Mathematical Thought And Its Application In High School Conic

"Equation of conic curve" is one of the important contents of high school mathematics,it has a rich realistic background and extensive practical applications.When students learn the "equation of the conic curve",they are mostly superficial in understanding,and it is difficult to achieve a deep understanding of its essence.Therefore,it is very necessary to explore the effective teaching strategy of "equation of conical curve",optimize its teaching design,and deepen the students' understanding of "equation of conical curve".The idea of mathematics was proposed by the Dutch mathematics educator Freudenthal,who believed that the real world process,namely mathematics.In the process of learning,students must go through the four levels of situational,reference,universal and formal level to complete the understanding of the nature of mathematical knowledge.Through experiencing the mathematical process,students can not only understand the background of mathematical knowledge,but also deeply understand the essence of mathematical knowledge.Therefore,it is of some practical significance to apply mathematics to the teaching design of "conical equation".How to use the mathematical idea to guide the teaching of "conical curve equation" ?In order to form a scientific understanding,firstly analyze the literature related to mathematical thought and "conical curve equation",then investigate the teaching status of "conical curve equation" in mathematics classroom from the perspective of students and teachers,and analyze the attribution results,thus provides the theoretical basis for the teaching strategy and teaching case design.The survey found that students' understanding level of "cone equation" can basically reach situational level and reference level,but the learning effect of general level and formal level is not ideal;the learning effect of students will directly affect the learning effect of the next level.As can be seen from the students 'answer paper,the students' understanding of the definition of the conic curve,the standard equations and other basic knowledge is not thorough enough.The interview found that although the first-line mathematics teachers are different in the analysis of "conical equation",they generally agreed to consolidate the basic knowledge of "conical equation"."conical equation" has important educational value;the front-line mathematics teachers do not have much understanding of mathematics,and rarely apply mathematical thought in real teaching,which refers to pedagogy and psychology while emphasizing teaching knowledge.Finally,based on two high school mathematics teaching cases,the teaching strategy of "conical equation" is proposed: to extract and analyze the mathematics to reach a higher level;problem-driven way to describe mathematical objects and to introduce example training and guide students to construct mathematical cognitive structure.According to the above teaching strategy,the teaching part of "equation of conic curve" is designed for the reference of front-line mathematics teachers.