Investigation And Research On High School Students' Problem Representation Ability In Solving "Plane Analytic Geometry" Problem

In mathematics teaching,cultivating students' problem-solving ability and improving students' problem-solving efficiency are not only the focus and core content of mathematics educators' research,but also the important goal of mathematics teachers' teaching.Cognitive psychologists believe that problem representation is the first step of problem solving,the choice of problem representation and the flexible transformation of various representation modes have an important impact on the process and result of problem solving.During the internship,the author found that many students could master the definition and related formulas of plane analytic geometry.However,in the process of solving practical problems,the information in the problem cannot be connected with the existing knowledge,encountered obstacles in the process of using words,symbols and graphics to represent the information of the question,which ultimately led to incorrect or incomplete problem solving.Therefore,students have obstacles in the process of problem representation.This study investigate the problem representation ability of senior high school students in the process of solving "plane analytic geometry" problem.Through literature research,the meaning,methods and characteristics of mathematical problem representation are defined,and students are divided into three levels according to their usual scores.Conduct the following studies: Firstly,students' psychological behavior and emotional state when solving plane analytic geometry problems;Secondly,the correlation between problem representation and solving plane analytic geometry problems;Thirdly,the present situation of students' representational characteristics in solving plane analytic geometry problems,and the differences in problem representation among students of different levels and genders;Fourthly,What are the factors that affect students' problem representation ability?The following conclusions are obtained: Most students can realize the importance of plane analytic geometry knowledge,but due to the difficulty and comprehensive,some students do not have high interest and lack of confidence;There is a positive correlation between high school students' problem representation ability and problem solving when solving plane analytic geometry problem.In the process of problem solving,students are weak in the diversity of problem representation,and often encounter obstacles in the process of switching from literal representation to symbolic representation;There are significant differences in problem representation ability among students of different levels.There is no significant difference in problem representation ability between students of different genders in solving analytic geometry problems.Through further analysis of oral reports and interviews,the influencing factors of problem representation mainly include topic information,mathematical knowledge system,students' own habits and psychological factors.Based on the research conclusions and the actual classroom teaching,the corresponding teaching suggestions are put forward as follows:(1)pay attention to the diversity of knowledge representation;(2)attach importance to the topic;(3)overall grasp of mathematical knowledge to build knowledge framework.