Investigation And Research On The Level Of P Roblem Representation In Solving The "Conic Section" Problem Of High School Students

As the core content of mathematics education,problem solving has a pivotal position in actual teaching,and it has also been a long-term research hotspot in mathematics education circles at home and abroad.Problem representation is the most critical link in the process of problem solving.It is a cognitive structure constructed by students in the process of problem solving,and it is also a process of systematic representation of the conditions implicit in the problem.In addition,the study of analytic geometry can well exercise students' thinking quality and problem-solving ability.Therefore,studying the level of representation of high school students in the process of solving "analytic geometry" problems will not only help students develop their problem-solving skills,but also help teachers develop targeted teaching practices.This article mainly starts from two aspects of literature research and empirical research.In terms of literature research,the core concepts such as problem representation,problem solving and representation level are mainly determined,and the relevant theories to be used in this article are also determined.In terms of empirical research,first designed questionnaires and test papers based on literature,and then selected 439 second-and third-year high school students from HY Middle School in Shaanxi Province for investigation.The following contents are specifically studied:(1)Through the questionnaire survey to understand the mental behavior of students when solving the conic problem;(2)Five representation methods including "conceptual representation,property representation,equation representation,geometric representation and comprehensive representation” Design test papers to evaluate the differences in representation levels of different students in solving conic problems,and analyze the impact of mathematical representation on solving mathematical problems;(3)Propose problem-solving teaching principles from the perspective of representation based on the results of the survey,and Combining the teaching principles,take the"maximum and range,fixed point and fixed value problem in the comprehensive problem of conic section" as an example to make corresponding teaching design,as well as the deficiencies of this research and the future prospects.The main conclusions of the research are as follows:(1)Most students have the confidence and interest in learning conic section knowledge,and have good problemsolving habits in the problem-solving process;(2)The overall level of problem representation of high school students is low(3)The level of conceptual representation and property representation of students is slightly higher,while the level of equation representation,geometric representation and logical representation is low;(4)There is a significant difference in the representation level of boys and girls,and the representation levels of high school students and high school students There are significant differences in level;(5)There is a certain positive correlation between the test scores of high school students' representation level and their usual scores.