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Memory is crucial. I got much better at learning mathematics when I started memorizing the statements and proofs of key theorems. You also need the understandi

Memory is crucial. I got much better at learning mathematics when I started memorizing the statements and proofs of key theorems. You also need the understanding, of course. The largest mistake in mathematics education is to think that memorizing a rote process is the same as learning mathematics (see: US high schools). The second largest mistake in mathematics education is to swing too hard in the other direction.

nicklaf 10y ago
Learning without thought is labor lost, Confucius said. At any rate, symbolic representations of knowledge should be committed to memory (or pad and pencil) at the time of understanding (Hebb's rule), or else your "memory" will be isomorphic to random symbols and therefore inaccessible to future thoughts. That said, some of the greatest mathematicians (e.g., Gauss, von Neumann, Dieudonné) had phenomenal memory, so I suppose rote memorization isn't a terrible hack to try to approximate the advantages this kind of gift confers, but only in a pinch, since these mathematicians were keeping much more than definitions and statements of theorems in memory.
cle 10y ago
Absolutely. Being able to instantly recall concepts, definitions, syntax, etc. is incredibly empowering when solving problems, regardless of the subject (mathematics, programming, writing, etc.). Nobody would suggest that you try to learn a new language without memorizing words, phrases, idioms, etc. Communication is the foundation of any field of interest, so why do we think we can get away with "learning" them without memorizing the sub-language of the field? Just as memorization is only part of process of learning a new language, so it is for learning in other areas.
- Buttons840 10y ago
  If all you have is some rote memorization about mathmatics you can use those memorized items to study in your own head. So while you shower or drive you can think about the math you've memorized and develope a deeper understanding. As you say, memorization can be a useful part of a deeper understanding.

nicklaf 10y ago

Learning without thought is labor lost, Confucius said. At any rate, symbolic representations of knowledge should be committed to memory (or pad and pencil) at the time of understanding (Hebb's rule), or else your "memory" will be isomorphic to random symbols and therefore inaccessible to future thoughts. That said, some of the greatest mathematicians (e.g., Gauss, von Neumann, Dieudonné) had phenomenal memory, so I suppose rote memorization isn't a terrible hack to try to approximate the advantages this kind of gift confers, but only in a pinch, since these mathematicians were keeping much more than definitions and statements of theorems in memory.

cle 10y ago

Absolutely. Being able to instantly recall concepts, definitions, syntax, etc. is incredibly empowering when solving problems, regardless of the subject (mathematics, programming, writing, etc.). Nobody would suggest that you try to learn a new language without memorizing words, phrases, idioms, etc. Communication is the foundation of any field of interest, so why do we think we can get away with "learning" them without memorizing the sub-language of the field? Just as memorization is only part of process of learning a new language, so it is for learning in other areas.

Buttons840 10y ago
If all you have is some rote memorization about mathmatics you can use those memorized items to study in your own head. So while you shower or drive you can think about the math you've memorized and develope a deeper understanding. As you say, memorization can be a useful part of a deeper understanding.