Student learning of basis, span and linear independence in linear algebra
Student learning of basis, span and linear independence in linear algebra
复制标题
学生学习线性代数中的基、跨度和线性独立性
DOI：
10.1080/00207390903399620
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发表时间：
2010
影响因子：
0.9
通讯作者：
Michael O. J. Thomas
中科院分区：
文献类型：
--
作者：
Sepideh Stewart;Michael O. J. Thomas
大学线性代数中较早、更具挑战性的概念之一是基。学生经常被教授如何使用矩阵操作找到子空间的基础，但可能很难理解基础的构造，从而使进一步的进步变得更加困难。我们认为其中一个原因是学生对跨度和线性独立的概念有很大的困难，这些概念构成了一组向量形成基础的要求。在这项研究中，我们将基于塔尔数学学习三个世界和动作-过程-对象-图式（APOS）理论的理论框架应用于一群大学二年级学生对基础概念的学习。结果表明，强调矩阵过程可能无助于学生理解这个概念，并且通常缺乏可能有价值的具体视觉想法。
One of the earlier, more challenging concepts in linear algebra at university is that of basis. Students are often taught procedurally how to find a basis for a subspace using matrix manipulation, but may struggle with understanding the construct of basis, making further progress harder. We believe one reason for this is because students have major difficulties with concepts of span and linear independence which form the requirements for a set of vectors to form a basis. In this research we applied a theoretical framework based on Tall's three worlds of mathematics learning and action-process-object-schema (APOS) theory to the learning of the concept of basis by a group of second year university students. The results suggest that an emphasis on matrix processes may not help students understand the concept, and embodied, visual ideas that could be valuable were usually lacking.