Research On Teaching Design Of Ellipse From The Perspective Of HPM

The conic section is an important part of the plane analytical geometry.It is the continuation of the study of the "preliminary plane analytical geometry " in the compulsory phase.The ellipse serves as the initial content of the conic section.It is not only a continuation of the straight line and circle content in the preliminary analysis geometry,but also the basis for learning the parabola and hyperbola.The ellipse learning experience has a good analogy value for learning parabola and hyperbola.In the new curriculum standard,it is required that ellipses be used as the carrier to highlight the mathematics idea of the combination of numbers and shapes in the teaching.Therefore,the ellipse is the curve that is focused on in the conic section.However,in practical teaching,it is found that students generally lack interest in learning about ellipses,and they feel confused about the similarities of the conceptual nature between ellipses and hyperbola.The computational complexity of calculations also makes students fear.Traditional instructional design focuses on the logical sequence of knowledge,and to a certain extent neglects the cognitive order of students.Meanwhile,under the teaching pressure of college entrance examination,teachers also have the phenomenon of “instillation” in pursuit of “high efficiency”.Compared with conventional teaching design,the teaching design of HPM perspective pays more attention to the occurrence and development process of mathematics content,and plays a unique role in enhancing the students’ interest of learning and promoting their understanding and mastery of mathematics content.This paper will discuss the teaching design which integrates the history of mathematics into elliptical teaching from the theory of HPM.Firstly,in the research the history of the ellipse is sorted out and the materials used for teaching design are selected.Secondly,the questionnaire system is designed to understand the emotional attitude of the rural high school students to the oval content,the understanding of the concept,equation and nature of the ellipse.By interviews,it is known that the villages and towns high school teachers’ teaching methods of the contents of the elliptical,the situation of integrating the history of mathematics into the class,and their attitude to the integration of the history of mathematics as well as the problems in the teaching of elliptical;Finally,based on the present situation of teaching,the concept,equation and nature of the ellipse are designed from the perspective of HPM.Compared with conventional instructional design,the study finds that the elliptical instructional design of HPM has the following characteristics:(1)The history of mathematics can be integrated into the concept of teaching to help students understand the concept of ellipse;(2)Mathematical history can be used to reduce the amount of computation in equation teaching,and deepen students’ understanding of the relationship between circle and ellipse;(3)The introduction of the origin of eccentricity helps students understand the definition of eccentricity.