Research On Trigonometric Function Teaching Based On Polya's Problem Solving Theory

Trigonometric function plays an important role in high school mathematics teaching,and this part of knowledge plays an important role in the development of students' logical thinking ability and innovative practice ability.However,because there are more trigonometric formulas and more abstract content,students' problem-solving situations and learning effects are not good.Polya,an American mathematics educator,devoted his life to the research of mathematics education,based on his own educational experience,he put forward "How to Solve the Problem Table",which is of great significance to the teaching of mathematics problem-solving.This paper is based on Polya's theory of problem-solving and combines it with trigonometric function teaching.At first,this paper introduces the research background,research problems and significance as well as research ideas and methods.At the same time,based on Polya's problem-solving theory and constructivism theory,we summarize the research status of Polya's problem-solving theory and trigonometric function at home and abroad and then form the theoretical basis of this paper.Secondly,the present situation of trigonometric function learning and teaching in senior high school is investigated and analyzed.According to the literature analysis and internship experience,the questionnaire and interview outline are made,and the survey is carried out from the two dimensions of students and teachers.The questionnaire is designed from the following aspects: Students' interest in learning,the analysis of problems,the monitoring of problem solving,and the review.The conclusions are as follows:(1)Students lack interest,enthusiasm and initiative in learning trigonometric functions;(2)Students' problem-solving habits are not good,which are specifically manifested in the lack of examination and understanding of the problem,lack of overall grasp of the problem,unclear ideas,chaotic and lax problem-solving steps,and few after-class review and reflection.The interview with the teacher involved 7questions,we have investigated the current situation of the teacher's trigonometric function teaching and the level of understanding and views on Polya's problem-solving theory.Then,according to the problems existing in the teaching of trigonometric functions,combining the requirements of the new curriculum standard and the characteristics of trigonometric functions,four teaching strategies are put forward under the guidance of Polya's theory of problem-solving:(1)Guide the students to understand the problem in depth and analyze the known conditions;(2)Pay attention to the overall grasp of the problem conditions,the construction of problem-solving ideas;(3)Strengthen the cultivation of students' self-monitoring ability;(4)Cultivate the habit of reviewing and reflecting after solving problems.Finally,given the current situation of trigonometric function teaching,taking Polya's problem-solving theory as the model,two teaching design cases(new teaching and exercise class)are given,and the experimental group and the control group are set up for implementation.It is found that the experimental group is better than the control group,and there is a statistically significant difference between the two groups.The conclusion that the trigonometric function teaching effect based on Polya's problem-solving theory is better is obtained.