The Distribution Of Triangle Knowledge In Primary And Middle Schools And Its Teaching Research

Geometric curriculum and teaching innovation are always the central issues of educational studies in mathematics. Various opinions arise due to different understandings of the value of mathematical education. Someone thinks that geometric education is limited in its value and should be weakened in its ranking and reduced in its class hours. However, some researchers hold the view that it plays an important role in developing space conception, geometric intuition and reasoning abilities for students. The content of triangle is throughout the geometric curriculum of both the compulsory and high school education. Many researchers have done some research about it from various perspectives. In the existing studies, they just conduct studies on plane geometry as a whole without furthering research about the knowledge of triangle systematically. Thus, the thesis takes the textbooks published by people’s education press as study materials to carry out a systematic study on the knowledge of triangle learned in elementary and secondary shool.Based on the mathematic curriculum standards, the thesis explicitly analyses the way of placement and arrangement about the knowledge of triangle reflected in different periods of schooling. And it relies on Van Helie Theory to highlight the requirements for the level of students’geometric thinking. Finally, it puts forward some teaching suggestions in accordance with the influence of the conclusion on the teaching of triangle in different periods of schooling. It mainly adopts the methods of analyzing the literature and content.The thesis consists of five chapters. In Chapter One, it introduces the history and present situation of research about geometry curriculum at home and abroad. Based on the related literature, it puts forward the research problems, expounds the purpose and meaning of the research and briefs the research methods and the outline of the thesis.In Chapter Two, it carries out an in-depth analysis of the way of placement of triangle learned in different periods of schooling. And it organizes the knowledge of triangle systematically and discusses the problems concerning the linkage of the knowledge in different periods of schooling. Finally, it undertakes a classificatory analysis to triangle completely. In Chapter Three, it firstly introduces Van Helie Theory. Then it analyses the thinking level of geometry implied in the knowledge of triangle by applying the theory. In the research, the compiling of triangle is found to be accordant to Van Helie Theory of Geometric Thinking Level. It is evolving spirally for both the knowledge of triangle and the geometric thinking level.In Chapter Four, based on Chapter Two and Chapter Three, it proposes some specific teaching suggestions for the teaching of triangle in different periods of schooling. The suggestions are as follows. Firstly, we should guide students to properly understand the basic concept. Secondly, we should encourage students to participate in the generation of the conclusion. Thirdly, we should strengthen the cultivation of students’ reasoning ability. Fourthly, we should pay attention to penetrate the mathematical thinking methods. Fifthly, we should strengthen the connection between the geometric knowledge and the practice and we need to elaborate it by using a few specific examples.In Chapter Five, it is the retrospect and prospect of the thesis. During the retrospect and prospect, it points out the limitations of the thesis. Meanwhile, it gives a prospect for the curriculum, the teaching and the study of triangle.