Practical Methods of Solving Math Problems – a Restart

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.

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.

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