Research On Teaching Design Of Integrating Mathematical History Into Trigonometric Function

Trigonometric function is a kind of important basic elementary function that students learn in senior high school,and it is the key point and difficult point of teaching.for a long time,senior high school students have been staying in the ability to calculate and do problems for trigonometric function.But I can't understand the nature of trigonometric functions.This is because trigonometric functions connect geometry and algebra and combine trigonometric and functional knowledge.The deepening of the concept of function and trigonometric function from junior middle school to high school will lead to strong cognitive conflict among students.There are obstacles in students' understanding of the concept of trigonometric function.they are not used to the representation of trigonometric function from trigonometric ratio to coordinates.The problems encountered by these students in learning reflect the shortcomings of teachers in teaching,and teachers do not pay enough attention to these cognitive conflict problems.The history of mathematics reflects the causes and development process of mathematics,reveals the essential characteristics of mathematics,in line with the cognitive law of students,the occurrence of students' knowledge and the development process of human knowledge has similar attributes.This study chooses trigonometric function as the carrier,carries on the teaching design and the teaching practice from the angle of mathematics history,summarizes the strategy of integrating the mathematics history into the classroom teaching,develops the teaching mode,and carries on the further teaching design.The purpose of the paper is to integrate the history of mathematics into the trigonometric function teaching on the impact of students,so through classroom observation,questionnaire feedback and other methods to collect data.The author records the teacher-student interaction and student-student interaction in class,and assists in collecting data in the form of recording.after class,the author carries out simple questionnaire feedback and interviews with students.In order to understand the history of mathematics on the students to learn the trigonometric function part of the trigonometric function knowledge.Data processing is mainly a qualitative research method,assisted by quantitative research.In the aspect of quantitative research,according to the results of "Student feedback questionnaire",the results are analyzed and discussed in detail;in qualitative research,combined with the data collected from classroom observation,detailed analysis and discussion are carried out.The main work of this study is as follows:1.The history of trigonometry and trigonometric functions.After consulting a large number of literature,this paper combs the occurrence and development history of trigonometry and trigonometric function,takes the origin,development and independence of trigonometry as the main line,and sorts out the historical resources of trigonometric function with educational value.On this basis for the follow-up trigonometric function part of the knowledge of the teaching design to pave the way.2.The present situation of the teaching of "cosine formula of two-angle difference".The author carried out classroom observation and questionnaire survey in the classroom of two front-line teachers in order to truly understand the current situation of teaching and analyze the problems existing in teaching and learning.After investigation and analysis,the author summarizes three problems:(1)the "geometric method" of the formula is not familiar with the knowledge,(2)the derivation of the formula is not paid enough attention to in the process,and(2)the derivation of the formula is not paid enough attention to in the process.(3)the classroom activity of emotion is not high,and the enthusiasm of learning needs to be strengthened.3.Form the history of mathematics into the trigonometric function of the teaching design process.This paper puts forward the selection principle of mathematical historical data and the application method of mathematical history in teaching design,and forms an operable teaching design framework from the perspective of mathematical history.4.Carry on the teaching design under the angle of view of the history of mathematics and verify the teaching effect.The results show that the selection of appropriate historical materials into the teaching design can improve classroom efficiency,is effective for breaking through thinking difficulties,and can improve students' interest in learning.It makes students realize the cultural value of mathematicst.