By this point in the course you have already met many problems: literal equations, systems, plane-geometry proofs, exercises on similarity and on Pythagoras’ theorem. You will have noticed that not all of them are solved “in one go”: some require you to stop, reorganise your ideas, try a route and — if it does not work — go back and try another.
In this chapter we try to give a shape to that “thought process” that takes place (often in a disordered way) in your head when you tackle a problem. Many of the ideas presented belong to a pedagogical tradition that runs from George Pólya to more recent contributions, such as those of John Mason: books in which every page is an invitation to reflect on the way of thinking, rather than on the single result. The four “moves of the problem-solver” — understanding, searching for a route, carrying out, reviewing — are the guiding thread, illustrated step by step on two guiding problems: a rectangle whose perimeter and area are known, and the bisector of an isosceles triangle.
Sections
- The four moves of the problem-solver
- First move: understanding the problem
- Second move: searching for a route
- Third move: carrying out
- Fourth move: reviewing