Proofs and refutations in the undergraduate mathematics classroom
Proofs and refutations in the undergraduate mathematics classroom
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本科数学课堂上的证明与反驳
DOI：
10.1007/s10649-007-9106-0
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发表时间：
2008
影响因子：
3.2
通讯作者：
Michelle Zandieh
中科院分区：
文献类型：
--
作者：
Sean Larsen;Michelle Zandieh
在他1976年的著作《证明与反驳》（Proofs and Refutations）中，拉卡托斯提出了一系列案例研究来说明数学史上数学发现的方法。在本文中，我们重新构建这些方法的方式，我们已经发现，使他们更适合作为一个框架的学习和教学的数学研究。我们提出了一个插曲，从本科抽象代数教室来说明引导重塑数学的过程中，强烈平行拉卡托斯所描述的。我们的分析表明，拉卡托斯所描述的结构可以提供一个有用的框架，使意义上的数学活动在课堂上，学生积极参与数学思想的发展，并提供设计教学方法，支持数学学习的过程中指导再造。
In his 1976 book, Proofs and Refutations, Lakatos presents a collection of case studies to illustrate methods of mathematical discovery in the history of mathematics. In this paper, we reframe these methods in ways that we have found make them more amenable for use as a framework for research on learning and teaching mathematics. We present an episode from an undergraduate abstract algebra classroom to illustrate the guided reinvention of mathematics through processes that strongly parallel those described by Lakatos. Our analysis suggests that the constructs described by Lakatos can provide a useful framework for making sense of the mathematical activity in classrooms where students are actively engaged in the development of mathematical ideas and provide design heuristics for instructional approaches that support the learning of mathematics through the process of guided reinvention.