Research On The Conic Curve Problem Solving Based On Polya's Theory Of Problem Solving

As the core of plane analytic geometry,conic curve possesses the dual identities of geometric form and algebraic form.It is a bridge that connects geometry with algebra,playing an important role in enhancing students' mathematical competencies and cultivating students' capacity of symbolic-graphic combination.Since conic curve problems themselves involve a large amount of thinking and operation,students have not done well in the problem solving in the university entrance exams over the years.Therefore,it is necessary to carry out research on conic curve problem solving.This thesis takes Polya's theory of problem solving as the theoretical basis,and comprehensively adopts literature review,questionnaire survey,interview,and classroom observation methods to carry out theoretical research and practical exploration.Firstly,the author investigates students' current status on conic curve problem solving and teachers' status on problem solving teaching.Secondly,based on the research findings and Polya's table from How to Solve it,the thesis proposes the problem-solving model on conic curve problems.Finally,the thesis adopts the problem-solving model in the solution seeking and teaching of conic curve problems,proposes teaching suggestions for various problem-solving stages,and offers teaching cases.Major conclusions of the research include:(1)students' current status on conic curve problem solving and teachers' status on problem solving teaching.(2)The problem-solving model for conic curve problems.Step One,understand the problem.Use Symbolic and text language to represent known conditions and solution-seeking targets;draw corresponding figures and properly mark them;use coordinate and equation to represent dot and curve respectively;and dig implied conditions.Step Two,devise a plan.Properly convert the conditions;describe geometric objects or relations;and seek for the correlation between conditions and targets.Step Three,carry out the plan.Patiently do the operation and write down the process.Step Four,look back.Verify the process of problem solving;consider other solutions;summarize the key to solutions;and try to promote solutions.(3)Suggestions on the teaching of conic curve problem solving at each stage.At the stage of understanding the problem: Stress multi-representations and the digging of implied conditions.At the stage of devising a plan: guide students to rationally convert conditions,cultivate students' algebraic translation ability,and stress the application of knowledge on plane geometry.At the stage of carrying out the plan: Cultivate students' operation capacity and problem-solving will.At the stage of looking back: Strengthen reflection on problem solving and offer the teaching of multiple solutions to one problem.