a legendary construct whispered about as a hypothetical possibility in high school classrooms. A problem solving exercise that has you think, with a logical progression from base rules and assumptions. "Math" and Math both use the same language and the same symbols, with a lot of the same concepts. I've never seen Math, and only know of it's existence through hear say from mathematicians, but been through a lot of "Math". Imagine if we tried to teach English this way. It would look a lot like memorizing words out of the dictionary. And then playing ad-libs with out of context sentences.

sp332 14y ago
You should check out Vi Hart's Youtube channel. It's always been completely awesome, and then she got hired by Khan Academy to just make videos all the time! https://www.youtube.com/user/Vihart https://www.youtube.com/user/Vihart
arkitaip 14y ago
Nice metaphor. Going through the motions of learning seems to be a systemic problem that permeates all levels of our societies, not just primary school's "math" (to use your terms) education. It's just that Math operates on such a high level of abstraction that the motions we go through quickly takes us to the uncanny valley where all bullshit is instantly exposed.
excuse-me 14y ago
Not just kids in school - you can get to grad school in science with lectures that consist of: What's an eigenvector? It's the solution to an eigenfuction! What's an eigenfunction? It's an equation that has an eigenvector as the solution - now goto the next chapter...
- unimpressive 14y ago
  http://lesswrong.com/lw/iq/guessing_the_teachers_password/ http://lesswrong.com/lw/iq/guessing_the_teachers_password/ Now kids, what did you learn?[0] Don't guess the teachers password?! Excellent! Next chapter... [0] As I was writing that I thought that there could be a paradox somewhere in there if you phrased it right.
- jasomill 14y ago
  Seriously? That's not even a sensible mutually recursive set of definitions. And to think I've been told I'll have trouble getting into grad school on account of my GPA... Then again, functional analysis as an admission requirement for a graduate science program seems like it'd be a bit of a stretch in most places.
- JadeNB 14y ago
  I hope no one gives this definition, since it's wrong. An eigenvector (for a linear map `T`) is a non-`0` solution `v` to an equation of the form `Tv = λv`. (I suppose one could call the equation an eigenequation, but I've never seen anyone do that.) An eigenfunction is exactly the same thing; we just tend to use the terminology when `T` is operating on a space of functions. (For example, one may refer to an exponential map as an eigenfunction of the differentiation operator on the space of smooth functions; it would be equally correct, but probably confusing, to call it an eigenvector for that operator.)
philwelch 14y ago
It turns out that as a kid, I always hated "math". This lasted well into college and actually hurt me quite a bit. When I found out later what math actually was, I felt immensely screwed. If I'd been taught to be a mathematician instead of a computer when I was a kid, I'm sure I'd have appreciated math a lot more.
rimantas 14y ago
> It would look a lot like memorizing words out of the > dictionary. That was a big part of me learning English (my fourth language). You need to memorize something when learning something — just to get a foundation to operate on.
- unimpressive 14y ago
  Sure. But the "memorize" period shouldn't go on for 8+ years.
Tichy 14y ago
Hm, except for the multiplication table I don't recall many rote techniques in maths. There was one called "rule of three" (according to dict.cc) for solving very simple equations. I never managed to memorize that one and always just solved the equations the normal way instead (substract the same things on both sides and so on - very logical).
fleitz 14y ago
We do do that in English, that's why most people with Degrees in English can't write a convincing piece of prose to save their life. But they can tell you all sorts of arbitrary rules about English, and probably something about iambic pentameter.
jeffdavis 14y ago
I think arithmetic has a lot of merit in the teaching process, and shouldn't be dismissed. Maybe it's overemphasized, but it does have value. Arithmetic can help show some deep mathematical concepts that might not be obvious if you study theory alone. For example, the advantages of arabic numerals over roman numerals. There are important mathematical distinctions between the two representations, but without actually using them both, it's hard to understand why arabic numerals are so much more useful for so many purposes. I think it's best to switch between concepts and practical applications. I also don't think there is a problem with memorization. In any field, to exercise good judgement or gain deep insight, logic and reason are not enough. You need a collection of facts to guide you as well as other people's ideas to draw from.
deleted 14y ago
[deleted]

sp332 14y ago

You should check out Vi Hart's Youtube channel. It's always been completely awesome, and then she got hired by Khan Academy to just make videos all the time! https://www.youtube.com/user/Vihart https://www.youtube.com/user/Vihart

arkitaip 14y ago

Nice metaphor. Going through the motions of learning seems to be a systemic problem that permeates all levels of our societies, not just primary school's "math" (to use your terms) education. It's just that Math operates on such a high level of abstraction that the motions we go through quickly takes us to the uncanny valley where all bullshit is instantly exposed.

excuse-me 14y ago

Not just kids in school - you can get to grad school in science with lectures that consist of: What's an eigenvector? It's the solution to an eigenfuction! What's an eigenfunction? It's an equation that has an eigenvector as the solution - now goto the next chapter...

unimpressive 14y ago
http://lesswrong.com/lw/iq/guessing_the_teachers_password/ http://lesswrong.com/lw/iq/guessing_the_teachers_password/ Now kids, what did you learn?[0] Don't guess the teachers password?! Excellent! Next chapter... [0] As I was writing that I thought that there could be a paradox somewhere in there if you phrased it right.
jasomill 14y ago
Seriously? That's not even a sensible mutually recursive set of definitions. And to think I've been told I'll have trouble getting into grad school on account of my GPA... Then again, functional analysis as an admission requirement for a graduate science program seems like it'd be a bit of a stretch in most places.
JadeNB 14y ago
I hope no one gives this definition, since it's wrong. An eigenvector (for a linear map `T`) is a non-`0` solution `v` to an equation of the form `Tv = λv`. (I suppose one could call the equation an eigenequation, but I've never seen anyone do that.) An eigenfunction is exactly the same thing; we just tend to use the terminology when `T` is operating on a space of functions. (For example, one may refer to an exponential map as an eigenfunction of the differentiation operator on the space of smooth functions; it would be equally correct, but probably confusing, to call it an eigenvector for that operator.)

philwelch 14y ago

It turns out that as a kid, I always hated "math". This lasted well into college and actually hurt me quite a bit. When I found out later what math actually was, I felt immensely screwed. If I'd been taught to be a mathematician instead of a computer when I was a kid, I'm sure I'd have appreciated math a lot more.

rimantas 14y ago

> It would look a lot like memorizing words out of the > dictionary. That was a big part of me learning English (my fourth language). You need to memorize something when learning something — just to get a foundation to operate on.

unimpressive 14y ago
Sure. But the "memorize" period shouldn't go on for 8+ years.

Tichy 14y ago

Hm, except for the multiplication table I don't recall many rote techniques in maths. There was one called "rule of three" (according to dict.cc) for solving very simple equations. I never managed to memorize that one and always just solved the equations the normal way instead (substract the same things on both sides and so on - very logical).

fleitz 14y ago

We do do that in English, that's why most people with Degrees in English can't write a convincing piece of prose to save their life. But they can tell you all sorts of arbitrary rules about English, and probably something about iambic pentameter.

jeffdavis 14y ago

I think arithmetic has a lot of merit in the teaching process, and shouldn't be dismissed. Maybe it's overemphasized, but it does have value. Arithmetic can help show some deep mathematical concepts that might not be obvious if you study theory alone. For example, the advantages of arabic numerals over roman numerals. There are important mathematical distinctions between the two representations, but without actually using them both, it's hard to understand why arabic numerals are so much more useful for so many purposes. I think it's best to switch between concepts and practical applications. I also don't think there is a problem with memorization. In any field, to exercise good judgement or gain deep insight, logic and reason are not enough. You need a collection of facts to guide you as well as other people's ideas to draw from.

deleted 14y ago

[deleted]