基于“历史发生原理”的三角函数教学研究

发布时间：2018-06-19 10:59

本文选题：历史发生原理 + 三角函数　；参考：《新疆师范大学》2015年硕士论文

【摘要】：随着新课程改革的深入推进,新课程改革也开始从理念上进行突破,将学生的被动学习向主动学习转变作为新课程改革的一个重要目标。新课程中,三角函数的学习有利于提高学生的思维能力,培养学生的分析问题和解决问题的能力,使学生感受数学建模的思想。但是本人在实际的三角函数教学中发现,教师的教存在着许多困难,同时学生学习时也常感到困惑。主要由于在初中阶段的三角比是以角度为自变量,但是到了高中三角函数的角是用任意实数表示;其次,三角函数是学生在高中阶段唯一进行全面研究的周期函数,这对于学生而言是一个难点;第三,学生在学习三角函数的时候,需要熟练掌握和运用大量的公式;第四,高中阶段,函数的概念开始逐渐地向集合与集合间的“对应说”过渡,面对如此多的抽象概念复合在一起,能够让学生真正地理解和消化掉这些内容是有一定难度的。因此,为了解决三角函数教与学中的一些困难,对基于历史发生原理的三角函数教学展开研究。首先对历史发生原理的文献资料和三角函数教与学的已有研究做了一定的研究和分析,在此基础上,对三角函数的历史发展过程进行了较为详尽的梳理,并收集总结了历史中出现过的一些不同的两角三角函数关系的推导方法。其次是结合高中数学教材中三角函数的教与学的现状情况,以两角和与差的正弦公式作为教学设计的切入点,对两角的三角函数关系的推导进行了历史重构,从而设计出基于历史发生原理的两角和(差)公式的教学。并根据课堂实践法将教学设计付诸实践,然后与接受依据教材设计的教学方案的班级进行测验比较,并对教师进行问卷调查和访谈,最后对得到的结果进行分析,对之前的教学设计进行了修改和完善。通过对学生测验结果的比较分析,得到了基于历史发生原理的教学设计较基于教材的教学设计在解决学生的学习困难上更为有效,使学生可以经历知识的发生发展过程,提高了学生的学习兴趣,促进了学生对知识的掌握和理解。对教师进行问卷调查和访谈中发现,教师倾向于使用基于历史发生原理的两角和(差)公式的教学设计。最后,结合访谈的一些结果对研究的过程进行反思,探究了历史发生原理应用于中学数学教学存在的困难,并根据已有的教学工作经验提出一些解决策略,以促进历史发生原理在中学数学教学中能够有更为广泛地应用。
[Abstract]:With the deepening of the new curriculum reform, the new curriculum reform has begun to break through from the concept of passive learning to active learning as an important goal of the new curriculum reform. In the new curriculum, the study of trigonometric function is helpful to improve students' thinking ability, to cultivate their ability to analyze and solve problems, and to make students feel the idea of mathematical modeling. However, in the teaching of trigonometric functions, I find that there are many difficulties in the teaching of teachers, and students often feel confused when they study. The main reason is that the trigonometric ratio in junior middle school is dependent on angle, but the angle of trigonometric function in senior high school is expressed as arbitrary real number. Secondly, trigonometric function is the only periodic function that students study comprehensively in senior high school. This is a difficult point for students; third, students need to master and use a large number of formulas skillfully in learning trigonometric functions; and fourth, in high school, The concept of function begins to transition gradually to the "correspondence" between the set and the set. It is difficult for students to truly understand and digest these contents when they are combined with so many abstract concepts. Therefore, in order to solve some difficulties in the teaching and learning of trigonometric functions, the teaching of trigonometric functions based on the principle of historical occurrence is studied. First of all, it makes a certain research and analysis on the literature of historical occurrence principle and the existing research on trigonometric function teaching and learning. On this basis, the historical development process of trigonometric function is sorted out in detail. The derivation methods of some different trigonometric function relations in history are also collected and summarized. Secondly, according to the current situation of trigonometric function teaching and learning in senior high school mathematics teaching materials, this paper takes the sinusoidal formula of two-angle sum and difference as the starting point of teaching design, and reconstructs the derivation of trigonometric function relationship between two angles. Thus, the teaching of biangular and (differential) formula based on the principle of historical occurrence is designed. According to the classroom practice method, the teaching design is put into practice, and then compared with the class which accepts the teaching plan according to the teaching material design, and the teachers are surveyed and interviewed, and the results obtained are analyzed. The former teaching design has been modified and perfected. Through the comparative analysis of the students' test results, it is concluded that the teaching design based on the principle of historical occurrence is more effective in solving the students' learning difficulties than the teaching design based on the textbook, so that the students can experience the process of the development of knowledge. Improve the students' interest in learning, and promote the students to master and understand knowledge. Through the questionnaire survey and interview, it is found that teachers tend to use the two-angle (poor) formula based on the principle of historical occurrence in the teaching design. Finally, based on the results of the interview, this paper reflects on the process of the research, explores the difficulties of applying the principle of historical occurrence to mathematics teaching in middle schools, and puts forward some solving strategies according to the existing teaching experience. In order to promote the principle of historical occurrence in middle school mathematics teaching can be applied more widely.
【学位授予单位】：新疆师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

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