In an earlier entry, I had mentioned the first five of Polya’s ten commandments for teaching. In a similar fashion to that entry, here are the last five rules with some comments on them:
6. Let them learn to guess: guessing can be a pathway to proof (in the case of mathematics) and discovery (in the case of sciences). The key is to make more educated guesses. It helps if an easier approach can be taken. In algorithm design, we are also used to first trying out easier methods and then resort to more subtle approaches.
7. Let them learn proving: proving is indeed the central aim in mathematics. However the logical thinking involved in proofs can be a useful lesson in many fields.
8. Look for useful features of the problem: while tackling any mathematical problem, we have always been taught to identify any features of the problem which may show the way to the solution. It is almost like a detective utilizing clues to understand what happened.
9. Do not give away the whole secret at once: a teacher who kills the thinking process of the student is hardly doing a good job. It is a challenge to keeps things interactive in a class every time. However it is a no-brainer that spoon-feeding does not help.
10.Suggest but do not force: keeping a student interested is better than putting too much pressure on him or her. The power of suggestion is also relevant when a student makes a mistake. It is helpful to nudge the student in the right direction rather than drive him there. This is also better for the student’s self-esteem.