“任意角的三角函数”概念教学的现状与改进研究

发布时间：2018-01-21 02:42

本文关键词： 三角函数概念教学现状改进　出处：《四川师范大学》2015年硕士论文　论文类型：学位论文

【摘要】：数学概念教学一直受到广泛的关注,新课程标准更加重视数学概念的形成过程,提倡揭示概念的本质、背景以及蕴含的数学思想方法。“任意角的三角函数”概念历史发展悠久,其单位圆定义体现了高中数学最重要的数形结合思想。本研究以三角函数知识和概念教学的理论知识作为研究的基础,一方面,对“任意角的三角函数”教学进行现状调查：访谈教师对三角函数知识的理解,观察教师实际的教学课堂并检测其教学质量,分析教学问题以及原因,对有关三角函数的教学研究有一定参考作用。另一方面,在现状调查的基础上,改进“任意角的三角函数”概念的教学方案,并在课堂中实施、检测、对比分析,旨在优化“任意角的三角函数”概念教学,对教师的实践教学具有现实意义。具体的研究内容与结论如下：首先,对“任意角的三角函数”和“概念教学”进行文献研究。从三角函数的历史发展与教学内容对“任意角的三角函数”解读,并简述数学概念及其教学理论,将数学概念教学理论知识作为本研究的理论基础。然后,在理论基础上,通过访谈、课堂观察、试卷测试重点调查了“任意角的三角函数”概念教学的现状.现状表现为：(1)大多数教师对“任意角的三角函数”概念的认识限制于教材中呈现的知识逻辑。(2)教师对教学内容的认识基本上达到了教学要求,但是对教学内容的处理缺乏技巧。(3)教师对教学内容的呈现顺序与教材呈现的顺序一致。(4)教学方法主要以“讲授法”为主,“引导-问答-讲解”的教学模式。最后,与教师交流,将教学内容的处理方式,教学方法进行分析和改进,设计教学方案并实施,得到研究结论：(1)以师生活动为主的问答法和讨论法的教学方式,更容易引起学生学习兴趣。(2)从函数角度认识锐角三角函数,并通过类比学习任意角的三角函数概念,可以消除旧知识对新知识获得的负迁移作用。(3)以单位圆定义为中心,利用单位圆解决三角求值,符号判断等问题可以突出教学重点,促进“任意角的三角函数”概念的形成。
[Abstract]:Mathematics concept teaching has attracted extensive attention, the new curriculum standard pays more attention to the forming process of mathematics concept, advocate explain the essence of the concepts, background and ways of thinking mathematically. "Trigonometric function" arbitrary angle concept of the long history of development, the definition of the unit circle is the most important high school mathematics Shuoxingjiehe thinking of this. Study on the theoretical knowledge of trigonometric function knowledge and concept teaching as the basis of the study, on the one hand, the investigation of "teaching trigonometric function" arbitrary angle: interview the teachers' understanding of the knowledge of the trigonometric function, observation of teachers' actual teaching and test the quality of teaching, analysis of teaching problems and reasons, have a certain reference study on the teaching of trigonometric function. On the other hand, on the basis of the survey, the teaching plan to improve the "trigonometric function" arbitrary angle concept, and in the classroom In the implementation, testing, comparison and analysis, in order to optimize the teaching of "trigonometric function" arbitrary angle concept, it has realistic significance to the teaching practice of teachers. The specific research contents and conclusions are as follows: firstly, research literature on "trigonometric function" arbitrary angle and "teaching". From the historical development and the teaching content of triangle the function of interpretation of "trigonometric function" arbitrary angle, and the mathematical concepts and teaching theory, the teaching theory of knowledge of mathematical concepts as the theoretical basis of this study. Then, on the basis of the theory, through interviews, classroom observation, test papers focusing on the investigation of the "trigonometric function" arbitrary angle of concept teaching status the status quo. Performance: (1) most of the teachers' understanding of the "trigonometric function" arbitrary angle limits of the concept of logic of knowledge in the teaching materials presented. (2) the teachers' understanding of teaching content basically achieve the teaching However, the lack of teaching content processing skills. (3) the same teachers show the order sequence and teaching materials for the presentation of teaching content. (4) the main teaching method in "teaching method", "Guide - Q - explanation" teaching mode. Finally, to communicate with the teacher, will teach the way of learning content the teaching method is analyzed and improved, teaching design and implementation, the research conclusion: (1) to students based question answering and discussion teaching method, easier to arouse students' interest in learning. (2) acute angle function from three known function angle, and by analogy learning trigonometric functions of arbitrary angle that can eliminate the negative transfer of old knowledge to new knowledge obtained. (3) to the unit circle is defined as the center, using the unit circle to solve the triangle evaluation, symbol judgment can highlight the focus of teaching, promote the "trigonometric function" concept of arbitrary angle Formation.

【学位授予单位】：四川师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

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