Research On The Teaching Of Basic Inequality Problem-Solving Based On Polya’s Theory Of Problem-Solving

Inequalities are the most basic quantity relations in mathematics,and learning inequalities can develop students’ independent learning ability,analytical ability and inductive reasoning ability.As an important chapter of inequality,basic inequality is also an important bridge between middle and high school mathematics,so it is of great value and significance to study the teaching of solving basic inequality.The "How to Solve Problems" proposed by the mathematics educator Polya is a general approach to solving mathematical problems,and his "How to Solve Problems Table" is of great significance to the study of mathematical problem solving.Therefore,the study of teaching basic inequalities based on Polya’s problem solving theory is the subject of the thesis.This study is based on the problem-solving theory of Polya and the teaching of basic inequalities by using literature research,questionnaires,test papers and interviews.At the same time,on the basis of Polya’s "How to solve a problem table" and Polya’s mathematical education ideas,the research results on Polya’s problem solving theory and basic inequalities are reviewed.Firstly,the questionnaire was used to understand the students’ application of Polya’s problem solving theory in the process of learning basic inequalities,and the test papers and interviews were used to understand what problems existed in the process of solving and teaching basic inequalities for students and teachers.Secondly,based on the results of the above survey,we propose four stages of problem teaching strategies for Polya’s problem solving theory.The main teaching strategies are as follows: in the problem-solving stage,one is to guide students to examine the problem independently and develop good problem-solving habits,and the other is to focus on the introduction link before class to stimulate students’ interest in learning.In the planning stage,one is to guide students to change their way of thinking,and the other is to guide them to explore the essence of the problem.In the implementation stage,one is to focus on developing students’ metacognitive skills and the other is to focus on the formation of students’ core literacy.In the review and reflection stage,one is to focus on cultivating students’ awareness of problem sets,and the other is to focus on variable teaching.Finally,the proposed problem-solving strategies are used to develop corresponding teaching design cases and applied to the actual teaching of basic inequalities.