类比思想在高中数学教学中的应用研究

发布时间：2018-07-11 17:48

本文选题：数学思维 + 类比思想　；参考：《南京师范大学》2015年硕士论文

【摘要】：培养数学思维能力是高中数学教学强调的内在要求和重要任务,类比思维作为数学思维的重要组成部分,在高中数学教学中需要被高度重视并广泛应用。针对当前高中数学教师和学生应用类比思想更多的出于自发性和随机性,缺乏系统性和规范性,与《普通高中数学课程标准(实验稿)》目标对教师应用类比教学和对学生掌握类比思维方法提出的要求存在差距,对此,本文对类比思想在高中数学教学中的应用情况展开了研究。本文在查阅大量国内外类比思想研究文献的基础上,对当前关于类比思想研究及应用的现状、特点进行综述,发掘类比思想与数学乃至高中数学的密切联系,提出类比思想在高中数学教学应用的必要性和可行性,通过找出影响类比思想教学的内在因素,避免日常类比教学产生的局限性,从而掌握类比思想教学策略的一般原则和基本环节。基于类比思想在数学学科发展的密切联系,开展类比教学在高中数学教学中的应用研究显得尤为重要。本文立足高中数学教学目标及实际需要,通过高中数学教学中类比思想的应用,阐述了类比思想的科学性、联系性和联想性,以及类比思想在教学中的实效性。重点突出对高中数学苏教版教科书中类比内容进行应用研究,运用文献研究、课堂观察法、个人访谈、问卷调查等研究方法,系统地从高中数学课堂的教与学两个方面进行综合研究,动态与静态分析相结合,理论与实证分析相结合,既分析教师运用类比思想的教学策略情况,又研究高中学生运用类比思想学习的情况,力图呈现高中数学教学中教师和学生关于类比思想的应用现状,寻找出类比思想与高中数学切入点和契合点,通过设计运用类比思想教学的一般路径,总结出类比思想在高中数学教学应用中的基本规律,并就如何提高类比教学策略的效果提出意见和建议。通过研究,得出结论包括：在高中数学教学中注重应用类比思想,有助于展示数学的内在和谐和数学知识的统一性,丰富教师的教学手段,实现教学目标；通过运用类比思想教学策略,可以激发学生主动参与数学探究积极性,引导学生在学习数学知识,掌握数学技能的过程中形成创新扩散思维；学生在高中数学学习中恰当地运用类比推理,能够提高他们解决问题的能力、攻克难题的信心和数学学习效率。希望本论文对类比思想在高中数学课堂教学中进一步扩大应用范围的研究有一定帮助。
[Abstract]:It is an internal requirement and an important task to cultivate mathematics thinking ability in senior high school mathematics teaching. As an important part of mathematics thinking, analogical thinking needs to be attached great importance to and widely used in high school mathematics teaching. In view of the present high school mathematics teacher and student application analogy thought more out of spontaneity and randomness, the lack of systematic and normative, There is a gap between the goal of ordinary Senior Middle School Mathematics Curriculum Standard (Experimental draft) and the requirements of teachers' application of analogy teaching and students' mastery of analogical thinking methods. This paper studies the application of analogy thought in mathematics teaching in senior high school. On the basis of consulting a large number of domestic and foreign literature on analogical thought research, this paper summarizes the present situation and characteristics of the research and application of analogy thought, and explores the close relationship between analogy thought and mathematics, even mathematics in senior high school. This paper puts forward the necessity and feasibility of the application of analogy thought in mathematics teaching in senior high school, and by finding out the internal factors that influence the teaching of analogy thought, it avoids the limitation of daily analogy teaching. In order to master the general principles and basic links of analogical ideological teaching strategy. Based on the close relationship between the thought of analogy and the development of mathematics, it is very important to carry out the research on the application of analogy teaching in mathematics teaching in senior high school. Based on the goal and practical needs of mathematics teaching in senior high school, this paper expounds the scientific, associative, associative and practical effects of analogy thought through the application of analogy thought in mathematics teaching in senior high school. Emphasis is placed on the applied research on the analogical content in the textbooks of senior high school mathematics education, including literature research, classroom observation, personal interviews, questionnaires and other research methods. This paper systematically studies the teaching and learning of mathematics classroom in senior high school, combines the dynamic and static analysis, the theory and the empirical analysis, analyzes the teachers' teaching strategies using analogy thought. It also studies the situation of high school students' learning with analogy thought, and tries to present the present situation of the application of analogy thought between teachers and students in high school mathematics teaching, and find out the starting point and the point of convergence between analogy thought and senior high school mathematics. By designing the general path of analogical thought teaching, this paper sums up the basic law of the application of analogy thought in mathematics teaching in senior high school, and puts forward some suggestions on how to improve the effect of analogy teaching strategy. The conclusions are as follows: paying attention to the thought of applying analogy in mathematics teaching in senior high school is helpful to show the inherent harmony of mathematics and the unity of mathematics knowledge enrich the teaching means of teachers and realize the teaching goal; Through the use of analogy thought teaching strategy, it can stimulate students' initiative to participate in mathematical inquiry enthusiasm, guide students to form innovative and diffusive thinking in the process of learning mathematical knowledge and mastering mathematical skills. Students can improve their ability to solve problems, solve problems with confidence and study efficiency by using analogy reasoning properly in senior high school mathematics learning. It is hoped that this paper will be helpful to further expand the scope of application of analogical thinking in senior high school mathematics classroom teaching.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

【参考文献】