3 ms·

A memory is also crucial. Things like standard derivatives/integrals or standard probability laws need to be memorised be it by this method or by experience.

OJFord 10y ago
I agree to the extent that once understood, things need (presumably!) to then be remembered. I suppose people's methods differ, but personally I don't think I could have an effective memory without understanding, and that my memory follows understanding. By "effective memory", I mean that I could actually apply some definition, not merely remember the pattern of notation on the page. I fancy if I learnt it from a flash card I'd struggle when variables were named differently, or with the slightest variation in form.
- drieddust 10y ago
  I used to be in your camp but now I think they go hand in hand. If you insist on understanding before remembering, how do you start? When we start a lot of things are interrelated and unless you a bare minimum is committed to memory, it's difficult to start. It is akin to learning a language where one need to cram the basics building blocks i.e. words and grammar rules before applying them. I think idea of trying to understand before remembering ends up impairing learning at least in my case. I have a two year old and I see this process in action. She will first cram things like counting and then start attaching meaning to it slowly.
  - OJFord 10y ago
    There are some things we must remember, of course. A child has no choice but to memorise the digits. Axioms, essentially. When it comes to addition however, any attempt to learn addition by tabulation and memory would clearly be futile. I certainly don't mean to suggest that one should study a theorem in a particular corner of mathematics from fundamentals up; rather understand it "one level down", to something previously interned in a similar manner (and since forgotten because one no longer had need of it) or to somemething axiomatic. For example, say I come across an equation for the area of a right triangle for the first time. I've previously understood and accepted some other problem that I can reduce it to - area of a rectangle, say, or integration - so I can do so and actually understand why, and be able to reproduce it. Easier to learn, recall, and apply than rote memorisation in my opinion.

OJFord 10y ago

I agree to the extent that once understood, things need (presumably!) to then be remembered. I suppose people's methods differ, but personally I don't think I could have an effective memory without understanding, and that my memory follows understanding. By "effective memory", I mean that I could actually apply some definition, not merely remember the pattern of notation on the page. I fancy if I learnt it from a flash card I'd struggle when variables were named differently, or with the slightest variation in form.

drieddust 10y ago
I used to be in your camp but now I think they go hand in hand. If you insist on understanding before remembering, how do you start? When we start a lot of things are interrelated and unless you a bare minimum is committed to memory, it's difficult to start. It is akin to learning a language where one need to cram the basics building blocks i.e. words and grammar rules before applying them. I think idea of trying to understand before remembering ends up impairing learning at least in my case. I have a two year old and I see this process in action. She will first cram things like counting and then start attaching meaning to it slowly.
- OJFord 10y ago
  There are some things we must remember, of course. A child has no choice but to memorise the digits. Axioms, essentially. When it comes to addition however, any attempt to learn addition by tabulation and memory would clearly be futile. I certainly don't mean to suggest that one should study a theorem in a particular corner of mathematics from fundamentals up; rather understand it "one level down", to something previously interned in a similar manner (and since forgotten because one no longer had need of it) or to somemething axiomatic. For example, say I come across an equation for the area of a right triangle for the first time. I've previously understood and accepted some other problem that I can reduce it to - area of a rectangle, say, or integration - so I can do so and actually understand why, and be able to reproduce it. Easier to learn, recall, and apply than rote memorisation in my opinion.