Application Of Combination Of Number And Shape In Analytic Geometry

This article focuses on the analysis and research of the application of “combination of number and shape” in high school mathematics analytic geometry education and teaching,focusing on the following aspects of current high school mathematics teaching by means of questionnaires: students’ interest in analytic geometry;the thinking method of using the“combination of number and shape”;the habit of solving problems;the degree of adaptation to the "combination of number and shape" thinking method,and the difficulties and problems in the application.This article analyzes the specific application of the “combination of number and shape” in high school mathematics analytic geometry teaching from the perspective of cases.On this basis,it also uses the form of field interviews to discuss the current high school mathematics analytic geometry teaching based on the teacher’s goal and thinking of the method of “combination of number and shape” in the current high school mathematics analytic geometry teaching.Combining with the previous investigation and research questions,this article puts forward targeted improvement strategies and suggestions,as well as testing and analyzing the actual application effect of the “combination of number and shape” thinking method in high school mathematics teaching.This research is divided into 5 parts.The first part is the introduction,focusing on the introduction of the research background,the questioning,the purpose and significance of the research,the ideas and content of the research,and the research methods.The second chapter is the definition of related concepts and the basic part of the research theory,focusing on the origin of “number-shape combination”,the concept of “number-shape combination”,the application principles and approaches of “number-shape combination”,and its application value in high school mathematics teaching together with interpretation and analysis of the status and role of the applied cognitive psychology and the theoretical basis of constructivism.The third chapter is the application strategy of combining number and shape in analytic geometry,focusing on the relationship between number and shape,how the two complement each other,and the effective transformation,etc.,and analyzing the common parameter ranges and maximum values in analytic geometry.Questions,fixed-point problems and fixed-value problems etc.are summarized.Based on this,the basic thinking strategy of analyzing and combining problem solving in the combination of number and shape is proposed.The fourth chapter is the application and practice research of the combination of number and shape in analytic geometry,focusing on the comparison and analysis of the degree of interest,participation and results achieved by the combination of number and shape in high school mathematics analytic geometry teaching.The fifth chapter is summary and reflection,focusing on summarizing and prospecting the results of this research,reflecting on the problems and deficiencies in the research,and looking forward to future research directions and target measures.