The Cosine Formula Of The Horns' Sum And Difference Of Instructional Design From The Perspective Of HPM And The Teachers' MKT Study

Trigonometry plays an important role in the high school mathematics curriculum.Not only it is an important model to describe the phenomenon of the real world cycle,but also it's one of the basic elementary functions in textbooks for senior high school;students may not in-depth understanding of the concepts,formula and theorems of trigonometric functions,but can acquire these by the historical development of trigonometric functions.With the deep research for Mathematics History and Mathematics Education(History & Pedagogy of Mathematics,referred to as HPM),Chinese new curriculum standards of mathematics began to pay attention to the history of mathematics,meanwhile increased 11 topics that related to the history of mathematics.In mathematic teaching,teachers also be required to teach mathematic history,develop student's mathematics history accomplishment.Related research shows that mathematics history not only can help students more understand the mathematics,but also can promote teacher to teach mathematical knowledge(Mathematical Knowledge for Teaching,MKT).The purpose of this article is to explore the influence of teaching of two angles and difference formulas on students 'knowledge of trigonometric functions in HPM perspective,and the influence of mathematics history on teachers' knowledge of trigonometric functions.In this study,a high school mathematics teacher in a middle school in Luzhou,W and his classes were chosen as the research object.In view of HPM corners and teaching design difference cosine formula as a tool,study the history of mathematics into effect of trigonometric function teaching for students.At the same time,the author analyzes the influence of the history of mathematics on Teachers' knowledge of trigonometric function in combination with teachers' interviews.The conclusions of this study are as follows:1.Students learning trigonometric function(1)HPM perspective under the angle and the difference cosine formula teaching,can help students better memory and in-depth understanding of the formula.(2)Students to understand the history of the development of trigonometric function,can stimulate students' learning motivation of trigonometric function,to understand the process of trigonometric function knowledge,to reveal mathematical knowledge is the product of human culture,and the change of mathematics is only formula and algorithm and so on.2.The influence of the history of mathematics on teaching trigonometric function.(1)The influence of the history of mathematics on the content knowledge of teachers.The history of mathematics can help teachers better understand the related concepts,formulas and theorems of trigonometric functions,the teacher through the occurrence and development of the reduction of trigonometric function knowledge,consciously "Deconstruction" teaching materials,teaching materials will be compressed,the static knowledge of the trigonometric function,reverse trigonometric function and dynamic process of knowledge.(2)The influence of the history of mathematics on Teachers' teaching content knowledge.The teacher through the understanding of trigonometric functions related to history,to better understand the textbook knowledge of the trigonometric function arrangement,and presentation;promote teachers to fully understand the students in the learning of trigonometric function knowledge problems,and understand their mistakes;enrich the teachers' classroom teaching experience of three angle function,such as the use of Ptolemy's theorem is derived and two difference the cosine formula.