数学文化—高中数学教学中的渗透
发布时间：2018-11-22 06:11
【摘要】：“数学文化”一词对于我们并不生疏,由于越来越多的人喜欢把它列入写作范畴,因此被广泛运用,说明大家都希望从一个新颖的角度来研究数学。近几年来,随着数学文化研究热潮的到来,许多优秀作品也相继问世。更有一些研究生也写出了与数学文化相关的论文。到现在为止,越来越多的人重视数学文化,数学文化已经成为数学教育界的焦点之一。数学作为一种文化不仅可以提高我们的数学素养,还可以陶冶情操,提高我们的文化修养。数学史不仅仅记录着数学成果,也记载着数学家们客服艰难险阻的伟大历程。认识相关数学分支的数学家以及他们探索的历程,可以帮助我们了解伟大数学成就的来源,而在了解这些数学成就的同时,我们可以从前人的探索中吸取经验,增加数学学习的兴趣和自信心。同时,可以也开阔眼界,既可以把我们以前学习的知识上升到新的高度,又可以从其他学科的角度来探索数学发展中的其它规律;通过数学史中的典型案例,可以培养我们缜密的思维力、敏锐的洞察力、敢于质疑的意识、丰富的想象力、和灵活的思维模式。只有接触数学文化,才可以知道数学发展的历史,又可以了解数学家的思想、人生和价值观。数学文化中的数学史无论对于这门学科的自身发展,还是对于全人类文明的进步都具有深远影响。因此,可以说了解数学文化就是了解整个数学科学。因为数学文化的涉及范围宽阔,所以要想把数学文化的内容引入中学数学教学中还是有点难度,教学效果也不见得理想。本文则主要从数学文化的两个方面(数学家及其数学分支)着手,对高中数学教学如何渗透数学文化方面展开研究。通过介绍数学家的奇闻异事,激发学生学习的兴趣;通过相关数学史史的介绍,可以更好的帮助学生拓展知识面,增加认识。本论文主要围绕数学家以及他们所涉及的数学领域进行研究,捡取数学中几个重要的分支进行分析探讨:1、了解数学文化的研究背景、国内外研究现状和研究意义,并简单介绍数学文化的内涵。2、从与高中紧密联系的几个数学分支展开研究探讨,主要包括集合论方面:介绍康托尔并引出集合论,讨论集合论的诞生及其研究意义;数列方面:由数列来源的历史,引出数列中经典例子—斐波那契数列,并讨论该数列的性质和相关问题。并简单介绍高中课本中经典的数列求和例子,引出了另一个数学天才—高斯;解析几何方面:介绍笛卡尔并引出笛卡尔解析几何,讨论相关经典应用及其意义;复数方面:介绍复数的来源、概念,及其意义的建构。运筹学方面:介绍和博弈论紧密相关的冯·诺依曼和约翰·纳什,并对他们在博弈论方面的贡献进行一一介绍,接着引出我们高中线性规划部分的教学建议。最后,笔者结合自己的理解粗略的对以上内容进行简单总结概括。
[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.
【学位授予单位】：河南大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：G633.6
本文编号：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.
【学位授予单位】：河南大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：G633.6
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