Mathematical Problem-solving Strategies Of Thinking And Its Teaching

Problem is the heart of mathematics. The real mathematics component is problems and problems-solving.The key purpose of mathematics education is to develop the students' ability to solve the mathematics problems. This thesis analyses thinking strategy in solving mathematical problems and its instruction. It includes four parts. (1) First, the author discusses the conception and basic properties of mathematical problems with educational values in accordance with the situation in the middle school education, pointing out that mathematical problems must be suit for the students. Second, combining the theory of modern cognition psychology, the author gives a very general account of the conception , basic properties and thinking model of the solution of mathematical problems. (2) Following thinking model and the phase of the solution of mathematical problems, the author probes into a certain number of thinking strategies ,and analyses their apply conditions, operate principles, the aim of which is to guide instruction. (3) Adopting the method of thinking aloud, the author researches the distinguishing characteristics of the thinking strategies in the process of the solution of mathematical problems. It shows which thinking strategies are often used by senior middle school students , and shows which one existes defect. Basing on the research, the author puts forward some instruction suggestion indicates the purpose of which is to help the problem-solving instruction. (4) The author elaborates educational significance, instructive ways and means on thinking strategy training.