Application Of The Polya’s Problem-Solving Theory To Eighth-Grade Dynamic Geometry Problems

Dynamic geometry is a key and difficult problem in middle school mathematics learning,which requires students to master knowledge and solve problems.In daily teaching,students’ solutions to dynamic geometry problems are not very optimistic,so it is necessary to carry out research on solving dynamic geometry problems.Based on the Polya’s problem-solving theory,this paper adopts a variety of research methods to carry out theoretical exploration and practical research.The research questions are as follows:(1)The current situation of solving dynamic geometry problems for Grade 8 students;(2)How to promote the teaching of dynamic geometry problems in junior middle school by using the Polya’s problem-solving theory.Firstly,this paper introduces the research status at home and abroad,Polya’s problemsolving theory and the research of dynamic geometry problem solving through literature research.Then according to the curriculum standards,textbooks and dynamic geometry problems related research design test paper,combined with the idea of solving the problem design questionnaire,to understand the actual situation of students solving problems.The results show that most of the students read the question at least twice in the stage of understanding the problem,and there are errors in the movement representation(such as direction,speed,path,critical point).In the planning stage,students can use some problemsolving methods(such as tool awareness,specialization,reverse thinking,transfer,etc.),but there are problems such as "improper classification,ignoring the applicable conditions of formula theorems,and insufficient mining of implicit conditions".In the implementation stage,students will miss the steps to solve the problem,resulting in simplification and calculation problems.In the review stage,students lack the review consciousness,which is reflected in the weak reflection consciousness of wrong questions,and the weak awareness of the induction and transfer of problem-solving methods.It is worth noting that students often make more than one kind of problem solving mistakes.Secondly,combining with the Polya’s problem-solving theory,this paper puts forward teaching suggestions according to the current situation: in the stage of understanding the topic,teachers should pay attention to the teaching of basic knowledge and problem reading methods,so as to improve students’ ability to recognize and translate information;In the planning stage,students can use mathematical problem-solving strategies such as pattern recognition,and mathematical problem-solving ideas such as analogy,classification and discussion to help students improve their ability to dig hidden conditions.In the implementation stage,students should develop good problem-solving habits,such as self-questioning,accurate calculation,independent thinking;In the review link,we should cultivate the reflection consciousness after the question and make good use of the wrong question,accumulate experience in solving the question.The application of the above advice is presented in the form of a teaching case.Finally,the teaching experiment is used to test the teaching effect of the of Polya’s problem-solving theory in the eighth grade dynamic geometry problems.The experimental results show that the average score of the experimental class is 7.9 points higher than that of the control class,which verifies the validity of Polya’s problem-solving theory.Through the interview,it is found that students prefer the teaching mode under the Polya’s problem-solving theory,and the new teaching mode has the most obvious improvement on the problem solving habits and ideas of the underperforming students.