Improving Mathematics Teaching Through Scientifically Setting Mathematical Problems

Mathematical problems and mathematical problem solving are an essential concern of mathematics teaching, and a lot of research has been done in this field by many scholars at home and abroad. However, much of the work mainly focuses on the methods of mathematical problem solving, leaving comparatively less touched the principles, methods and process of the setting of mathematical problems themselves, which are discussed in this thesis.This thesis consists of 7 chapters, among which chapter 2 and chapter 6 constitute the core. Chapter 2 starts with an analysis of the properties and development of mathematical thinking with high school students. This is followed by the definition of two critical notions——mathematical problems and the setting of mathematical problems. In addition, examples are given to illustrate six principles of the setting of mathematical problems, i.e., scientific, appropriate, effective, well-focalized, rigid and aesthetic.Categorization of mathematical problems is a tough work, mainly because results may vary due to different view points taken by different viewers. Based on current domestic opinions as well as our teaching practice, three categories of mathematical problems are distinguished in this thesis , namely, ordinary, competence-oriented and experimental mathematical problems.In chapter 3 we define ordinary mathematical problems and discuss their setting methods. With the help of examples, we elaborate in five aspects on the methods of careful selection and construction of qualified mathematical problems.In chapter 4 and 5, we discuss the definition and setting methods of competence-oriented mathematical problems and experimental mathematical problems respectively respectively, focusing on the properties of the former and the patterns of the latter.In chapter 6 we discuss the setting of three major types of mathematical problems at high school level, i.e. choice, blank filling and problem solving, focusing on the wording, selection, tested points, construction, and examining function of mathematical problems.In the appendix, we give three episodes of our teaching practice to demonstrate how to set mathematical problems.