A Practical Study On Problem Solving And Teaching (Design) Based On Pólya’s Problem Solving Theory

As we all know,there are common problems among students when studying plane geometry,such as improper learning attitudes,lack of self-confidence,difficulties in reading,recognizing and drawing figures,weak reasoning and proof abilities,insufficient understanding of theorems and concepts and inability to correctly convert graphical language,textual language and symbolic language.During my internship at a junior high school in D county,I conducted a survey of students and teachers on the problem-solving situation in plane geometry through questionnaires and interviews.Based on Pólya’s theory of problem solving,I carried out practical research on problem solving and teaching(design)using the examples of plane geometry problems in junior high school,and proposed a problem-solving chart for plane geometry problems,presenting a teaching design.This thesis consists of five chapters.The main contents of each chapter are as follows.Chapter 1 is the introduction,including the reasons and significance of the topic selection,the research status at home and abroad,the research content and methods of this thesis and its innovation.Chapter 2 is based on the four stages of Pólya’s problem-solving chart.Through questionnaires and interviews,it is found that students encounter the following problems when solving plane geometry problems: insufficient understanding of the problem,unclear problem-solving methods,inflexible problem-solving processes,and lack of reflection and summary after problem-solving.This provides a research basis for subsequent problem solving and teaching(design)practices.Chapter 3 is a research on problem-solving and teaching practices based on Pólya’s problem-solving theory.A general problem-solving strategy is proposed: first,carefully read the problem and clarify the known information and what needs to be proved;second,draw the figure and simplify the known conditions,marking them;then,ponder over the geometric concepts and relevant properties and theorems mentioned in the problem;after that,check the problem-solving steps patiently to ensure that the problem-solving method is correct and meets the writing specifications;finally,test the answer and summarize the relevant theorems and thought processes involved in problem-solving.Chapter 4 proposes a problem-solving chart for junior high school plane geometry problems based on the research conclusions of problem-solving and teaching practices,and applies it to teaching practices,presenting a teaching design.Chapter 5 is the conclusion and outlook.