The Application Of Polya Problem-solving Model In Mathematical Problem-solving Teaching In High School

Problem solving is an essential work in mathematics learning, problem-solving errors also tend to be an inevitable phenomenon in mathematics learning, so it is crucial for teachers to grasp problem-solving teaching correctly. Polya problem-solving has been widely used in mathematics problem-solving teaching. Teachers tend to pay more attention to how to promote students'problem-solving efficiency and problem-solving capabilities in problem-solving teaching, while ignoring the importance of depth exploration into students'problem-solving errors This paper through in-depth analysis of Polya problem-solving model, and refinement it to concrete steps, and then apply it to high school mathematics problem-solving teaching, try to use problem-solving model to identify and analyze student errors. The main research question of this paper are:(1) what is the connotation of Polya problem-solving model? (2) how to use the Polya problem-solving model to identify students'errors in problem-solving? (3) how to use the Polya problem-solving model to analyze students' problem-solving errors? (4) how to use the Polya problem-solving model to guide the students to overcome obstacles in problem-solving process?The basic structure of this paper is:Chapter 1 is an introduction, mainly on the background of the problem, significance of research and research status. Research status includes two aspects. One is the research status of Polya problem-solving thoughts, and the other is research status of problem-solving errors.Chapter 2 is the Polya problem-solving model. Mainly includes two parts, one part is the overview of problem-solving model.In this part, some classic problem-solving models will be introduced. The other part is a detailed analysis of Polya problem-solving model. Chapter 3 is the expansion of Polya problem-solving model. This part is the core of this thesis, mainly analyze the sub-phase of the four stages of Polya' problem-solving model, thus expands the problem-solving model and error model. In addition, the paper also briefly describes the analyze angle of problem-solving error. Chapter 4 is the applications of Polya problem-solving model. This section through four cases to illustrate how to use the Polya problem-solving model for solving problem, looking for problem-solving errors, analyzing errors and guiding students to overcome obstacles in problem-solving process. Chapter 5 is an case study. In this case, the Polya problem-solving model will be used for identifying and analyzing the student's problem-solving errors. Chapter 6 is research conclusions. Primarily give the thesis conclusions and recommendations...