A Study On Teaching＆Learning Of Trigonology From The Perspective Of HPM ——A Case Study Of Review Lessons Of Sine Theorem,Cosine Theorem And Sum Of Angle Formulas

Plane trigonometry is not only an important content of high school mathematics,but also a popular and high-frequency test conten of college entrance examination.Its rich mathematical history can provide ideas,materials and methods for teaching,and mathematical review course is an indispensable and important link in mathematical teaching.The integration of mathematical history into review course can be used as a new exploration direction of HPM.This paper mainly uses the methods of literature research,questionnaire survey and individual interview to study the teaching and learning of trigonometry from the perspective of HPM.This paper analyzes and compares four kinds of domestic mainstream new and old textbooks;sorts out and compare the literature according to HPM research and review course research;sorts out the mathematical history data related to Sine theorem,Cosine theorem and Sum of Angle formulas,to select appropriate mathematical history data to integrate into the teaching design according to the investigation of learning situation;understands the students’ learning situation and their views on the integration of mathematical history into mathematics teaching through questionnaire survey and individual interview after teaching practice.Through teaching practice,combined with questionnaires and individual interviews,taking the review course of Sine theorem,Cosine theorem and Sum of Angle formulas as an example,the following conclusions are obtained:1.Under the guidance of teachers,students have the interest and ability to prove the relationship among Sine theorem,Cosine theorem and Sum of Angle formulas and Projective formula.The discussion and exploration of them can not only tests students’ mastery,but also expands students’ thinking.In the review class integrated into the history of mathematics,students are also more active,can actively participate in discussion and exploration,they have a higher degree of classroom participation,they eliminate fear in derivation,establish mathematical self-confidence,improve learning enthusiasm,and realize that mathematics is not only mathematical knowledge,but also mathematical culture.2.In this study,I obtained many mathematical historical materials related to trigonometry,and learned to look at mathematics from multiple perspectives such as society,culture and life;I understood that the difficulties of students in mathematics learning have historical similarities,and the teaching design should be based on the problems reflected by students;I felt that mathematics can also be created by students;In addition,the history of mathematics also plays an enlightening and guiding role in students’ mathematics learning after class.