三角是联系几何与代数的一座桥梁，沟通初等数学和高等数学的一条通道。函 数、向量、坐标、复数等许多重要的数学知识与三角有关，大量的实际问题的解决 要用到三角知识。在我国中学数学教学大纲推进和改革过程中，代数、三角、几何 的教学内容、要求和重点也在不断调整。学生通常认为三角函数难学，有关三角公 式和定理的推导也是教学的难点。 张景中院士经过30多年持续地探讨面积解题的规律，为三角函数的定义找到一 种更简单更便于推理论证的几何模型，用单位菱形的面积来定义正弦，并发展出相 应的一套适用于初中数学教学的逻辑体系。与传统定义相比，新定义可以在小学数 学知识的基础上建立三角，更直观、更严谨、更具一般性。笔者依据张景中院士提 出的新体系和对初中数学课程改革的建议，在一所市属重点中学进行了新体系的教 学尝试，希望通过教学实验，初步论证初中数学课程结构改革的可行性，了解教师 和学生对其的看法和评价，结合教学实验的结果，对中学阶段的教学提出一些建议， 为新一轮的课程改革提供参考案例。 本文第一章介绍了研究的背景、研究的意义、研究的思路和方法。第二章通过 对文献的检索和分析，评述了国内外初中数学课程改革的历程和中学数学课程中三 角函数的变迁。第三章系统地介绍了张景中院士提出的新定义体系和他对初中数学 课程结构性改革提出的建议，在对新体系的研读和分析基础上，笔者设计了相应的 教案，在第四章详细叙述了教学实验的过程，及教学测验和问卷调查的情况，并对 部分教师进行了访谈。结合教学实践情况，笔者在第五章提出了新定义体系与传统 课程的整合建议。 关键词，初中；数学课程结构；改革；可行性IV Abstract Trigonometry is a bridge between Analytic Geometry and Algebra， and a gateway from Elementary Mathematics to Advanced Mathematics. Much important mathematical knowledge is relevant to Trigonometry，such as Function，Vector，Coordinate system， Complex number etc. A large number of practical problems are solved with trigonometry knowledge. In the process of propelling and innovating Secondary School Mathematics Syllabus， the content， requirements and emphasis of algebra， trigonometry， and geometry adjust accordingly. Many students usually thought trigonometric function is difficult to learn， the derivation of trigonometric formulas and theorem are difficult points in teaching trigonometric function. Academician Zhang Jingzhong found a new geometric model (the area of the unit diamond or isosceles triangle) to define sine， based on his continuing investigation on the law of solving problems by area-method， he put forward a new corresponding logical system of math teaching in junior middle schools. Compare with the traditional definition， the new definition of sine on the basis of elementary math is more intuitive， precise， generalized. According to the new teaching system and the suggestion of junior middle school mathematics curriculum reform by Academician Zhang Jingzhong， the author carried out a pilot study of teaching trigonometric function in a key municipal middle school. It is hoped to demonstrate the feasibility of mathematics curriculum reform in junior middle school， and collect the teachers and students’ comments and assessment. Based on the teaching practice， the author raised some suggestions for teaching middle-school mathematics， in order to afford some gist for junior middle school mathematics curriculum reform. The first chapter of this paper introduced the research background， significance， method etc. On the retrieval and analysis of literature，the author summed up the process history of mathematics curriculum reform at home and abroad in the second chapter. The third chapter systematically described the new teaching system and the suggestion ofjunior middle school mathematics curriculum reform by Academician Zhang Jingzhong， the author designed the corresponding teaching plans， and went into particulars the process of teaching experiments ， the results of examination， and the data of questionnaire survey and interview in the fourth part. Based on the findings， the author affords some gist for integrating the new teaching system with traditional system. Key words: Junior Middle School; The Structure of Mathematics Curriculum; Reform; FeasibilityV 目录 摘要.....................................................................................................................................II Abstract ............................................................................................................................. IV 第一章 绪论.....................................................................................................................1 1.1 研究背景................................................................................................................ 1 1.2 研究的意义........................................................................................................... 2 1.3 研究的思路与方法............................................................................................... 3 1.3.1 研究的思路.................................................................................................. 3 1.3.2 研究的方法.................................................................................................. 3 第二章 初中数学课程改革的历史回顾.........................................................................5 2.1 国际初中数学课程结构改革............................................................................... 5 2.2 我国初中数学课程结构改革............................................................................... 7 2.2.1 构建社会主义的数学课程......................................................................... 7 2.2.2 构建独立自主的数学课程......................................................................... 8 2.2.3 重建基础教育数学课程............................................................................. 8 2.2.4 改革基础教育数学课程............................................................................. 9 2.3 中学课程中的三角函数..................................................................................... 10 2.3.1 三角的起源............................................................................................... 10 2.3.2 中学课程中三角函数的改革................................................................... 11 2.3.3 中美教材中三角函数的差异................................................................... 13 2.4 本章小结............................................................................................................. 14 第三章 张景中的新定义体系.......................................................................................15 3.1 张景中对初中课程结构改革的建议................................................................. 15 3.2 新定义体系......................................................................................................... 16 3.2.1 新定义体系............................................................................................... 16 3.2.2 与传统课程内容结构的比较................................................................... 17 3.3 国内外评价及教学实验..................................................................................... 18 3.4 本章小结............................................................................................................. 20 第四章 教学实验分析...................................................................................................21 4.1 教学实验............................................................................................................. 21 4.1.1 实验对象................................................................................................... 21 4.1.2 教学实验................................................................................................... 21 4.2 学习情况调查..................................................................................................... 23 4.2.1 教学调查................................................................................................... 23 4.2.2 学生对新定义的掌握情况分析............................................................... 27 4.2.3 学生对新定义体系的学习情况分析.................................