An institutional approach to university mathematics education: from dual vector spaces to questioning the world
An institutional approach to university mathematics education: from dual vector spaces to questioning the world
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大学数学教育的制度方法：从双向量空间到质疑世界
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Nadia Hardy
中科院分区：
文献类型：
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作者：
C. Winsløw;Berta Barquero;M. De Vleeschouwer;Nadia Hardy
大学数学教育（UME）被认为是一种教学实践，其特点是机构设置，并以诱导学生进行数学实践为目的。我们提出了一个研究计划——教学的人类学理论（ATD）——在这个研究计划中，这个粗略的定义可以变得更加精确；我们还概述了一些基于atd的UME研究案例。详细介绍了三个案例。首先是对偶向量空间主题的理论和实证研究，因为它出现在线性代数的本科课程中。第二个案例是关于函数极限的实践和理论的类似研究，这是学生在微积分课程中可能会学到的。最后，第三项研究说明了在工科学生的第一门数学课程中使用ATD来设计和实验数学建模的创新方法。
University mathematics education (UME) is considered, in this paper, as a kind of didactic practice – characterised by institutional settings and by the purpose of inducting students into mathematical practices. We present a research programme – the anthropological theory of the didactic (ATD) – in which this rough definition can be made much more precise; we also outline some cases of ATD-based research on UME. Three cases are presented in more detail. The first is a theoretical and empirical study of the topic of dual vector spaces, as it appears in undergraduate courses on linear algebra. The second case concerns a similar study of the practices and theories on limits of functions which students may develop in calculus courses. Finally, a third study illustrates the use of ATD to design and experiment innovative approaches to mathematical modelling in the setting of a first mathematics course for engineering students.