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1.
数学与哲学是互为关联、相互印证的,"你中有我,我中有你"。严格地讲,数学讲究定义的准确与清晰,是考察对象的量的规定,哲学则着重分析语言及概念的含义。许多哲学命题可用数学去阐释,许多数学问题又蕴涵着深刻的哲学意义。本文试图利用微积分中的一些数学概念来说明这一问题。 相似文献
2.
Michael Friedrich Otte Tânia M. M. Campos Alexandre S. Abido 《Educational Studies in Mathematics》2013,82(3):397-415
Abstract educational practices are to be based on proven scientific knowledge, not least because the function science has to perform in human culture consists of unifying practical skills and general beliefs, the episteme and the techne (Amsterdamski, 1975, pp. 43–44). Now, modern societies first of all presuppose regular and standardized ways of organizing both our concepts and our institutions. The explanatory schemata resulting from this standardization tend to destroy individualism and enchantment. But mathematics education is in fact the only place in which to treat the human subject’s relationship with mathematics. And that is what mathematics education is all about: make the human subject grow intellectually and as a person by means of mathematics. At first sight, mathematics, in its formal guise, seems the opposite of philosophy, because philosophy constructs concepts (meanings), whereas mathematics deals with extensions of concepts (sets). We shall, however, turn this problem into an instrument, using the complementarity of intensions and extensions of theoretical terms as our main device for discussing the relationship between philosophy and mathematics education. The complementarity of the “how” and the “what” of our representations outlines, in fact, the terrain on which epistemology and education are to meet. 相似文献
3.
对哲学的不同理解将导致对数学教育哲学的不同理解。将数学教育哲学置于公开的科学争论中,一般认为主要受两个方面的影响,即本国所特有的各种文化传统和不同的哲学观。本文从哲学的视角出发,通过一则隐喻对数学教育哲学是什么进行了反思,分析了哲学、数学哲学、教育哲学对数学教育哲学的影响。 相似文献
4.
Paul Ernest 《Interchange》2000,31(2-3):225-241
In Principia Mathematica Whitehead and Russell erected one of the cornerstones of modernist philosophy of mathematics. However, as an epistemological project seeking to secure the foundations of mathematics, this attempt failed, as Whitehead acknowledged. His later work in process philosophy represented a new direction. Although not explicitly a philosophy of mathematics, it provides a suggested metaphor for philosophy of mathematics. This paper explores the possible implications of organismic and process philosophy, both for the philosophy of mathematics, and for mathematics education and teaching. 相似文献
5.
数学哲学对数学教育有着深刻的影响。首先回顾了数学哲学的发展 ,明确了现在数学哲学中的数学观由绝对主义向可误主义的转变 ,接着论述了数学哲学对数学教育诸方面所产生的影响 ,最后列举了新的数学观点对现代数学教育的影响。 相似文献
6.
20世纪70年代以来,我国数学教育研究队伍不断壮大,学术组织稳步发展,学术期刊质量不断提升,初步形成数学教育研究的良好环境.研究的主要成果:建立了数学教育哲学基本理论,开展一系列有成效的数学教学实验,在数学学习心理方面作了有益探索,民族数学教育跨文化研究初见成效,数学方法论研究不断深入,"教育数学"思想独树一帜.反思我国数学教育的当代研究,我们应当在数学教育学科定位、研究队伍的知识结构完善、研究课题、方向的选择等方面作不懈努力. 相似文献
7.
数学和哲学都产生于生产劳动的实践,它们都是随着社会的进步,科学的日益发展而发展。哲学的观点决定了数学的思想,哲学思想指导着数学的发展。在数学中处处体现了唯物辨证法的思想的光辉,处处闪烁着人类思维进步的理论结晶。要想学好数学,教好数学,必须具有哲学的理性思维的头脑,必须掌握哲学科学的认识方法,这无论对于数学理论工作者,还是对于数学教学工作者来说都具有十分重要的意义。 相似文献
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The article elaborates and exemplifies a potential categorization of the reasons for using philosophy, in particular the philosophy of mathematics, in mathematics education and approaches to doing so—the so-called ‘whys’ and ‘hows’. More precisely, the ‘whys’ are divided into the two categories of ‘philosophy as a tool’ for teaching and learning mathematics, and ‘philosophy as a goal’, referring to a stance of considering it a purpose in itself to teach students certain aspects regarding the philosophy of mathematics. A division of the ‘hows’ into three different categories is offered: illumination approaches; modules approaches; and philosophy-based approaches. A major part of the article is spent on providing illustrative exemplifications of each of these approaches by referring to already implemented uses of philosophy of mathematics in mathematics education as well as by suggesting new ones. 相似文献
9.
Much reference has been made to Paul Ernest??s ??philosophy of mathematics education?? to legitimise a strong fallibilist trend in mathematics education. This article presents the argument that: (1) This philosophy makes unwarranted assumptions that have been taken as ??given??. For example, that ??absolutist?? or ??Platonist?? views of mathematics necessarily imply the transmission model of teaching mathematics. (2) The very basis of this philosophy contains a contradiction: that mathematics cannot be separated from its social origins, yet mathematics has a logical necessity that is independent of its origin. (3) This philosophy downplays mathematics as a formal, academic system of knowledge in the attempt to promote a child-centred pedagogy or the mathematics of social practices. (4) Ernest??s attempt to semiotically reduce proof to calculation is flawed. This article explores what is meant by fallibilism in relation to the views of many educationalists who appear not to like mathematics as a formal, academic body of knowledge and draws out the educational implications of these views. 相似文献
10.
谢明初 《广东教育学院学报》2008,28(5):97-100
基础主义和拟经验主义是数学哲学的两个主要派别,通过对其哲学立场的分析提出这两种哲学观的对立表现在数学教育中就是行为主义和建构主义的对立,从一个侧面表明数学哲学对实际数学活动的影响．这对我们有重要的启示,即不论是对数学教育研究还是数学课程改革来说都应该加强对数学哲学观的研究,从而使得数学教育的发展避免盲目性,增加哲学的自觉性． 相似文献
11.
Karen François Kathleen Coessens Jean Paul Van Bendegem 《Journal of Philosophy of Education》2012,46(3):370-385
It is a rather safe statement to claim that the social dimensions of the scientific process are accepted in a fair share of studies in the philosophy of science. It is a somewhat safe statement to claim that the social dimensions are now seen as an essential element in the understanding of what human cognition is and how it functions. But it would be a rather unsafe statement to claim that the social is fully accepted in the philosophy of mathematics. And we are not quite sure what kind of statement it is to claim that the social dimensions in theories of mathematics education are becoming more prominent, compared to the psychological dimensions. In our contribution we will focus, after a brief presentation of the above claims, on this particular domain to understand the successes and failures of the development of theories of mathematics education that focus on the social and not primarily on the psychological. 相似文献
12.
国内外关于数学教育哲学的研究已经取得了不少开创性的成果.有鉴于哲学思考对于数学教育的重要性,在哲学上从不同视角对数学教育哲学加以定义是有益的.通过对数学教育哲学学科特征的揭示,可以进一步凸现数学教育哲学的研究对象,并为进一步开展数学教育的研究奠定理论基础. 相似文献
13.
我国数学教育学学科建设始于对“中学数学教材教法”相关问题的探讨,经历了作为一门课程的“数学教育学”、作为系列课程的“数学教育学”及作为学科群的“数学教育学”和“数学教育学”的主题研究繁荣等几个发展阶段,初步形成了具有中国特色的数学教育学学科。数学教育学是一门涉及数学、教育学、哲学、心理学、文化学、传播学、教育技术学、思维科学等有关内容的新兴交叉学科,在数学教育学的学科建设过程中,通过理论与实践两方面研究,形成了数学教育专门研究人员与一线教师组成的研究团队,发展、完善了有中国特色的数学教育学科体系。今后,数学教育学学科建设仍需关注理论体系建构、研究团队建设、研究视角拓展等问题。 相似文献
14.
张桂权 《科学技术哲学研究》2021,38(1):28-33
西方哲学有与数学结盟的强大传统,但黑格尔是西方哲学家中的异类,他尖锐地批判数学。文章分三部分。文章首先交代了西方哲学的强大数学传统,这是黑格尔批判数学的背景;其次,深入分析了黑格尔对数学的批判,包括他对数学证明、数学洞见、数学自明性的批判;最后,讨论了黑格尔的量的观点,作者认为这是黑格尔批判数学的哲学根据。 相似文献
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CHRISTOPHER DUBBS 《Journal of Philosophy of Education》2020,54(3):521-540
The philosophical branch of ethics is foundationally concerned with the question of right or wrong, benevolent or harmful, and ultimately what is proper conduct. The present inquiry addresses two related questions: (1) How have theories of ethics been applied to mathematics education research? and (2) What alternatives have not been considered? What might the implications be if these alternative formulations were considered? To answer the first question, I offer a review of the philosophy of mathematics education literature, considering those articles which discuss ethics and mathematics education together. The ethical perspectives adopted within the literature span normative and non-normative, modern and postmodern orientations towards ethics. To answer the second question, I explored philosophy literature to identify which philosophical perspectives of ethics have (not) been adopted by philosophers of mathematics education research. The structure of this paper parallels these two questions: the first part considers the philosophy of mathematics education research and how researchers have defined ethics while the second part discusses additional philosophical approaches to ethics and puts those approaches into conversation with those identified in part one. I conclude by intertwining these two strands into my central thesis: ethics per se is construed too narrowly in the philosophy of mathematics education literature and considering additional ethical perspectives from philosophy can be generative of new ideas. 相似文献
16.
Uffe Thomas Jankvist 《Science & Education》2013,22(3):635-656
The article first investigates the basis for designing teaching activities dealing with aspects of history, applications, and philosophy of mathematics in unison by discussing and analyzing the different ‘whys’ and ‘hows’ of including these three dimensions in mathematics education. Based on the observation that a use of history, applications, and philosophy as a ‘goal’ is best realized through a modules approach, the article goes on to discuss how to actually design such teaching modules. It is argued that a use of primary original sources through a so-called guided reading along with a use of student essay assignments, which are suitable for bringing out relevant meta-issues of mathematics, is a sensible way of realizing a design encompassing the three dimensions. Two concrete teaching modules on aspects of the history, applications, and philosophy of mathematics—HAPh-modules—are outlined and the mathematical cases of these, graph theory and Boolean algebra, are described. Excerpts of student groups’ essays from actual implementations of these modules are displayed as illustrative examples of the possible effect such HAPh-modules may have on students’ development of an awareness regarding history, applications, and philosophy in relation to mathematics as a (scientific) discipline. 相似文献
17.
竞赛数学课程是以问题为目标的数学课程。传统教学主要以＂问题为导向,能力为目标＂,以传授教学为主要教学活动,教学方法单一,学生无法获得数学智慧的发展,教学效果一般。鉴于此,我们借助开放式教学理念,在竞赛数学课程中引入开放式教学手段。实践表明,开放式教学能够实现教学的良好互动,使学生学习数学的积极性明显提升。本文对开放教学理念下的竞赛数学课程教学方法进行了探索,以期取得更好的教学效果。 相似文献
18.
Undergraduate students do not always make a clear distinction between physics and mathematics, particularly early in their studies. We offer a simple historical example and show how it can be used to illustrate some of the important differences and relationships between the two. The example is Galileo's treatment of motion under uniform acceleration, in which he uses geometry instead of algebra to represent quantities such as time and velocity and stresses the need to test the adequacy of the representation by experiment. The general importance of Galileo's work in the history of science and the fact that it is accessible to undergraduates not concentrating their studies in mathematics or the sciences make it particularly suitable for our purposes. In addition to undergraduate courses in physics or mathematics, many of the points we make should be useful in courses in the history and philosophy of science and mathematics. 相似文献
19.
张留华 《昆明师范高等专科学校学报》2011,(1):34-39,44
皮尔士试图从科学分类法阐明逻辑学与其他科学之间的诸种关联,从而让我们看到一个既有所主张又有所保留、既充分包容又严格限定的逻辑科学：1.逻辑学作为实证科学,被归在哲学分部中,位居数学这一非实证科学之后;2.即便在哲学内部,逻辑学作为规范科学也不是处在第一位,形而上学倒是排在逻辑学之后,但在逻辑学之前存在着现象学这一哲学分支,而且在规范科学内部还有伦理学、美学位居逻辑学之前;3.逻辑学自身也是一个复杂的学科体系,其不仅关注论证有效性的批判论即今天通常意义上的逻辑,而且把理论意义上的语法和修辞也包括在内。 相似文献
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