Research On High School Mathematics Problem Based On Polya’s Problem-Solving Idea

This thesis conducted a questionnaire survey and interviews based on the Polya problem-solving model rooted in logical reasoning.The results indicate that high school students have poor problem-solving habits,and their thinking processes align poorly with the Polya problem-solving model.Additionally,there are limitations in their understanding and comprehension of logical reasoning skills.Furthermore,teachers face obstacles in the process of teaching derivatives and lack effective teaching methods to develop students’ logical reasoning skills.In response to the teaching issues mentioned above,this paper explores high school mathematics teaching strategies from the perspective of logical reasoning skills,guided by the Polya problem-solving approach.Firstly,through extensive literature review and research,the Polya problem-solving model is effectively combined with logical reasoning,and three stages of problem-solving are identified based on the four-step process: thinking,reasoning,and reflection.Secondly,employing the method of case analysis and using recent years’ college entrance examination questions as the basis,the application of the Polya problem-solving mindset in derivative problem-solving is studied.Based on the analysis,specific strategies are proposed to develop logical reasoning skills under the Polya problem-solving approach: in the thinking stage-apply heuristic teaching to develop analogical reasoning abilities;in the reasoning stage-emphasize procedural teaching to develop deductive reasoning abilities;in the reflection stage-cultivate good thinking habits and develop inductive reasoning abilities.Finally,derivative problem-solving teaching cases are designed based on the teaching strategies and classroom practices are conducted to validate their effectiveness.