小学数学中渗透抽象思想的研究

发布时间：2018-09-08 19:23

【摘要】：数学是怎么存在的呢?自从古希腊柏拉图、亚里士多德关于数学“名”与“实”存在的争论一直延续至今。从争论中我们发觉数学并非只研究那些来源于生活的东西,也研究那些来源于数学自身的东西。这就决定了数学研究对象的特殊性：抽象于现实的物质世界和抽象的物质世界。因此,抽象是数学的本质特征。但数学教学并不等同于数学研究,数学教学就是要把数学抽象形象化,这是数学教育的真谛。但我们将数学抽象形象化却需要学习数学家研究数学的思想。数学基本思想是认识数学对象的灵魂,而抽象思想是数学基本思想的核心。因此对抽象思想的深刻理解不仅有助于认识数学的抽象,也有助于在数学教学中将数学抽象形象化,获得对数学抽象的进一步认识。本研究在前人研究的基础上,进行分析归纳整理,并结合一定的教师教学经验,第一次比较系统地阐述了数学抽象思想的内涵,提出小学数学中抽象思想不仅仅指由抽象思想派生出来的一些具体数学思想方法,也包含对数学对象抽象的理解,以及在学习数学抽象内容的过程,渗透抽象思想,促进学生数学抽象思维能力的发展,并探索小学数学课程内容的抽象发展以及如何在教学中渗透抽象思想,形成了对数学抽象思想更为全面、系统的认识。本论文主要分为五部分：第一部分介绍研究本论题的缘由、意义及基本研究思路、方法；第二部分,从抽象与概括、抽象思维与抽象思想、渗透抽象思想的意义三方面探索对抽象思想的认识；第三部分,着重分析了小学数学抽象思想的内涵、小学数学教材内容的抽象发展分析以及基本的数学抽象思想方法(分类思想、符号化思想、变与不变思想)；第四部分,主要是在小学生数学思维特点的基础上,探讨怎样在小学数学教学中渗透抽象思想,并提供经典的教学片断设计,为教学实践提供借鉴；第五部分,是对本论题研究的总结归纳,在此之上,提出本研究的不足及创新之处。
[Abstract]:How does mathematics exist? Since Plato in ancient Greece, Aristotle's argument about the existence of mathematical "name" and "reality" has continued to this day. From the argument we find that mathematics not only studies what comes from life, but also what comes from mathematics itself. This determines the particularity of mathematical research object: abstract from the real material world and abstract material world. Therefore, abstraction is the essential characteristic of mathematics. But mathematics teaching is not equal to mathematics research, mathematics teaching is to abstract mathematics visualization, this is the true meaning of mathematics education. But we need to study mathematicians' thinking of mathematics in order to visualize mathematics abstractly. The basic thought of mathematics is the soul of understanding the object of mathematics, and abstract thought is the core of the basic thought of mathematics. Therefore, the deep understanding of abstract thought is not only helpful to understand the abstract of mathematics, but also helpful to visualize the abstract of mathematics in mathematics teaching, and to get a further understanding of abstract of mathematics. On the basis of previous studies, this study analyzes and summarizes the connotation of mathematical abstract thought, and combines with certain teachers' teaching experience, for the first time, it systematically expounds the connotation of mathematical abstract thought. It is put forward that abstract thought in primary school mathematics not only refers to some concrete mathematical thought methods derived from abstract thought, but also includes the abstract understanding of mathematical object, and the process of learning abstract content of mathematics, which permeates abstract thought. In order to promote the development of students' abstract thinking ability and explore the abstract development of mathematics curriculum content in primary school and how to infiltrate abstract thought in teaching, a more comprehensive and systematic understanding of abstract thought of mathematics has been formed. This paper is divided into five parts: the first part introduces the reason, significance, basic research ideas and methods of the research, the second part, from the abstract and summary, abstract thinking and abstract thinking, the second part, abstract thinking, abstract thinking and abstract thinking. The third part focuses on the analysis of the connotation of abstract thought in primary school mathematics. An Analysis of the Abstract Development of the contents of Primary School Mathematics textbooks and the basic methods of Mathematical Abstract thinking (classified thought, symbolic thought, change and invariance); the fourth part is mainly based on the characteristics of elementary school students' mathematical thinking. To explore how to infiltrate abstract ideas in primary school mathematics teaching, and to provide classical teaching fragment design to provide reference for teaching practice. The fifth part is a summary of the research on this topic. The deficiency and innovation of this study are put forward.
【学位授予单位】：华中师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G623.5

【参考文献】