The Thinking Of Solving Mathematical Problem Indirectly And Research On Teaching Practice

It is an important mathematical thought to solve a problem indirectly when you have difficulties in solving it directly. The importance of the thought can not only be found in the process of solving a mathematical problem, but also in many other aspects. If students can be trained to think in this way when solving mathematical problems, they will develop an effective pattern of thinking, which can improve their ability to solve problems in daily life.The thesis first analyzes the history of the idea of solving a problem indirectly while difficult to solve it directly applied in the field of mathematics, the theory proposed by Polia, as well as the application in solving specific problems, which form the theoretical foundation of the idea of solving a problem indirectly while difficult to solve it directly. Following this, it will research several specific methods to solve problems representing the mathematical thought, including analytical method, proof by contraction, transformation of converse proposition, formation of counter example, complementary set, and so on. It explains the detailed process of the application of every method in solving problems, their features, and the questions types they can solve.In the fifth chapter, it provides two teaching cases in which the thought of solving a problem indirectly while difficult to solve it directly on the basis of personal experience. The thesis intends to probe into how to inspire and train students to think with the mathematical thoughts and enable students to put the thought into practice in daily life. In the last part, it provides some personal suggestions on teaching practice.