解析高中数学教学中的分类讨论思想

发布时间：2018-08-10 20:30

【摘要】：随着新课程改革的进行,高中数学的教学对数学思想方法的研究和渗透逐步加强,高考命题也更加注重能力的考查。分类讨论作为贯穿整个中学数学的一种重要的数学思想,通过对它的学习和训练,不仅能加深学生对书本知识的巩固,也有利于培养学生严谨而完整的思维,提高学生的综合素养,对于培养学生的创新能力也有显著的现实意义。本文从四个方面论述了分类讨论思想。第一,分类讨论思想综述,首先从教学实践、高考考查和实际应用三个方面提出了研究分类讨论的背景,其次介绍了分类讨论思想在古今中外的发展情况、研究状况及教学中存在的一些问题,最后根据提出的背景、研究现状及当下实际教学中存在的问题着重分析了研究分类讨论的现实意义。第二,相关理论研究,首先阐明了数学思想、数学方法、分类讨论的含义,接着又阐述了分类讨论的诱因、原则、步骤及结论总结。这部分为第三章分析例题提供了理论基础。第三,挖掘梳理目前所用教材(人教A版)中基础知识所蕴含的分类讨论思想,并辅以例题说明。教材中没有明确出现“分类讨论”概念,也没有将基础知识和习题按数学思想方法分类,学生学习这部分时较为吃力。笔者结合自己的教学经验,将零碎的知识点和题目中的分类讨论进行了挖掘总结,有利于学生学习。第四,根据第三章的分析,结合自己的教学实践,对于学生研究学习分类讨论从克服畏难心理、培养良好的学习习惯和提高运算能力三个方面提出一些建议,并就优化解题思路回避分类讨论做了一个总结归纳,辅以例题说明。本文在写作过程中查阅大量资料,结合前人的研究基础和自己的教学实践,对分类讨论进行了一个多方面的探讨和研究,如果能对一线教师的教学和学生的学习有所帮助,于我而言便是小小的愉悦。由于自身水平局限,本文中也存在不成熟和不完善之处,比如第三章在梳理基础知识和习题时用到的教材是人教A版,而且是根据文科授课内容来梳理的,对于使用其他版本教材的学生和使用人教A版的理科学生来说可能知识点和习题就不够齐全。另外,第三章分析习题时,与第二章的理论结合得不是十分紧密。衷心希望以后有更多的人来研究分类讨论,使大家对这种思想方法的认识越来越完善。
[Abstract]:With the development of the new curriculum reform, the research and infiltration of mathematics thinking methods in mathematics teaching in senior high school is gradually strengthened, and the examination of ability is paid more attention to in college entrance examination. As an important mathematical thought running through the whole middle school mathematics, the classification discussion can not only deepen the students' consolidation of book knowledge, but also help to train the students' rigorous and complete thinking through its study and training. Improving students' comprehensive accomplishment is also of great practical significance to the cultivation of students'innovation ability. This paper discusses the idea of classification discussion from four aspects. First, the summary of classified discussion thoughts. Firstly, the background of classification discussion is put forward from three aspects: teaching practice, college entrance examination and practical application. Secondly, the development of classification discussion thought in ancient, modern and modern countries is introduced. In the end, according to the background, the present research situation and the problems existing in the present teaching, the practical significance of the research classification discussion is analyzed. Second, the related theoretical research, first clarified the mathematics thought, the mathematics method, the classification discussion meaning, then elaborated the classification discussion the inducement, the principle, the step and the conclusion summary. This part provides a theoretical basis for the analysis of examples in Chapter 3. Thirdly, the classification and discussion ideas contained in the basic knowledge in the current teaching materials (version A) are explored and illustrated with examples. The concept of "classified discussion" does not appear clearly in the teaching material, and the basic knowledge and exercises are not classified according to the method of mathematics thought, so it is difficult for the students to learn this part. Combining with my own teaching experience, the author excavates and summarizes the scattered knowledge points and the classification and discussion of the topics, which is beneficial to the students' learning. Fourthly, according to the analysis of the third chapter, combined with the teaching practice, some suggestions are put forward for the students to study the classification of learning from three aspects: overcoming the psychology of fear of difficulties, cultivating good study habits and improving the ability of operation. A conclusion is made for the discussion of optimization problem solving and the discussion of avoidance classification is supplemented by an example explanation. In the process of writing, this paper refers to a large number of materials, combines the research basis of predecessors and their own teaching practice, carries on a multi-faceted discussion and research on the classification discussion, if it can be helpful to the teaching of front-line teachers and the study of students. To me it was a little pleasure. Due to the limitations of their own level, there are also some immaturity and imperfections in this paper. For example, the teaching materials used in the third chapter in combing basic knowledge and exercises are human teaching A edition, and they are combed according to the contents of liberal arts teaching. Knowledge and exercises may not be complete for students who use other versions of the textbook and those who teach science version A. In addition, the third chapter analysis exercises, and the second chapter of the theory is not very close. I sincerely hope that more people will study and discuss the classification in the future, so that the understanding of this way of thinking becomes more and more perfect.
【学位授予单位】：山东师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6

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