Following the posts on note-making in math and on basic thinking tools, here come first ideas on thinking tools for math problem solving.

Finding a solution to a math problem can be broken down into parts in several ways – for example by asking questions.

A first useful catalogue of questions could look like this, where each main question is followed by more specific ones.

(The catalogue is *massively* inspired by the famous list of questions from George Polya’s classic book “How to Solve It”. – Polya’s list is reproduced here.)

The next posts shall give *some* answers to these questions.

How can I get started?

- How can I approach a problem? Are there established methods that work for a large variety of cases? How can I use them?
- How can I represent a given problem, using equations, diagrams and other means that allow a math treatment?

How can I construct a solution?

- How can I generate seminal ideas? What
*methods*can I use to generate ideas? - How can I exploit these ideas?
- How can I start from what is given and work forward?

How can I start from the end and work backward? - How can I decide whether to proceed with an idea or whether to try a new one?
- How can I deal with multiple ideas?

Should I produce several of them and pick the most promising one, or should I start with one and remodel it until it works?

How to deal with obstacles?

(This part is closely connected to the previous and the next one.)

- How can I make sure I
*realize*there are obstacles that need attention? - How can I use established ways of dealing with obstacles?
- How can I analyze an obstacle?
- How can I generate ideas to overcome an obstacle?

How to deal with other troubles?

- How can I deal with frustration, with the impression that I’m no good at math, with a lack of interest?

How to look back?

(This part is not exactly necessary, but a great opportunity to improve problem solving skills.)

Remember: Looking back should happen *not only at the end*, but also on the way!

- What’s bothering me? What doesn’t feel right?
- How can I clarify these intuitions?
- How can I check if my solution is correct?
- What can I learn from what I’ve done so far?

Finding answers to these questions may lead to a collection of math problem solving tools. Read more in the next post.