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1.
Bettina Pedemonte 《Educational Studies in Mathematics》2007,66(1):23-41
The paper presents a characterisation about argumentation and proof in mathematics. On the basis of contemporary linguistic
theories, the hypothesis that proof is a special case of argumentation is put forward and Toulmin’s model is proposed as a
methodological tool to compare them. This model can be used to detect and analyse the structure of an argumentation supporting
a conjecture (abduction, induction, etc.) and the structure of its proof. The aim of the paper is to highlight the importance
of structural analysis between argumentation and proof. This analysis shows that although there are clear cases of continuity
between argumentation supporting a conjecture and its proof, there is often a structural distance between the two (from an
abductive argumentation to a deductive proof, from an inductive argumentation to a mathematical inductive proof). 相似文献
2.
在近现代数学中,通常认为Cantor-Hilbert对角线论证方法是有效的.特别有如文献[1]之2.4,列举多条理由论证Cantor-Hilbert对角线论证方法是无懈可击的,但经分析研究文献[1]之2.4中所列之论据,其中每一条论据都是没有根据的.文献[2]之6.6指出：在兼容两种无穷观之分析方法前提下,可以证明Cantor-Hilbert对角线论证方法并不是无懈可击的.文献[3]又在逻辑演算之谓词与集合的层面上,给出了一个不同于文献[2]之6.6中的证明方法.因此该文既是一篇评论性文章,其实更是一篇研究性论文. 相似文献
3.
Gila Hanna 《Interchange》2000,31(1):21-33
Proof seems to have been losing ground in the secondary mathematics curriculum despite its importance in mathematical theory and practice. The present paper critically examines three specific factors that have lent impetus to the decline of proof in the curriculum: a) The idea that proof need be taught only to those students who intend to pursue post-secondary education, b) the view that deductive proof need no longer be taught because heuristic techniques are more useful than proof in developing skills in reasoning and justification, c) the idea that deductive proof might profitably be abandoned in the classroom in favour of a dynamic visual approach to mathematical justification. The paper concludes that proof should be an essential component in mathematics education at all levels and compatible with both heuristic techniques and dynamic visual approaches. 相似文献
4.
Takeshi Miyakawa 《Educational Studies in Mathematics》2017,94(1):37-54
This paper reports the results of an international comparative study on the nature of proof to be taught in geometry. Proofs in French and Japanese lower secondary schools were explored by analyzing curricular documents: mathematics textbooks and national curricula. Analyses on the three aspects of proof—statement, proof, and theory—suggested by the notion of Mathematical Theorem showed differences in these aspects and also differences in the three functions of proof—justification, systematization, and communication—that are seemingly commonly performed in these countries. The results of analyses imply two major elements that form the nature of proof: (a) the nature of the geometrical theory that is chosen to teach and (b) the principal function of proof related to that theory. This paper suggests alternative approaches to teach proof and proving and shows that these approaches are deeply related to the way geometry is taught. 相似文献
5.
本文提出了论证的四个预设，认为它们是保证一段话语成为一个论证的基本条件，而且，这些预设在某种意义上把论证与推理区别开来。正是这些预设，使得我们把一些包括演绎有效推理的论证判定为谬误 相似文献
6.
In this paper, we distinguish between two ways that an individual can construct a formal proof. We define a syntactic proof production to occur when the prover draws inferences by manipulating symbolic formulae in a logically permissible way. We define a semantic proof production to occur when the prover uses instantiations of mathematical concepts to guide the formal inferences that he or she draws. We present two independent exploratory case studies from group theory and real analysis that illustrate both types of proofs. We conclude by discussing what types of concept understanding are required for each type of proof production and by illustrating the weaknesses of syntactic proof productions. 相似文献
7.
随着数学课程改革的深入,关于数学证明的教育价值的研究已经引起了越来越广泛的关注.数学证明是以一些基本概念和公理为基础,使用合乎逻辑的推理去决定判断是否正确.数学证明具有二重性,即它既是客观的,又是主观的.数学证明的教育价值应该体现在:从文化上,让学生体会数学的理性精神,懂得理性地思考问题;从知识上,证明能加深对概念和定理的理解,并能导致发现;从思维上,证明能训练和培养逻辑和非逻辑的思维能力. 相似文献
8.
魏全顺 《湖南第一师范学报》2006,6(1):110-111,114
利用函数的微分证明不等式的思想方法,在诸多数学分析论著中有所提及,是微分的一个重要应用。其主要方法有:利用函数的单调性证明不等式;利用函数的凸凹性证明不等式;利用Lagrange微分中值定理或泰勒公式证明不等式;利用求函数极值的方法证明不等式。 相似文献
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10.
As a key objective, secondary school mathematics teachers seek to improve the proof skills of students. In this paper we present an analytic framework to describe and analyze students' answers to proof problems. We employ this framework to investigate ways in which dynamic geometry software can be used to improve students' understanding of the nature of mathematical proof and to improve their proof skills. We present the results of two case studies where secondary school students worked with Cabri-Géeomèetre to solve geometry problems structured in a teaching unit. The teaching unit had theaims of: i) Teaching geometric concepts and properties, and ii) helping students to improve their conception of the nature of mathematical proof and to improve their proof skills. By applying the framework defined here, we analyze students' answers to proof problems, observe the types of justifications produced, and verify the usefulness of learning in dynamicgeometry computer environments to improve students' proof skills. 相似文献
11.
针对高等代数中许多结论、定理的证明有时虽然可以用构造法、数学归纳法等其他方法证明,但证明过程较复杂;有时结果虽然是数值却无法用求解的方法来求解,提出了用反证法来证明或求解的思想,从而达到了化复杂为简明、化难为易的效果. 相似文献
12.
As a key objective, secondary school mathematics teachers seek to improve the proof skills of students. In this paper we present an analytic framework to describe and analyze students' answers to proof problems. We employ this framework to investigate ways in which dynamic geometry software can be used to improve students' understanding of the nature of mathematical proof and to improve their proof skills. We present the results of two case studies where secondary school students worked with Cabri-Géeomèetre to solve geometry problems structured in a teaching unit. The teaching unit had theaims of: i) Teaching geometric concepts and properties, and ii) helping students to improve their conception of the nature of mathematical proof and to improve their proof skills. By applying the framework defined here, we analyze students' answers to proof problems, observe the types of justifications produced, and verify the usefulness of learning in dynamicgeometry computer environments to improve students' proof skills.This revised version was published online in September 2005 with corrections to the Cover Date. 相似文献
13.
针对行列式计算中常用的按行（列）展开定理,对部分线性代数教材所给证明提出一点质疑,并给出两种不同的证明方法。 相似文献
14.
胡承钧 《南通职业大学学报》2009,23(3):65-66
代数学基本定理的经典证明用到较多的代数知识,且难以理解,文章探讨用数学分析的方法予以证明。该证明从复变多项式无非零最小模引入,并在此基础上简单证明了代数学的基本定理。 相似文献
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在证明责任倒置的肯定说与否定说之争中，肯定说是符合我国实际情况的，然而持肯定说的学者们在界定证明责任倒置的概念时，又存在种种偏颇。本文在重塑了证明责任倒置的概念之后，阐明了我国当前民事诉讼中证明责任倒置的情形。 相似文献
18.
陈占军 《北京城市学院学报》2004,(4):86-89
最高人民法院关于《民事诉讼证据的若干规定》规范了证明责任的一般原则,还规定了具体的特殊举证规则及认证规则,本文拟就主观证明责任和客观证明责任、证明责任的分配及法院认证规则结合《规定》作一粗浅分析。 相似文献
19.
M. Raman 《Educational Studies in Mathematics》2003,52(3):319-325
This paper examines the views of proof held by university level mathematics students and teachers. A framework is developed
for characterizing people's views of proof, based on a distinction between public and private aspects of proof and the key
ideas which link these two domains.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
20.
关于Black-Scholes期权定价模型的证明 总被引：1，自引：0，他引：1
lack-Scholes期权定价模型是20世纪70年代以来金融理论发展的最重要的基石,但是在各类文献中却几乎没有关于它的详细、准确的证明.本文将有关文献中出现的错误加以更正,并优化了证明过程,给出一个关于Black-Scholes期权定价模型严格的数学证明. 相似文献