Application Of Polya's Problem Solving Thought In Problem Solving Teaching ——Taking Conic Curve And Equation As An Example

George Polya is a famous Hungarian American mathematician.By reading and sorting out the classic works of Pappus,Descartes,Leibniz and Polchano,and combining the background of philosophy,logic and psychology,he published the classic work guided by heuristic teaching-"how to solve problems".The core of the book is the great achievement of problem-solving Art-"how to solve problems table",It is divided into four links: understanding the topic,making a plan,implementing the plan and reviewing.Conic curve and equation are the key and difficult points in the whole high school mathematics teaching.Their examination forms are relatively comprehensive,which can be combined with the knowledge points of each module,as well as the combination of geometry and algebra.When solving the synthesis problem of conic and equation,there are many problem-solving methods,but not all of them are applicable.How to find the appropriate problem-solving method and solve the problem correctly is the focus of problem-solving teaching.In view of the strong abstraction of conic and equation problems,the wide range of knowledge points examined and the difficult application,Polya's problem-solving thought helps to simplify the logic and operability of the problem,and plays an inestimable role in strengthening students' problem-solving ability.In order to better realize Polya's problem-solving thought to guide problem-solving teaching,the research questions of this paper are set as follows:(1)How do students perform in solving conic problems without any theoretical guidance? What are the shortcomings? Can these deficiencies be improved by using Polya's problem-solving thought?(2)After applying Polya's problem-solving thought,have the problems of students in solving conic problems been improved? In addition to improving the correct rate of problem solving,what abilities have students improved?Based on the above problems,this paper will take the literature analysis method for sorting and analysis,with the help of questionnaire survey and interview,and combined with case analysis method for practical testing.In the questionnaire survey,92 students in parallel classes in the sophomore year of Harbin No.6 middle school were selected as the test objects,and the pre-test and post-test were adopted.The pre-test was committed to understanding the implementation of students in the four links of Polya's "how to solve problems table",and the post-test was committed to testing the effect of Polya's problem-solving thought and problem-solving teaching strategy;The focus of the interview is to understand students' problem-solving ability,problem-solving attitude and problem-solving difficulties.According to the investigation and analysis,the following teaching strategies are obtained: in the stage of understanding the topic: 1 Accurately excavate known conditions,2 Multiple interpretation of the topic;In the planning stage: 1 Strict analysis,fine analysis,problem cultivation 2 Pay attention to foundation laying and continuous thinking training,3 Enhance the transformation of thinking and strengthen reasonable reasoning;In the implementation plan stage: 1 Explore the general method of question types,summarize the laws and principles,2 Strengthen multiple occurrences of the same problem and improve logical thinking,3 Analyze problem-solving methods and cultivate efficient problem-solving;In the review stage: 1 Summarize the causes of problems and achieve breakthroughs one by one.2 Turn passivity into initiative and consolidate the problem-solving process.In the application of strategy,the six common test problems summarized by combining the college entrance examination questions over the years: trajectory equation,unity problem related to conic curve,maximum value problem,fixed-point problem,exploratory problem and "adjoint circle" problem are applied.Finally,according to the comparative analysis before and after the application of teaching strategy,the effect of Polya's application in problem-solving teaching strategy is obtained.The conclusions of this paper are as follows:(1)In the feedback of the questionnaire,it is found that the students do not understand the topic carefully,do not interpret the known conditions deeply enough,the problem-solving ideas are vague,the understanding of the problem-solving steps is rigid,the computing ability is weak,and the reflection after class is not in place.(2)According to the results of the questionnaire,in view of the students' careless understanding of the topic and the lack of in-depth interpretation of the known conditions,The known,condition and unknown can be classified in the "understanding topic" link,and the known conditions can be replaced in combination with the derivation of formula and theorem,so as to gradually move closer to the unknown;for the case of fuzzy thinking of problem solving,the problems that have been done in the past can be connected in the "making plan" link,so as to carry out association and build the thinking from the known to the unknown;In the case of rigid understanding of problem-solving steps and weak computing ability,students can explain the problem-solving steps in the "implementation plan" link,take appropriate verification,and strengthen the mastery of computing principles at the same time;For the situation that the reflection after class is not in place,the students can make a secondary proof in the "review" link,and apply the conclusion to other topics to verify the mastery of knowledge.