Ebook: The Art of Problem Posing

The Art of Problem Posing is a great book. The authors provide a step by step method for learning about, and solving problems in, mathematics. The method is as follows:
Level O:
Choose a starting point ie a problem or a concept in math
Level 1:
Define the attributes of a problem or concept
Level 2:
Ask what if not for each concept.
Level 3:
Ask Questions about the results of 0 - 2.
Level 4:
Analyze (solve) the problem

The authors use fairly accessible math in the process of explaining their techniques, including the Pythagorean Theorem and a few other concepts that most people will know.

I want to emphasize that this book is not just about problem posing; it also offers a technique for problem solving. The authors note that the two cannot really be completely separated.