How to Solve It
By George Polya
A classic book about problem solving, How to Solve It seems an excellent metacognitive tool, or collection of tools, for how to frame problems, tease them apart, and search for solutions.
It’s all about applying mathematical principles to “any problem that can be reasoned out”. It’s described as an “[e]lementary textbook on heuristic reasoning” — and while it has a mathematical focus, it seems applicable to many areas.
Polya was renowned as an influential mathematician as well as a great teacher, and this is one of the most successful math books ever written…raising the question: why didn’t I ever read this in schoo?!
I like the structure — it starts with two pages listing essential questions and outlining the problem solving process, followed by an explanation of the purpose this list, and a short dialogue. The main section follows: a “Short Dictionary of Heuristics” with 67 sections on various problem solving approaches. Things like: analogy, carrying out, decomposing and recombining, diagnosis, figures, generalization, induction, notation, puzzles, symmetry, and more.
It seems a book ahead of its time, encouraging active learning and attempting to foster deep understanding of how problems can be approached more fruitfully. One great feature: the book ends with a section containing 20 short practice problems, which makes this particular useful as a tool for both learning and teaching!