數(shù)學(xué)文化—高中數(shù)學(xué)教學(xué)中的滲透
發(fā)布時間：2018-11-22 06:11
【摘要】：“數(shù)學(xué)文化”一詞對于我們并不生疏,由于越來越多的人喜歡把它列入寫作范疇,因此被廣泛運(yùn)用,說明大家都希望從一個新穎的角度來研究數(shù)學(xué)。近幾年來,隨著數(shù)學(xué)文化研究熱潮的到來,許多優(yōu)秀作品也相繼問世。更有一些研究生也寫出了與數(shù)學(xué)文化相關(guān)的論文。到現(xiàn)在為止,越來越多的人重視數(shù)學(xué)文化,數(shù)學(xué)文化已經(jīng)成為數(shù)學(xué)教育界的焦點(diǎn)之一。數(shù)學(xué)作為一種文化不僅可以提高我們的數(shù)學(xué)素養(yǎng),還可以陶冶情操,提高我們的文化修養(yǎng)。數(shù)學(xué)史不僅僅記錄著數(shù)學(xué)成果,也記載著數(shù)學(xué)家們客服艱難險阻的偉大歷程。認(rèn)識相關(guān)數(shù)學(xué)分支的數(shù)學(xué)家以及他們探索的歷程,可以幫助我們了解偉大數(shù)學(xué)成就的來源,而在了解這些數(shù)學(xué)成就的同時,我們可以從前人的探索中吸取經(jīng)驗(yàn),增加數(shù)學(xué)學(xué)習(xí)的興趣和自信心。同時,可以也開闊眼界,既可以把我們以前學(xué)習(xí)的知識上升到新的高度,又可以從其他學(xué)科的角度來探索數(shù)學(xué)發(fā)展中的其它規(guī)律;通過數(shù)學(xué)史中的典型案例,可以培養(yǎng)我們縝密的思維力、敏銳的洞察力、敢于質(zhì)疑的意識、豐富的想象力、和靈活的思維模式。只有接觸數(shù)學(xué)文化,才可以知道數(shù)學(xué)發(fā)展的歷史,又可以了解數(shù)學(xué)家的思想、人生和價值觀。數(shù)學(xué)文化中的數(shù)學(xué)史無論對于這門學(xué)科的自身發(fā)展,還是對于全人類文明的進(jìn)步都具有深遠(yuǎn)影響。因此,可以說了解數(shù)學(xué)文化就是了解整個數(shù)學(xué)科學(xué)。因?yàn)閿?shù)學(xué)文化的涉及范圍寬闊,所以要想把數(shù)學(xué)文化的內(nèi)容引入中學(xué)數(shù)學(xué)教學(xué)中還是有點(diǎn)難度,教學(xué)效果也不見得理想。本文則主要從數(shù)學(xué)文化的兩個方面(數(shù)學(xué)家及其數(shù)學(xué)分支)著手,對高中數(shù)學(xué)教學(xué)如何滲透數(shù)學(xué)文化方面展開研究。通過介紹數(shù)學(xué)家的奇聞異事,激發(fā)學(xué)生學(xué)習(xí)的興趣;通過相關(guān)數(shù)學(xué)史史的介紹,可以更好的幫助學(xué)生拓展知識面,增加認(rèn)識。本論文主要圍繞數(shù)學(xué)家以及他們所涉及的數(shù)學(xué)領(lǐng)域進(jìn)行研究,撿取數(shù)學(xué)中幾個重要的分支進(jìn)行分析探討:1、了解數(shù)學(xué)文化的研究背景、國內(nèi)外研究現(xiàn)狀和研究意義,并簡單介紹數(shù)學(xué)文化的內(nèi)涵。2、從與高中緊密聯(lián)系的幾個數(shù)學(xué)分支展開研究探討,主要包括集合論方面:介紹康托爾并引出集合論,討論集合論的誕生及其研究意義;數(shù)列方面:由數(shù)列來源的歷史,引出數(shù)列中經(jīng)典例子—斐波那契數(shù)列,并討論該數(shù)列的性質(zhì)和相關(guān)問題。并簡單介紹高中課本中經(jīng)典的數(shù)列求和例子,引出了另一個數(shù)學(xué)天才—高斯;解析幾何方面:介紹笛卡爾并引出笛卡爾解析幾何,討論相關(guān)經(jīng)典應(yīng)用及其意義;復(fù)數(shù)方面:介紹復(fù)數(shù)的來源、概念,及其意義的建構(gòu)。運(yùn)籌學(xué)方面:介紹和博弈論緊密相關(guān)的馮·諾依曼和約翰·納什,并對他們在博弈論方面的貢獻(xiàn)進(jìn)行一一介紹,接著引出我們高中線性規(guī)劃部分的教學(xué)建議。最后,筆者結(jié)合自己的理解粗略的對以上內(nèi)容進(jìn)行簡單總結(jié)概括。
[Abstract]:The term "mathematical culture" is not unfamiliar to us. Because more and more people like to include it in the category of writing, it is widely used, indicating that everyone wants to study mathematics from a new angle. In recent years, with the arrival of mathematical culture research boom, many excellent works have been published. Some graduate students have also written papers related to mathematics culture. Up to now, more and more people attach importance to mathematics culture, mathematics culture has become one of the focus of mathematics education. Mathematics as a culture can not only improve our mathematical literacy, but also cultivate sentiment and improve our cultural accomplishment. The history of mathematics not only records the achievements of mathematics, but also records the great course of mathematicians'customer service. The mathematicians who know the relevant branches of mathematics and the course of their exploration can help us understand the source of great mathematical achievements, and we can learn from the explorations of our predecessors while understanding these achievements. Increase interest and confidence in math learning. At the same time, we can also broaden our horizons, not only can we learn the knowledge to a new height, but also from the perspective of other disciplines to explore other laws in the development of mathematics; Through typical cases in the history of mathematics, we can cultivate careful thinking, sharp insight, a sense of dare to question, rich imagination, and flexible mode of thinking. Only by contact with mathematical culture can we know the history of mathematical development and understand mathematicians' thoughts, life and values. The history of mathematics in mathematics culture has a profound influence on the development of this subject and on the progress of human civilization. Therefore, it can be said that understanding mathematical culture is to understand the whole mathematical science. Because of the wide range of mathematics culture, it is difficult to introduce the content of mathematics culture into mathematics teaching in middle school, and the teaching effect is not ideal. This paper mainly starts with two aspects of mathematics culture (mathematicians and their branches) and studies how to infiltrate mathematics culture in mathematics teaching in senior high school. Through introducing mathematicians, arousing students' interest in learning, and introducing the history of mathematics, we can better help students expand their knowledge and increase their understanding. This paper mainly focuses on mathematicians and their mathematical fields, picking up several important branches of mathematics for analysis and discussion: 1. Understand the research background of mathematics culture, the current situation and significance of research at home and abroad. And briefly introduces the connotation of mathematical culture. 2, from the close relationship with several branches of mathematics, mainly including set theory: introduce Cantor and elicit set theory, discuss the birth of set theory and its significance; Sequence aspect: from the history of the sequence source, the classical example of the series-Fibonacci sequence is introduced, and the properties and related problems of the series are discussed. It also briefly introduces the examples of classical summation of number series in high school textbooks, leads to another mathematical genius, Gao Si, Analytical Geometry, introduces Descartes and leads to Cartesian Analytical Geometry, discusses the application of relevant classics and its significance. Plural aspect: introduces the source, concept, and meaning of plural. Operational research: introduces von Neumann and John Nash, who are closely related to game theory, and introduces their contributions to game theory, and then leads to the teaching suggestions of our senior high school linear programming. Finally, the author combined with his understanding of rough summary of the above content.
【學(xué)位授予單位】：河南大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：G633.6
本文編號：2348319
[Abstract]:The term "mathematical culture" is not unfamiliar to us. Because more and more people like to include it in the category of writing, it is widely used, indicating that everyone wants to study mathematics from a new angle. In recent years, with the arrival of mathematical culture research boom, many excellent works have been published. Some graduate students have also written papers related to mathematics culture. Up to now, more and more people attach importance to mathematics culture, mathematics culture has become one of the focus of mathematics education. Mathematics as a culture can not only improve our mathematical literacy, but also cultivate sentiment and improve our cultural accomplishment. The history of mathematics not only records the achievements of mathematics, but also records the great course of mathematicians'customer service. The mathematicians who know the relevant branches of mathematics and the course of their exploration can help us understand the source of great mathematical achievements, and we can learn from the explorations of our predecessors while understanding these achievements. Increase interest and confidence in math learning. At the same time, we can also broaden our horizons, not only can we learn the knowledge to a new height, but also from the perspective of other disciplines to explore other laws in the development of mathematics; Through typical cases in the history of mathematics, we can cultivate careful thinking, sharp insight, a sense of dare to question, rich imagination, and flexible mode of thinking. Only by contact with mathematical culture can we know the history of mathematical development and understand mathematicians' thoughts, life and values. The history of mathematics in mathematics culture has a profound influence on the development of this subject and on the progress of human civilization. Therefore, it can be said that understanding mathematical culture is to understand the whole mathematical science. Because of the wide range of mathematics culture, it is difficult to introduce the content of mathematics culture into mathematics teaching in middle school, and the teaching effect is not ideal. This paper mainly starts with two aspects of mathematics culture (mathematicians and their branches) and studies how to infiltrate mathematics culture in mathematics teaching in senior high school. Through introducing mathematicians, arousing students' interest in learning, and introducing the history of mathematics, we can better help students expand their knowledge and increase their understanding. This paper mainly focuses on mathematicians and their mathematical fields, picking up several important branches of mathematics for analysis and discussion: 1. Understand the research background of mathematics culture, the current situation and significance of research at home and abroad. And briefly introduces the connotation of mathematical culture. 2, from the close relationship with several branches of mathematics, mainly including set theory: introduce Cantor and elicit set theory, discuss the birth of set theory and its significance; Sequence aspect: from the history of the sequence source, the classical example of the series-Fibonacci sequence is introduced, and the properties and related problems of the series are discussed. It also briefly introduces the examples of classical summation of number series in high school textbooks, leads to another mathematical genius, Gao Si, Analytical Geometry, introduces Descartes and leads to Cartesian Analytical Geometry, discusses the application of relevant classics and its significance. Plural aspect: introduces the source, concept, and meaning of plural. Operational research: introduces von Neumann and John Nash, who are closely related to game theory, and introduces their contributions to game theory, and then leads to the teaching suggestions of our senior high school linear programming. Finally, the author combined with his understanding of rough summary of the above content.
【學(xué)位授予單位】：河南大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：G633.6
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，本文編號：2348319
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