初中数学类比思想方法的探究与应用

发布时间：2018-04-11 05:13

本文选题：初中数学 + 类比思想　；参考：《上海师范大学》2016年硕士论文

【摘要】：2001年,教育部颁布了《全日制义务教育数学课程标准》(实验稿),对数学思想的培养与数学应用意识的养成提出明确要求。10年后,国家颁布最新《全日制义务教育数学课程标准》,对学生的合情推理与演绎能力提出更高的要求,数学思想的培养受到前所未有的重视。类比思想是数学思想的核心组成部分之一,在初中数学应用中具有非常重要的地位,更是人类认识世界与改造世界的工具,但就目前教学实践而言,类比思想方法在日常教学中的应用不尽人意,与其地位不相符。类比思想最早发源于古希腊,著名学者亚里士多德对其进行了一定的研究,并随着时代的发展而不断完善。所以类比思想方法的界定得以确定,其包括类比思想方法的概念、类比的模式与过程以及类比与归纳之间的关系。同时根据教学规律与学生的认知规律,我们将类比分为简化类比、结构类比、降纬类比等三大类。此外,由于类比在培养学生直觉思想能力、增强课堂教学的有效性与有助于学生探索新知识等方面具有重要意义,而引起教育界的广泛重视。类比思想方法不仅仅停留在文本上,而且已经在初中数学课本上、日常教学中以及中考命题中都得到一定程度的应用,特别是在中考所占比重呈现上升的趋势。但由于学生、教师以及评价体系等存在一定的问题,导致类比思想方法的应用受到严重影响,须引起广大师生的重视。探究问题的来源,也主要是学生学习的主动性不高、教师的教法不到位与评价体系欠科学等方面导致的。类比思想方法不仅在教学方面具有积极作用,而且在提高人类思想纬度与认识及改造世界方面具有重大作用,所以我们应从学生、教师与评价体系三个方面采取有效措施来解决存在的问题。从学生方面主要表现在学生主动改变自身学习方式与培养自身类比思想方法的策略;教师角度则从善于选择类比对象、正确把握类比思想方法教学的时机以及改变传统教学模式这三个措施。最后,通过一个运用类比思想方法解题的案例来具体详细的分析类比思想方法的应用。期望这个该案例,让学生切实把握与理解类比思想方法的定义、切入点、关键点与解题步骤,形成类比思维。当然,教师是教学的引导者与组织者,更须深入钻研数学思想,给学生扮演好引路人的角色。
[Abstract]:In 2001, the Ministry of Education promulgated the "Mathematics Curriculum Standard for Full-time compulsory Education" (experimental draft), which puts forward clear requirements for the cultivation of mathematical thought and the cultivation of mathematical application consciousness. Ten years later,The state promulgates the newest Mathematics Curriculum Standard of Full-time compulsory Education, which puts forward higher demands on the students' reasonable reasoning and deductive ability, and the cultivation of mathematical thought is paid more attention to than ever before.The thought of analogy is one of the core components of mathematics thought. It plays a very important role in the application of mathematics in junior high school. It is also a tool for human beings to understand and transform the world. However, as far as the present teaching practice is concerned,The application of analogy thought method in daily teaching is unsatisfactory and does not accord with its status.The thought of analogy originated in ancient Greece. Aristotle, a famous scholar, studied it and perfected it with the development of the times.So the definition of analogy thought method can be determined, which includes the concept of analogy thought method, the model and process of analogy, and the relationship between analogy and induction.At the same time, according to the teaching law and the students' cognitive law, we divide the scores into three categories: simplified analogy, structural analogy and latitude drop analogy.In addition, analogy is of great significance in cultivating students' intuitive and ideological ability, enhancing the effectiveness of classroom teaching and helping students explore new knowledge, which has aroused widespread attention in the educational circles.The analogy thought method not only stays on the text, but also has been applied to a certain extent in the junior middle school mathematics textbook, in the daily teaching and in the middle school examination proposition, especially in the middle school examination takes the proportion to present the rising tendency.However, due to the problems of students, teachers and evaluation system, the application of analogy thought method has been seriously affected, which should be attached importance to by teachers and students.Exploring the source of the problem is mainly caused by the students' low initiative in learning, the lack of teaching methods and the unscientific evaluation system.The analogy thought method not only plays a positive role in teaching, but also plays an important role in raising the latitude of human thought and understanding and transforming the world, so we should start with the students,Teachers and evaluation system to take effective measures to solve the existing problems.From the aspect of students, it is mainly manifested in the strategies of students' initiative to change their own learning methods and to cultivate their own analogical thinking methods, while the teachers' perspective is to be good at selecting the objects of analogy.Correctly grasp the time of analogical ideological method teaching and change the traditional teaching mode.Finally, the application of analogy thought method is analyzed in detail by a case of solving problems by analogy thought method.It is expected that this case will enable students to grasp and understand the definition, entry point, key points and problem-solving steps of analogical thinking, so as to form analogical thinking.Of course, the teacher is the guide and organizer of teaching.
【学位授予单位】：上海师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：G633.6

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