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Comment by crazygringo | Hacker News Reader

Can you give an example?

I'm not saying math practice isn't useful -- after all, that's what homework problems are for, to figure out which concepts apply and use them. Repetition itself is useful.

But in my experience, this doesn't benefit from being spaced over time, and it's more about achieving full understanding of the concept.

You seem to be describing pattern recognition, but pattern recognition is conceptual -- you need time/experience to build that up, but it can be done in a day and doesn't need to be revisited days/weeks later in order to not be forgotten.

What kind of math content do you think benefits from repetition that is necessarily spaced over time?

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In my experience, which is graduate level mathematics, spaced repetition is essential. Once you get beyond basic mathematics and algebra, recalling and understanding concepts and definitions is essential. This is true at the calculus level where you need to remember things like the chain rule, integration by parts, various theorems, etc. But it is even more true at the higher levels of mathematics where there are many more theorems, lemmas, and definitions to remember. I find that at that level, just having a huge depth of recall for definitions alone is incredibly useful. If you remember enough definitions you can start to piece things together. If you can recall theorems, lemmas, and some key proofs you can achieve quite a bit.

Personally, I only understood logarithms after memorizing the log laws using spaced repetition. I had been taught logarithms before descriptively, but only once the equations were in my head could my brain make sense of how they work.

Good example. I know people frown on memorization, but personally I would say the following are useful to know deeply:

- Log laws

- Exponent laws

- Derivative rules

- Probability laws

- Combinations/Permutations

- Matrix algebra

- more?

When you're reading through math derivations, or trying to work one out yourself, you absolutely need to have some basic literacy in these rules.

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