High School Calculus Teaching Research Under The HPM Perspective

End of the17th century, Newton and Leibniz independently created calculus,which makes variable mathematics since the founding of analytic geometry, enter thegolden period of development in an all-round way. The creation of calculus is not only agreat victory of mathematics, but also human science. In order to adapt to thedevelopment of the Times, calculus teaching has become an important part ofmathematics teaching on China’s current high school calculus teaching. And， Owing tothe distinctive position in the mathematical development and the difficulty which isharder than other knowledge, calculus has become the emphasis and difficulty of highschool mathematics curriculum.History and Pedagogy of Mathematics research is through the history ofmathematics into mathematics education research which has now become an importantmethod of the mathematics education research, and plays a reference role in the face ofmathematics education.The main research method in this article is literature research method andcomparative research method, and draw the below conclusions by HPM view:Firstly, concerning the meaning of high school calculus teaching and learning, it isnot only the excellent means of exercising thinking and the important mathematicaltools for further study in learning, but also the important carrier to carry mathematicsculture.Secondly, under HPM view high school calculus teaching content analysis. Fromthe knowledge level, it is necessary to carry out basic calculus teaching in high school,however the strictly limit theory teaching in high school is not necessary. From thecultural level, by analyzing the history of the development of calculus and its impact,this article reaches calculus historical and cultural inspiration for middle school students.They include: being good at asking questions, being good at looking at problems frommultiple perspectives, Being not afraid of difficulties and moving forward, Being adhereto friendly competition, Taking the initiative to communicate. Finally, this article designs a differential case and an integral case, and provide thereference to middle school teacher by the two cases.