【摘要】：數(shù)學(xué)是怎么存在的呢?自從古希臘柏拉圖、亞里士多德關(guān)于數(shù)學(xué)“名”與“實(shí)”存在的爭(zhēng)論一直延續(xù)至今。從爭(zhēng)論中我們發(fā)覺(jué)數(shù)學(xué)并非只研究那些來(lái)源于生活的東西,也研究那些來(lái)源于數(shù)學(xué)自身的東西。這就決定了數(shù)學(xué)研究對(duì)象的特殊性：抽象于現(xiàn)實(shí)的物質(zhì)世界和抽象的物質(zhì)世界。因此,抽象是數(shù)學(xué)的本質(zhì)特征。但數(shù)學(xué)教學(xué)并不等同于數(shù)學(xué)研究,數(shù)學(xué)教學(xué)就是要把數(shù)學(xué)抽象形象化,這是數(shù)學(xué)教育的真諦。但我們將數(shù)學(xué)抽象形象化卻需要學(xué)習(xí)數(shù)學(xué)家研究數(shù)學(xué)的思想。數(shù)學(xué)基本思想是認(rèn)識(shí)數(shù)學(xué)對(duì)象的靈魂,而抽象思想是數(shù)學(xué)基本思想的核心。因此對(duì)抽象思想的深刻理解不僅有助于認(rèn)識(shí)數(shù)學(xué)的抽象,也有助于在數(shù)學(xué)教學(xué)中將數(shù)學(xué)抽象形象化,獲得對(duì)數(shù)學(xué)抽象的進(jìn)一步認(rèn)識(shí)。本研究在前人研究的基礎(chǔ)上,進(jìn)行分析歸納整理,并結(jié)合一定的教師教學(xué)經(jīng)驗(yàn),第一次比較系統(tǒng)地闡述了數(shù)學(xué)抽象思想的內(nèi)涵,提出小學(xué)數(shù)學(xué)中抽象思想不僅僅指由抽象思想派生出來(lái)的一些具體數(shù)學(xué)思想方法,也包含對(duì)數(shù)學(xué)對(duì)象抽象的理解,以及在學(xué)習(xí)數(shù)學(xué)抽象內(nèi)容的過(guò)程,滲透抽象思想,促進(jìn)學(xué)生數(shù)學(xué)抽象思維能力的發(fā)展,并探索小學(xué)數(shù)學(xué)課程內(nèi)容的抽象發(fā)展以及如何在教學(xué)中滲透抽象思想,形成了對(duì)數(shù)學(xué)抽象思想更為全面、系統(tǒng)的認(rèn)識(shí)。本論文主要分為五部分：第一部分介紹研究本論題的緣由、意義及基本研究思路、方法；第二部分,從抽象與概括、抽象思維與抽象思想、滲透抽象思想的意義三方面探索對(duì)抽象思想的認(rèn)識(shí)；第三部分,著重分析了小學(xué)數(shù)學(xué)抽象思想的內(nèi)涵、小學(xué)數(shù)學(xué)教材內(nèi)容的抽象發(fā)展分析以及基本的數(shù)學(xué)抽象思想方法(分類(lèi)思想、符號(hào)化思想、變與不變思想)；第四部分,主要是在小學(xué)生數(shù)學(xué)思維特點(diǎn)的基礎(chǔ)上,探討怎樣在小學(xué)數(shù)學(xué)教學(xué)中滲透抽象思想,并提供經(jīng)典的教學(xué)片斷設(shè)計(jì),為教學(xué)實(shí)踐提供借鑒；第五部分,是對(duì)本論題研究的總結(jié)歸納,在此之上,提出本研究的不足及創(chuàng)新之處。
[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.
【學(xué)位授予單位】：華中師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類(lèi)號(hào)】：G623.5

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