本文關(guān)鍵詞： 極限概念 無(wú)窮 文化 導(dǎo)數(shù)　出處：《華中師范大學(xué)》2015年碩士論文　論文類(lèi)型：學(xué)位論文

【摘要】：極限是數(shù)學(xué)中由常量到變量、有限到無(wú)限、近似到精確思想轉(zhuǎn)變的重要概念,在數(shù)學(xué)發(fā)展史上占有重要地位.極限是大學(xué)數(shù)學(xué)課程中微積分的基礎(chǔ)概念.隨著新課程改革,導(dǎo)數(shù)(一種特殊的極限)的內(nèi)容已進(jìn)入高中數(shù)學(xué)教材.極限作為大學(xué)乃至中學(xué)數(shù)學(xué)中一種重要的數(shù)學(xué)思想方法,在整個(gè)數(shù)學(xué)學(xué)習(xí)中也是最基本的思想方法之一.因此,筆者想系統(tǒng)地探討極限概念的發(fā)展過(guò)程,以利于教師與學(xué)生全面了解極限的歷史、現(xiàn)狀.然而,從數(shù)學(xué)史的角度進(jìn)行研究是數(shù)學(xué)史家已做過(guò)的工作,價(jià)值不大且枯燥無(wú)味.而數(shù)學(xué)文化是探討在數(shù)學(xué)的起源、發(fā)展、完善和應(yīng)用方面對(duì)人的觀念、思想和思維方式有所影響的內(nèi)容,是研究極限概念的一個(gè)新視角,本文就試著從數(shù)學(xué)文化的視角探討極限概念的發(fā)展歷程,并考察高中數(shù)學(xué)課程中極限內(nèi)容的設(shè)置,剖析其中蘊(yùn)涵的文化性,給出教學(xué)建議,以期對(duì)高中數(shù)學(xué)教師的教學(xué)和學(xué)生的學(xué)習(xí)有所助益.本文主要采用文獻(xiàn)法與歷史溯源法,先綜述了文化、數(shù)學(xué)文化的含義與特征,極限概念的研究視角分析,這是研究極限概念文化性的理論基礎(chǔ).接著,探討極限概念在中西方數(shù)學(xué)中的發(fā)展過(guò)程,其中蘊(yùn)涵著極限的文化性,最重要的是展現(xiàn)對(duì)人類(lèi)思想觀念的轉(zhuǎn)變的影響與勇于探索進(jìn)取的精神.在中國(guó)數(shù)學(xué)對(duì)極限概念的認(rèn)識(shí)中,主要是追溯古代文化傳統(tǒng)下的極限思想,以及對(duì)其它數(shù)學(xué)問(wèn)題解決的影響.與之相對(duì)的是西方數(shù)學(xué)中極限的發(fā)展歷程.由于極限概念在西方得到了最終的嚴(yán)密化、形式化的發(fā)展,所以從符號(hào)化程度高低的角度,我將西方數(shù)學(xué)中極限的發(fā)展分四個(gè)階段進(jìn)行探究,分別是萌芽階段、神秘階段、統(tǒng)一階段和擴(kuò)展階段.最后,從數(shù)學(xué)課程標(biāo)準(zhǔn)、教材與教學(xué)的角度分析教育形態(tài)的極限的文化性.通過(guò)對(duì)極限概念的文化性探析過(guò)程,得到的主要結(jié)論與建議：1高中數(shù)學(xué)中的極限內(nèi)容基本上體現(xiàn)出極限文化發(fā)展歷程來(lái)進(jìn)行編排的.2高中生雖然對(duì)形式化的極限定義理解有難度,但極限作為“導(dǎo)數(shù)及其應(yīng)用”內(nèi)容的基礎(chǔ)性概念,教材中應(yīng)給出極限的描述性定義.3在數(shù)學(xué)課程中更主動(dòng)、有意識(shí)地滲透極限的本質(zhì)---無(wú)窮思想.在極限概念之前可適當(dāng)滲透無(wú)窮的思想,如對(duì)自然數(shù)個(gè)數(shù)的無(wú)窮性的體會(huì),無(wú)理數(shù)概念中小數(shù)無(wú)限性的認(rèn)識(shí).
[Abstract]:Limit is an important concept in mathematics, which changes from constant to variable, from finite to infinite, approximate to precise thought, and occupies an important position in the history of mathematics development. Limit is the basic concept of calculus in the course of university mathematics. The content of derivative (a special limit) has entered high school mathematics textbook. Limit, as an important mathematical thought method in university and middle school mathematics, is also one of the most basic thought methods in the whole mathematics study. The author wants to discuss the development process of the limit concept systematically, so as to help teachers and students to understand the history and present situation of the limit in an all-round way. However, it is the work of mathematics historians to study from the point of view of the history of mathematics. Mathematics culture is a new angle of view to study the concept, thought and mode of thinking of people in the origin, development, perfection and application of mathematics. This paper attempts to explore the development of the concept of limit from the perspective of mathematical culture, and to investigate the setting of the limit content in the mathematics curriculum of senior high school, to analyze the cultural content contained therein, and to give some teaching suggestions. This paper mainly adopts the literature method and the historical traceability method, first summarizes the culture, the mathematics culture meaning and the characteristic, the limit concept research angle of view analysis, the article mainly uses the literature method and the history tracing method, first summarizes the culture, the mathematics culture meaning and the characteristic, the limit concept research angle of view. This is the theoretical basis for studying the cultural nature of the limit concept. Then, the development process of the limit concept in Chinese and Western mathematics is discussed, which implies the cultural nature of the limit. The most important thing is to show the influence on the change of human ideology and the spirit of being enterprising. In the understanding of the concept of limit in Chinese mathematics, it is mainly traced back to the limit thought under the tradition of ancient culture. And its influence on the solution of other mathematical problems. In contrast, it is the development of limit in western mathematics. Because the concept of limit has finally developed in the west, so from the perspective of the degree of symbolization, I divided the development of the limit in western mathematics into four stages, namely, the budding stage, the mysterious stage, the unification stage and the extension stage. Finally, from the mathematics curriculum standard, The cultural nature of the limit of educational form is analyzed from the perspective of teaching materials and teaching. The main conclusions and suggestions obtained are that the limit content in Senior High School Mathematics of 1: 1 basically reflects the development course of limit culture, though it is difficult for the senior middle school students to understand the formalized definition of the limit although it is difficult for them to understand the formalized definition of the limit. However, as the basic concept of "derivative and its application", the descriptive definition of limit should be given in the textbook. The idea of infinity can be properly infiltrated before the concept of limit, such as the understanding of the infinity of the number of natural numbers and the understanding of infinity of the concept of irrational number.
【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)】：G633.6

【共引文獻(xiàn)】

相關(guān)期刊論文 前10條

1 馮素芬;試論數(shù)學(xué)反例及其構(gòu)造[J];北京工業(yè)職業(yè)技術(shù)學(xué)院學(xué)報(bào);2003年03期

2 陳愛(ài)清,種國(guó)富;類(lèi)比法在數(shù)學(xué)教學(xué)中的應(yīng)用[J];北京工業(yè)職業(yè)技術(shù)學(xué)院學(xué)報(bào);2004年02期

3 張玉;胡艷紅;;兼顧實(shí)用性與人文性的高等數(shù)學(xué)教學(xué)研究[J];邊疆經(jīng)濟(jì)與文化;2009年06期

4 張俊青;王保紅;;后現(xiàn)代視閾中的數(shù)學(xué)[J];北京科技大學(xué)學(xué)報(bào)(社會(huì)科學(xué)版);2010年01期

5 毛京中;數(shù)學(xué)教育的文化功能[J];北京理工大學(xué)學(xué)報(bào)(社會(huì)科學(xué)版);2002年04期

6 王路平,張虹;建構(gòu)主義觀點(diǎn)下的高等數(shù)學(xué)教學(xué)模式[J];山東工商學(xué)院學(xué)報(bào);2005年04期

7 趙慶沖;;淺析小學(xué)數(shù)學(xué)教學(xué)興趣的培養(yǎng)[J];才智;2010年36期

8 高明,康紀(jì)權(quán);淺析數(shù)學(xué)的文化價(jià)值[J];四川職業(yè)技術(shù)學(xué)院學(xué)報(bào);2003年03期

9 張其亮;;數(shù)學(xué)文化摭拾[J];成才之路;2007年02期

10 唐雯雯;;談新課改下的高職數(shù)學(xué)教育[J];成才之路;2010年28期

相關(guān)博士學(xué)位論文 前10條

1 曹榮榮;理工科大一學(xué)生高等數(shù)學(xué)思維的研究[D];華東師范大學(xué);2011年

2 畢力格圖;高中數(shù)學(xué)教師學(xué)科知識(shí)發(fā)展研究[D];東北師范大學(xué);2011年

3 曹一鳴;數(shù)學(xué)教學(xué)模式的重構(gòu)與超越[D];南京師范大學(xué);2003年

4 呂林海;數(shù)學(xué)理解性學(xué)習(xí)與教學(xué)研究[D];華東師范大學(xué);2005年

5 蘇羽;傳感器網(wǎng)絡(luò)中的無(wú)尺度路由問(wèn)題[D];東北大學(xué);2005年

6 朱華偉;高師奧林匹克數(shù)學(xué)課程研究[D];華中科技大學(xué);2005年

7 楊光偉;學(xué)生在應(yīng)用問(wèn)題解決上的元認(rèn)知行為表現(xiàn)與信念[D];華東師范大學(xué);2006年

8 李渺;教師的理性追求[D];南京師范大學(xué);2007年

9 李鐵安;基于笛卡兒數(shù)學(xué)思想的高中解析幾何教學(xué)策略研究[D];西南大學(xué);2007年

10 趙樹(shù)峰;數(shù)學(xué)建模教育的素質(zhì)培養(yǎng)內(nèi)涵與文化特征[D];吉林大學(xué);2008年

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