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Everything I remember about maths I remember because I understood the "why" of it. The stuff I learned rote - just to pass the exams - I have long since forgott

by enneff 16y ago

Everything I remember about maths I remember because I understood the "why" of it. The stuff I learned rote - just to pass the exams - I have long since forgotten. I'm now frustrated that I was expected to learn anything by rote, as it's all lost to the sands of time now. Rote memorization might help you with exams and book problems, but it won't help you develop long-term mathematical problem-solving skills. If you can't explain it from first principles, you don't truly understand it.

whatwhat 16y ago
I'm not saying that problem solving and understanding aren't important (see Bloom's taxonomy). I'm saying that you still need memory to justify whatever domain your knowledge is in, and that memory seems to be the bedrock of further knowledge (understanding, creativity, problem solving etc.). Am I missing something here? Do you not need some element of memory to explain things from first principles, and to have an understanding of something? edit: I've just realized from reading wtallis' comment that I might be confusing two different forms of knowledge: memory and reasoning, insofar as reasoning can produce further truths. Is that what you are getting at?
- Retric 16y ago
  You can easily manipulate symbols without understanding what's happening. The problem is it's hard to progress significantly past your understanding using this approach. Not that Math really has levels as such, but if you don't get Calculus at a fairly deep level DiffEQ ends up being fairly meaningless. PS: It's a common thing for most calculus classes to redirive old formulas. Not because they stoped working, but rather because you really should understand why it's 4/3 pi * r^3.
- Someone 16y ago
  It is similar to the difference between say svn and got: you should not remember the various revisions, but how to get there, because that will knowledge will be reusable in different branches. As an example, I had a maths professor who derived the formula for solving a quadratic equation in class (in 30 seconds or so) because he did not remember it.
hitonagashi 16y ago
Depends, I had that opinion too until I took university maths. The proofs they give you to learn by rote are actually extremely useful, as they add techniques to your repertoire that you otherwise wouldn't have..and the difference between 'learning the proof by rote' and 'learning the technique' is usually extremely small.

by enneff 16y ago

whatwhat 16y ago

I'm not saying that problem solving and understanding aren't important (see Bloom's taxonomy). I'm saying that you still need memory to justify whatever domain your knowledge is in, and that memory seems to be the bedrock of further knowledge (understanding, creativity, problem solving etc.). Am I missing something here? Do you not need some element of memory to explain things from first principles, and to have an understanding of something? edit: I've just realized from reading wtallis' comment that I might be confusing two different forms of knowledge: memory and reasoning, insofar as reasoning can produce further truths. Is that what you are getting at?

Retric 16y ago
You can easily manipulate symbols without understanding what's happening. The problem is it's hard to progress significantly past your understanding using this approach. Not that Math really has levels as such, but if you don't get Calculus at a fairly deep level DiffEQ ends up being fairly meaningless. PS: It's a common thing for most calculus classes to redirive old formulas. Not because they stoped working, but rather because you really should understand why it's 4/3 pi * r^3.
Someone 16y ago
It is similar to the difference between say svn and got: you should not remember the various revisions, but how to get there, because that will knowledge will be reusable in different branches. As an example, I had a maths professor who derived the formula for solving a quadratic equation in class (in 30 seconds or so) because he did not remember it.

hitonagashi 16y ago

Depends, I had that opinion too until I took university maths. The proofs they give you to learn by rote are actually extremely useful, as they add techniques to your repertoire that you otherwise wouldn't have..and the difference between 'learning the proof by rote' and 'learning the technique' is usually extremely small.