Common Strategies And Cognitive Analysis Of High School Students To Solve The Conic Focus Triangle Problem

The focus triangle of conic curve is a hot issue in college entrance examination and various mathematical examinations.Its information covers plane geometry,trigonometric function,triangle solution,analytic geometry and other fields of knowledge and methods.It is an important observation point in the study of senior high school students' mathematical cognitive status.What are the commonly used problem-solving strategies for senior high school students in solving the focus triangle problem? In order to understand the tendency of problem-solving strategies and cognitive status of high school students when they encounter the focus triangle problem,the author searched the relevant journal literature and found that almost all articles only stay on one problem and multiple solutions of the topic itself,lacking the research and analysis of students' cognitive level of the corresponding problem-solving process from the perspective of students.Based on the discovery of the problems and the reflection of the current research situation,the author defines the research content as "the common strategies and cognitive analysis for senior high school students to solve the problem of the focus triangle of conic curve".Through literature analysis,the analysis of the real questions of college entrance examination and interviews with teachers,the author establishes three types of typical problems of the focus triangle(the focus triangle of angle,the focus of centrifugal rate).The triangle problem involves the focus triangle problem of the median line.Based on the interviews of the front-line teachers,the improved test scale is continuously debugged.Finally,263 senior high school students are tested in three representative schools.Based on SOLO classification theory,the cognitive level analysis and problem-solving strategy orientation analysis of students' problem-solving process of solving focus triangle problem are carried out according to the test situation.Based on the thinking process of students' problem-solving,the author makes a statistical analysis of the path of problem-solving strategies used by students,and classifies the situation of each strategy by SOLO classification theory.The study finds that students solve the focus triangle problem,present diversified thinking strategies,and generally have a higher level of knowledge of some of the strategic paths.This paper obtains learning through investigation and statistical analysis.Students' common strategies to solve the focus triangle problem are analyzed in detail from the cognitive level.Finally,relevant teaching suggestions are given according to the research results.