Research On The Design And Application Of Mathematical Generative Teaching From A High-Point Perspective

High viewpoint,that is,middle school mathematics from high point of view,is a teaching and research activity that reveals the meaning of "generation" of secondary school mathematical knowledge from the perspective of mathematical knowledge.Under the current concept of core literacy-oriented high school mathematics curriculum,the research of secondary school mathematics teaching from a high perspective has become a research perspective,which can point out the direction for the development of mathematics generative teaching.The problem of ellipse fixing is a common problem type in high school plane analytic geometry,and it is also an important content in the college entrance examination review stage,but there are drawbacks that need to be improved urgently in the current teaching.In view of this,this study constructs the basic framework of mathematical generative teaching design from a high-perspective perspective,and applies it to the teaching of elliptic valuation problems in high schools,in order to promote the formation and development of students’ core literacy in mathematics and improve the teaching status of elliptical valuation problems in high schools.In this study,literature research,questionnaire survey and semi-structured interview were mainly used.Based on the research on the literature related to middle school mathematics,generative teaching and high school elliptic valuation problems from a high point of view,research enlightenment is obtained from existing research,and the research is mainly carried out from the following two parts:The first part is to build the basic framework of mathematical generative instructional design from a high-perspective perspective.First of all,clarify the meaning of the high-point generative mathematical knowledge concept,which means that by organically linking different local mathematical knowledge,it can generate mathematical knowledge that integrates with each other and form a unified viewpoint;Secondly,the theoretical basis of this research is clarified,including F.Klein’s ideas on mathematics education,R.Curran’s views on mathematics education,and Pierce’s "schema reasoning";Finally,on the basis of relevant concepts and theories,the basic framework of mathematical generative teaching design from a high-perspective perspective is constructed.From a highperspective perspective,the generative teaching design of mathematics includes three components: teaching goal design,teaching content design,and teaching process design.Among them,the teaching objectives should be designed to combine "mastering specific knowledge" with "comprehension of high perspectives";Teaching content design should pay attention to the selection and transformation of typical cases;The design of the teaching process should promote the three links of "joint construction→operation→ generation" in turn.The second part is to apply the mathematical generative teaching design from the perspective of high viewpoint to teach the high school ellipse fixing problem and test the application effect.Firstly,the essence of ellipse valuation problem and its educational value are analyzed from a high-perspective perspective.Secondly,through student questionnaire survey and teacher interview survey,it is analyzed that the main problems in the teaching of elliptical valuation problem in high schools are: focusing on presenting the solution results while ignoring the generation process,not revealing the essence of ellipse valuation problem,and not fully reflecting the educational value of ellipse valuation problem;Then,according to the basic framework of mathematical generative teaching design from the perspective of high viewpoint,the mathematical generative teaching design of elliptic valuation problem from high perspective is proposed and implemented.Finally,through student questionnaire survey and teacher interview survey,the application situation is analyzed and application suggestions are proposed.The survey results show that mathematics generative teaching from a high-perspective perspective can promote students’ experiential learning,understand the essence of mathematical content,and improve the core literacy of mathematics.Therefore,the teaching effect of using mathematical generative teaching design from the perspective of high school ellipse valuation is better,which can effectively improve the teaching status of high school ellipse fixing problem.This study not only enriches the theory of secondary school mathematics teaching from a high perspective,but also provides a teaching idea and implementation path for core literacy-oriented high school mathematics classroom teaching.It is hoped that teachers can establish a high-point awareness of mathematics,and carry out the design and implementation of mathematics generative teaching from a high-perspective perspective in combination with specific mathematics teaching content in actual teaching.