Which *practical* methods could help me solving math problems?

I will approach this question by splitting it into two parts:

Q1: How can I *make notes* that support thinking about math problems in the best possible way?

Q2: How can I *use thinking tools* that are helpful in solving math problems?

In Q1, I find the following aspects important:

- How can notes help me to develop ideas and to think straightforward?
- How can I add reflections on my thinking, to see what works well and what doesn’t?
- How can I deal with multiple approaches and chains of thought without getting lost?
- How can I store sudden ideas for later examination?

In Q2, I’m puzzled by the following things:

- How can I find useful representations of the problem?
- How can I generate and exploit seminal ideas that eventually lead to a complete solution?
- How can I deal with obstacles, mathematical and otherwise?

Answers to Q1 and Q2 are obviously closely linked, so I’m aiming at an “integrated method of math problem solving” – it’s not just about note-making and not just about thinking tools, but about combining both for good results.

This is the program for the following posts.

The next post is about note-making technique.

I’m focused on these topics for several years now, and I have written previous posts about them, see here or here. What I present now is a thoroughly revised version.