The Teaching Research Of Analytic Geometry Based On The Comparison Of Thought Path Between Descartes And Fermat

With the in-depth advancement of the basic education mathematics curriculum reform,related research on the core literacy of mathematics has become a hot and difficult point in the field of mathematics education.The in-depth integration of mathematics history and education reveals the origin of mathematics concepts,ideas and methods.Researchers are paying more and more attention to its important role in "grasp the essence of mathematics,inspire thinking and improve teaching".Analytical geometry,which is centered on the combination of numbers and shapes,is an important content of high school mathematics.And the combination of numbers and shapes is an important connotation of the core literacy of mathematics discipline such as mathematical abstraction,intuitive imagination and mathematical operation.Following the research paradigm of "why mathematics",this paper discusses the thought path of Descartes and Fermat in establishing analytic geometry based on mathematics education orientation,focusing on their similarities and differences in ideas and methods.At the same time,this paper explores the historical enlightenment and teaching significance,and applies its thinking method to the teaching practice of analytic geometry.Taking the teaching design and implementation of "hyperbola and its standard equation" as an example,this paper explores the effective path to implement the core literacy of mathematics discipline,verifies the teaching strategy based on "historical similarity principle",and reveals the educational value and practical significance of the history of mathematics for mathematics education,offers relevant teaching suggestions on the in-depth integration of mathematics history and mathematics education.