Design And Research Of Elliptical Teaching From The Perspective Of HPME

In recent years, the international History and Pedagogy of Mathematics (HPM) field,Psychology of Mathematics Education (PME) field is developing rapidly, more and more scholars and researchers are no longer engaged in theoretical research, access to teaching.Therefore, the teaching practice has become one of the most important research directions in the field of Mathematics Education. The combination of HPM and PME teaching practice will bring a different direction in high school mathematics teaching.The content of conic curve is one of the important contents of high school mathematics, is the core of plane analytic geometry, The study of ellipse is the beginning of conic curve, the introduction of the concept and the derivation of the equation is the basic idea of using algebraic method to study geometric problems in analytic geometry.Based on the existing research, this study chooses elliptical teaching as the carrier.From the perspective of the History of Mathematics and Psychology of Mathematics Education (HPME), and design the HPME teaching in practice of classroom. The study arrange the theory of mathematics history and mathematics education.On this basis, build bridges between HPM and PME,guide teaching practice from a new perspective -HPME.The study chose two key senior high school to carry on the teaching of the ellipse and its standard equation, one class carried on the normal teaching, and the other three classes respectively carried on the experiment teaching, divides into the class 1, class 2,class 3.The research questions are:how to combine HPM and PME for HPME teaching;to explore the influence of students' knowledge, understanding level and emotion, attitude and values based on HPME elliptical teaching practice;to explore the Enlightenment of the development of teachers' professional knowledge HPME based on elliptical teaching practice.This study used a variety of research methods to collect data, including interviews,questionnaires, classroom record analysis. Through the quantitative analysis of the data,as well as the qualitative analysis of the interviews and classroom records, the research conclusions are obtained.Based on the questionnaire test before and after the four teaching, the change of students' cognition of ellipse and cognitive level was analyzed.Analyed classroom elements in HPME through classroom teaching record, and determine the level of communication and integration of HPM, PME. The development of teachers in the field is analyzed through interviews with teachers .Finally, the research results are summarized.The main conclusions of this study are:(1)Students' understanding of the definition of ellipse shows some similarity.Flexible use of the definition needs to be improved, most levels of understanding are at A or B levels, and can not reach the level of flexible use.(2)Using comparative analys, after normal teaching and experimental class teaching,it was found that the students' understanding level of HPME teaching method was significantly higher than that of other methods, so takimg the HPME perspective, can help students to deepen their understanding of what they have learned.(3)After the teachers experience teaching in HPM, PME and HPME, their HPM,PME teaching knowledge and teaching ability has been greatly improved.(4)HPM, PME in classroom teaching design can effectively communicate, in order to improve teaching effect.