Problem-Solving Process

A great discovery solves a great problem but there is a grain of discovery in the solution of any problem. Your problem may be modest; but if it chanllenges your curiosity and brings into play your inventive facilities, and if you solve it by your own means, you may experience the tension and enjoy the triumph of  discovery.

---George Polya, How to solve it.

In trying the problems in tutorial sheet, some students may encounter some difficulties such as `I don't understand the questions'  or  `I understand the question, but I don't know what or how to do?'  or  `I have done/proved it this way, but how do I know whether it is correct or wrong?' or `OK, I am sure I have done the problem correctly, but this problem seems to have another way of doing it.' We hope that the following problem-solving process will be helpful to you when you are doing problems in mathematics. This process is natural to many of us who have done much in mathematics. Usually, you hear people saying, `I know how to do this, by experience'. This is quite true.

Problems in mathematics tutorial are selected with some aims: some are routine questions for familiarization with the skills, some are conceptual problems, some are open-ended questions

Step 1 Understand the problem

Step 2 Devise a Plan

Some useful strategies are

Step 3  Carry Out the plan

Step 4 Look Back