| Sine function was an important part of trigonometric function.As not only a bridge between geometry and algebra but a powerful tool to solve problems of geometric and algebra,trigonometric function was one of the main study contents of mathematics in middle school.However,the trigonometric function learning was plaguing the majority of middle school students.According to the characteristics of students' thinking and the need to learn other contents,the teaching of trigonometric function was divided into two sections: phase of junior high school and senior high school stage in middle school mathematics teaching material edited by People's education press.The sine was generally defined by “Ratio method to define sine”,“Terminal boundary definition method” and “unit circle definition method”.According to academician Jingzhong Zhang's teaching practice for many years,it was found that the concept and formulas of trigonometric function was simpler by using the area method.And the sine was defined by area of "unit diamond",which developed a new definition system of trigonometric function for junior high school mathematics teaching(referred to as the "new system" hereinafter).In this paper,according to the existing teaching materials and the new system of teaching and based on teaching experiments,the teaching effects of different definitions of sine method were compared.This research mainly included: 1.By consulting the related literature and books,the history and orientation of the sine function were expounded,a more comprehensive understanding of sine function's historical development and its background were form,the status of trigonometric in middle school mathematics was confirmed;2.The content and knowledge structure of triangle function in different teaching materials were compared,and the teaching plan of the different sine's definition methods were studied;3.Based on survey results of teaching experiment,the teaching effects of different definitions of sine were evaluated on the point of view of teachers and students,respectively.Through the analysis of teacher interview and student questionnaire and level test,it was found that early learning the new definition of sine at junior Grade One was more better for students' mastering the sine than learning definition of sine using the ratio method at junior Grade Three.And for the teaching effect of definition of sine,the teaching result of sine defined by the terminal side definition was better than that defined by the unit circle definition method.This research was helpful for educators to form a more comprehensive understanding of the trigonometric functions,and to provide reference for middle school mathematics curriculum reform. |
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