# An approach to learning math that does not emphasize problem solving

I know there have been many popular threads about how to learn math, and that it is universally agreed that solving problems is a key part of the learning process.

However, I would like to hear what is specifically wrong or inefficient or suboptimal about the following approach to learning math, which emphasizes understanding proofs but not solving problems at the end of the chapter:

1) When you read a math book, before reading a proof of a theorem, first try to prove the theorem yourself. (It's hard to say how much time should be spent on this step.)

2) When you read the proof, try to understand it very clearly. This includes trying to understand the intuition behind the result, and understand how someone might have thought of the proof (even if you were unable to prove it yourself). Possibly consult other books for more enlightening explanations.

3) Check that you understand the theorems and proofs well enough that you could state the theorems and write down proofs yourself. Write down the proofs on paper or using latex, trying not to look at the book for help. Ideally, you might often find that your explanation is a little more clear, in your own opinion, than the explanation given in the book.

Throughout this process, no time is spent solving end of chapter problems.

• It is not meaningful to discuss optimality without stating an objective. May 8, 2017 at 22:46
• Well, let's say that the objective is to master / understand deeply a particular math subject in a reasonable amount of time. May 8, 2017 at 22:48
• Maybe in that case you are right. It could simply be that not everyone agree on that objective. May 8, 2017 at 22:57
• @mathreadler Out of curiosity, what other objectives do you have in mind? Developing problem solving ability? May 9, 2017 at 7:05
• There can probably be many different reasons/objectives. Just wanted to give you the idea that differing objective functions could be the case. May 9, 2017 at 8:41