Research On Teaching Design Of Sinusoidal Theorem In High School From HPM Perspective

Sine theorem is an important proposition in trigonometry and one of the important theorems in high school mathematics.In the traditional teaching process,the teaching of the theorem is too boring,students generally do not have a high interest in the essence of "sine",can use the sine theorem to solve mathematical problems,but can not deeply understand the mathematical beauty of the sine theorem and the application value of the sine theorem.From the development history of trigonometry,we can know that sine theorem came into being with the development of astronomy,navigation,geography and so on,and has a close relationship with our life.It can be found from the existing research on the integration of the history of mathematics into the sine theorem that the teaching of the sine theorem from the perspective of HPM can well make up for the shortcomings of traditional teaching and improve the quality of teaching.Therefore,this paper will study the teaching design of the sine theorem from the perspective of HPM.The research questions of this paper are:(1)How is the teaching status of sine theorem?(2)How to prepare the teaching design scheme of sine theorem from HPM perspective?(3)How to evaluate the teaching design scheme?Based on the HPM teaching concept,this study studies the teaching of sine theorem.The main contents include:(1)Overview of the history of the sine theorem,including the origin of the string table,the development of the sine function,the 10 methods of proving the sine theorem.(2)To understand the teaching status of sine theorem through teacher questionnaire survey.(3)Combined with the teaching status,the teaching design of sine theorem from the perspective of HPM was conceived.The idea is divided into two steps: The first step is to construct the overall teaching design,and select the mathematical historical materials that fit the teaching theme.The historical materials selected in the introduction of theorems are the introduction of sinusoidal history,the historical materials selected in the exploration of theorems are Ptolemy’s construction of sine table and Mei Wenting’s proof method,and the historical materials selected in theorems proving are Harris’ s Zao Gao method.The historical material selected for the application of the theorem is the building survey problem in the history of mathematics.The second step is to carry out specific teaching design conception,and apply the selected materials of mathematics history to four parts:topic introduction,theorem exploration and proof,classroom exercises and homework.(4)Present a complete teaching design scheme of sine theorem from the perspective of HPM according to the teaching design concept.(5)Implement the teaching design scheme,conduct student questionnaire survey and teacher interview,and then feedback the teaching effect based on the performance of students in the class taught by the author.Through the feedback of teaching practice,it is found that the teaching scheme of sine theorem from the perspective of HPM designed by this research has the following characteristics:(1)Introducing the subject with "video + history of mathematics" is more conducive to stimulating students’ interest in learning;(2)Retracing the path of mathematician exploration is more conducive to students’ understanding of the essence of sine theorem,stimulating students’ confidence to learn mathematics well and cultivating students’ spirit of exploration;(3)Integrating the history of mathematics helps to enrich students’ spiritual world;(4)Integrating the history of mathematics into the teaching of sine theorem is helpful to cultivate the core quality of mathematics of students.