Knowledge Reconstruction Of Trigonometric Function

The Trigonometric Function is both a teaching difficulty of high school mathematics and a huge challenge for teachers' teaching and students' learning. The main difficulty of Trigonometric Function lies in the understanding of the knowledge's nature and the construction of knowledge's structure. Based on the analysis of the knowledge structure of the teaching material of PEP Edition's A-type version of the textbook, this paper utilized literature research and questionnaire survey to analyze the current teaching situation of the "Trigonometric Function of any angle" and put forward some suggestions on the reconstruction of the Trigonometric Function to show the importance of knowledge structure to the study . At the same time, from the perspective of the internal of mathematics, a new scheme to reconstruct the Trigonometric Function from the viewpoint of computing and generalizing the contents of the corresponding textbook to analyze the compiling effect was proposed.Combined with theory and practice, this paper made a comprehensive exploration of the knowledge, structure and teaching materials of the Trigonometric Function in order to provide a new understanding for the actual teaching, improve the teaching effect and promote the breakthrough development of trigonometric teaching.This paper is divided into five parts:The first chapter is the introduction. It mainly discussed the background and meaning of the study, ways and methods of the research process and the current situation and shortcomings of both domestic and foreign researches.The second chapter analyzed the current teaching situation of the Trigonometric Function. On the basis of analyzing the content of the trigonometric function of the teaching material of the PEP Edition's A-type version of the textbook, this paper classified and reviewed the teaching case of Trigonometric Function of any angle and analyzed some of the current schemes of knowledge reconstruction of the Trigonometric Function, which embodied the necessity of reconstruction of Trigonometric Function.The third chapter is the study of knowledge reconstruction of Trigonometric Function. The trigonometric function is also an operation, so this paper and reconstructed the Trigonometric Function content and constructed its knowledge structure according to the logic of internal development of mathematics.The fourth chapter is the design and analysis of the teaching material.This chapter reconstructed the teaching material content of the Trigonometric Function according to the logical of the operation promotion. Then from the whole book and the single chapter, it explained the process of the teaching material design and analyzed the design goal, the content arrangement, the knowledge structure and the preparation intention teaching recommendations and so on, reflecting the rationality of teaching materials and practicability.The fifth chapter is the analysis of the compilation effect of the teaching materials.By the comparison of the newly compiled teaching materials and the teaching material of the PEP Edition's A-type version of the textbook, the visual effects of the teaching materials, the characteristics of knowledge presentation, the arrangement structure and the knowledge comprehension were analyzed through the investigation and statistics to show the rationality and effectiveness of the newly compiled teaching materials.The sixth chapter is the conclusion and prospect.The innovation points of this research lied in reconstruction the Trigonometric Function from the internal angle of mathematics and compiling the corresponding teaching material content. Combining the two aspects of theory and practice, this paper made a comprehensive analysis for the knowledge reconstruction by using both qualitative and quantitative research methods to provide a new direction and reference for the improvement of teaching and the compilation of teaching materials.