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Application Of Polya’s Math Problem Solving Theory In Geometry Proof Problems Of Junior High School

Posted on:2022-05-29Degree:MasterType:Thesis
Country:ChinaCandidate:W J JinFull Text:PDF
GTID:2517306752973219Subject:Subject teaching
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To learn mathematics,we must first learn how to solve problems.As one of the key questions in junior middle school mathematics course,the geometry proof question occupies an important position in the middle school examination.At present,most students often make various mistakes when solving geometric proof problems,which makes it difficult to improve their problem-solving ability.The four links of Polya’s theory of problem solving provide a very meaningful way for students to solve problems and have a good reference value.Therefore,the application of Polya’s problem solving theory to solve the junior high school mathematics geometry proof problem is the problem to be discussed in this research.This dissertation takes Polya’s theory of problem solving as the guiding ideology and adopts a variety of research methods to carry out theoretical analysis and practical investigation.Through the literature analysis,this dissertation introduces the four links of Polya’s problem solving theory,the research status at home and abroad and the problem solving research of related geometric proof in detail.Questionnaires prepared by referring to curriculum standards,mathematics textbooks and related counseling materials are used to understand students’ actual situation of problem solving.At the same time,interviews with teachers and students are combined.Through the statistics and analysis of the wrong questions of the students in the questionnaire,the mistakes of the students in the four links are sorted out as follows:in the part of understanding the meaning of the questions,the common mistakes are misreading the requirements of the questions,confusing the known conditions of the questions,misreading the known conditions,misunderstanding the theorem and concept,and failing to understand or understand the written proposition.In the process of planning,the mistakes that are easy to appear are not good at digging out the hidden conditions,not adding auxiliary lines or adding auxiliary lines wrong,and not mastering the basic knowledge firmly.In the execution of the plan,the most common errors are errors in calculation and handwriting,routine skipping,and other non-intellectual factors.In the review section,common mistakes include not developing the habit of post-question reflection and sorting out the wrong questions.In view of the mistakes made by students,the corresponding teaching strategies are put forward.In the link of understanding the topic meaning,first of all,it is necessary to cultivate students’ habit of examining the topic seriously.Secondly,the teaching of theorems and concepts should be strengthened.Finally,it is necessary to strengthen the conversion training between students’ mathematical languages.In the process of drawing up the plan,the students’ ability to dig out the implicit conditions should be cultivated first.The second is to pay attention to the students to add auxiliary line training.In the implementation of the plan,we should first pay attention to the cultivation of standardized writing format of students.Secondly,it pays attention to the cultivation of strict logic of students’ proof.The third is to pay attention to the cultivation of students’ metacognitive monitoring ability;Finally,it is to pay attention to the dynamic role of non-intellectual factors.In the review link,we should pay attention to the cultivation of students’ habit of reflection after questions and students’ habit of sorting out wrong questions.
Keywords/Search Tags:Polya’s theory of problem solving, Geometric proofs, Problem solving status quo, Teaching strategy
PDF Full Text Request
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