Research On Problem-solving Teaching Based On Polya's Problem-solving Thought

The "General High School Mathematics Curriculum Standard(Experimental Draft)" pointed out: "Mathematics teaching should create problem situations based on reality to help students learn independently and guide students to acquire knowledge,skills and improve thinking ability through practicing,exploration,and communication.".In the teaching of mathematics problem-solving,teachers should guide students to conduct thinking activities and improve students' ability of thinking and problem-solving.However,in the actual problem-solving teaching process,it is found that the development of students' ability is often only reflected in the imitation of the problem-solving steps,and the expected teaching effect is not achieved.George Polia is a famous mathematician in the 20th century.He believes that solving problems can teach students to improve their ability to discover and solve problems.Therefore,he has conducted decades of research in problem-solving.Polya divides the problem-solving thinking process into four stages: clarifying the problem,plan,operation,and reviewing.In these four stages,common sense and universal issues are used to inspire people to engage in thinking activities,acquire knowledge and skills.The article investigate the problems,confusion and problem-solving habits of students in the process of problem-solving through questionnaires,test papers and interviews,analyzes the causes of problem based on the statistical results.These causes include: did not master the method of reviewing questions,lack the consciousness of independent thinking,did not pay attention to the logic of the problem-solving steps,and did not form the habit of retrospective reflection.Therefore,the article summarizes the corresponding problem-solving teaching tasks according.Combined with Polya's problem-solving thoughts,the article proposes corresponding problem-solving teaching strategies for the task of problem-solving teaching: guiding students to fully interpret the problem conditions and analyze the problem flexibly in the stage of clarifying the problem,refining the content of the problem and guiding students to analyze and internalizing the knowledge they have learned in the planning stage,strengthening training of contrast problem group andone method multiple problems group,analyzing the advantages and disadvantages of the problem-solving methods,and improve students' computing ability in the stage of operation.In the review phase,students are cultivated in the habit of collecting mistakes and reviewing the problem-solving process through independent lecturing.In order to combine with actual teaching,this article expound the application of the problem-solving teaching strategy in pre-class preparation,classroom teaching and after-class reflection.In terms of pre-class preparation,it is necessary to choose the question group form reasonably,and pay attention to the effectiveness and purpose of the classroom question setting.In classroom teaching,students should be given sufficient time and space for independent thinking,and their thinking process should be exposed as much as possible.In terms of after-school reflection,it is necessary to reflect on whether the choice of sample questions reflects the conventional problem-solving ideas and methods,and whether the problem setting conforms to the law of students' cognitive development.Finally,this paper compares and analyzes the questionnaire survey data through SPSS16.The analysis results show that the problem-solving teaching strategy can improve students' ability of problem-solving and thinking.