Student reasoning about the invertible matrix theorem in linear algebra
Student reasoning about the invertible matrix theorem in linear algebra
复制标题
学生推理线性代数中的可逆矩阵定理
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
M. Wawro
中科院分区：
文献类型：
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作者：
M. Wawro
我报告如何线性代数课堂社区的可逆矩阵定理（IMT）随着时间的推移推理。IMT是一个核心定理，它通过等价的概念连接了许多基本概念。随着学期的进展，全班学生以一种紧急的方式发展了IMT。因此，当学生们开始思考所涉及的关键思想是如何联系在一起的时候，各种等价关系就形成了，并发展了意义。微发生和个体发生分析（Saxe in J Learn Sci 11（2-3）：275-300，2002）构建了调查的结构。结果集中在随着时间的推移和中心的跨度和线性独立性在课堂上的论证的数学内容的变化。
I report on how a linear algebra classroom community reasoned about the invertible matrix theorem (IMT) over time. The IMT is a core theorem that connects many fundamental concepts through the notion of equivalency. As the semester progressed, the class developed the IMT in an emergent fashion. As such, the various equivalences took form and developed meaning as students came to reason about the ways in which key ideas involved were connected. Microgenetic and ontogenetic analyses (Saxe in J Learn Sci 11(2–3):275–300, 2002) framed the structure of the investigation. The results focus on shifts in the mathematical content of argumentation over time and the centrality of span and linear independence in classroom argumentation.