Research On Problem-solving Teaching Strategies To Improve Students’ Mathematical Thinking Ability Based On Polya’s Problem-solving Theory

Improving students’ mathematical thinking ability is the core of Polya’s problem-solving theory and the fundamental purpose of middle school mathematics education.With the advancement of the new college entrance examination reform,the current college entrance examination questions are becoming more flexible,the background is becoming more complex,and more emphasis is placed on testing students’ mathematical thinking abilities.It is urgent to explore a problem-solving teaching strategy aimed at improving students’ mathematical thinking ability,in order to transform the previous standardized problem-solving teaching methods.Polya’s problem-solving theory provides a problem-solving approach centered on improving students’ mathematical thinking ability.This study first analyzes the current research status at home and abroad,and then conducts a questionnaire survey to understand the mathematical thinking and problem-solving abilities of students at three different levels of schools in Jinan.Considering the teachers’ understanding of Polya’s problem-solving theory,a problem-solving teaching strategy based on Polya’s problem-solving theory is proposed to ensure students’ subjectivity.Finally,two teaching design cases for exercise classes are provided.The main content of this study is as follows:1.Based on Polya’s problem-solving theory,this paper designed a questionnaire on senior high school students’ mathematical thinking ability,a test paper on senior high school students’ problem-solving ability,and a questionnaire on teachers’ understanding of Polya’s problem-solving theory.The questionnaire investigated the mathematical thinking ability and problem-solving ability of students from three different levels of schools in Jinan,as well as the understanding of 48 teachers about Polya’s problem-solving theory.Using SPSS and other data analysis software to analyze the results of the questionnaire and test papers,it was found that the students’ mathematical thinking abilities in the three schools were above average,and there was no significant difference;Senior two students’ problem-solving ability is above the average,and there is no significant difference;The ability of senior three students to solve problems is greatly affected by the difficulty of the problem,and is generally at a medium level,with no significant difference.Teachers have a certain understanding of Polya’s problem-solving theory and have certain applications in practical teaching.2.Based on the results of the questionnaire,the training direction of mathematical thinking ability was determined.According to the "How to Solve Problem" table of Polya,a problem-solving teaching strategy was proposed to improve students’ mathematical thinking ability based on Polya’s problem-solving theory.The specific strategies are as follows:(1)cultivate students’ mathematical thinking ability of mathematical sense and judgment,mathematical representation,and mathematical modeling in the process of understanding problems;(2)Cultivate students’ mathematical thinking abilities of inductive conjecture and plausible reasoning,logical thinking,and deductive proof in the process of formulating plans;(3)In the process of implementing the plan,cultivate students’ mathematical thinking abilities in mathematical calculation and transformation,mathematical calculation and algorithm design;(4)In the process of reflection,cultivate students’ mathematical thinking abilities of mathematical connection,mathematical insight,rational thinking,and constructing systems;(5)Develop students’ mathematical thinking abilities in data collection and analysis,geometric intuition,and spatial imagination in the topics of probability and statistics,and geometry.3.According to the results of the questionnaire and test paper,this paper selected one exercise class from the two knowledge modules of probability and statistics and conic curve,where students’ mathematical thinking ability and problem-solving ability are weak,and gave a teaching design based on the problem-solving teaching strategy given earlier.In the probability and statistics section,the exercise course "Contingent Tables and Independence Testing" was selected to mainly cultivate students’ abilities in data collection and analysis,as well as various basic mathematical thinking abilities;The exercises of "Standard Equation of Ellipse" are selected for the conic section section to cultivate students’ basic mathematical thinking abilities.