The epistemological approach to education suggests that the best way to learn a subject is to learn how to think like the experts in the field: how to think like a scientist; how to think like an historian; how to think like an engineer; etc.
How to think like a mathematician is Kevin Houston‘s attempt to explain how one mathematician at least approaches problems. To whet your appetite, he has a free pamphlet, 10 Ways To Think Like a Mathematician, which starts off with:
- Question everything, and
- Write in sentences
Logic is, apparently, quite important.
If you want to understand mathematics and to think clearly, then the discipline of writing in sentences forces you to think very carefully about your arguments.
— Kevin Houston: 10 Ways To Think Like a Mathematician
It’s an interesting introduction to how mathematicians see the world, and its a useful reminder that many of the ways of thought that apply to any field can be useful in other places, or even in life in general.