分类讨论思想在高中数学中的研究与应用

发布时间：2018-01-14 16:03

本文关键词：分类讨论思想在高中数学中的研究与应用　出处：《信阳师范学院》2017年硕士论文　论文类型：学位论文

【摘要】：分类讨论思想是重要的数学思想方法之一,不仅可以指导学生有效地解题,更能有效地提高学生思考问题的条理性,严谨性,缜密性,完整性,促进学生思维能力的发展和数学素养的提高,因此,开展分类讨论思想的研究和应用,具有重要的意义。全文共分为六章。第一章主要通过参加实际课题的研究和对分类讨论思想的思考,提出了分类讨论思想在高中数学中的研究与应用问题,并介绍了研究问题的实际背景、研究现状与存在问题,阐述了研究目的和意义等;第二章主要介绍数学思想方法及其作用,并重点介绍了分类讨论思想的基本原则、一般步骤与结论归纳形式、应用范围等,这是灵活运用分类讨论思想的理论基础;第三章主要介绍“分类讨论思想在高中数学中的研究与应用学生调查问卷”和“分类讨论思想在高中数学中的研究与应用教师调查问卷”的设计过程和实施过程,并从学生总体、性别、年级和教师角度对问卷调查结果进行分析,真实反映分类讨论思想在高中数学中的应用现状和存在问题;第四章主要是根据调查问卷的分析结果,提出相应的提高高中生分类讨论思想应用水平的具体建议;第五章主要从高中数学教学的实际出发,精选并设计若干例题介绍分类讨论思想在高中数学中的具体应用,旨在帮助学生更好地理解和掌握分类讨论思想,并将此思想方法主动地应用于自己平时的解题中去;第六章是研究总结与反思部分,主要是针对自己所进行的研究工作进行总结并对研究过程中存在的不足之处进行反思以及对今后深入开展分类讨论思想的研究与应用加以展望。
[Abstract]:Classification discussion is one of the important mathematical thinking methods, which not only can guide students to solve problems effectively, but also can effectively improve the students' thinking of the methodical, rigorous, meticulous, integrity. To promote the development of students' thinking ability and the improvement of mathematical literacy, therefore, to carry out the research and application of classified discussion ideas. The whole text is divided into six chapters. The first chapter puts forward the research and application of classification discussion thought in senior high school mathematics by taking part in the research of practical topics and thinking about the thinking of classification discussion. And introduced the actual background of the research problem, the research present situation and the existence question, elaborated the research goal and the significance and so on; The second chapter mainly introduces the mathematics thought method and its function, and emphatically introduces the basic principle, the general steps and the conclusion induction form, the application scope and so on of the classification discussion thought. This is the theoretical basis of the flexible use of classification and discussion ideas; The third chapter mainly introduces "the Research and Application of Classification discussion thought in Senior Mathematics" and "the Research and Application teacher questionnaire of Classification discussion thought in Senior Middle School Mathematics". The design process and implementation process of. And from the students' general, gender, grade and teachers' point of view to analyze the results of the questionnaire, truly reflect the classification of discussion ideas in senior high school mathematics application status and existing problems; Chapter 4th is mainly based on the results of the questionnaire analysis, put forward the corresponding suggestions to improve the application of high school students' classification and discussion; Chapter 5th mainly from the high school mathematics teaching reality, selected and designed several examples to introduce the classification discussion thought in the high school mathematics concrete application, in order to help the student to understand and master the classification discussion thought better. And this thought method is applied to solve the problem in oneself in the ordinary time actively; Chapter 6th is the summary and reflection part of the research. It is mainly to summarize the research work carried out by oneself, to reflect on the shortcomings in the research process and to prospect the further research and application of the idea of classification discussion in the future.
【学位授予单位】：信阳师范学院
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6

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