Student reasoning about the invertible matrix theorem in linear algebra

Megan Wawro

doi:10.1007/s11858-014-0579-x

ZDM

July 2014, Volume 46, Issue 3, pp 389–406

Student reasoning about the invertible matrix theorem in linear algebra

Authors
Authors and affiliations

Megan WawroEmail author

Original Article

First Online:: 20 April 2014

Accepted:: 03 April 2014

DOI: 10.1007/s11858-014-0579-x

Cite this article as:: Wawro, M. ZDM Mathematics Education (2014) 46: 389. doi:10.1007/s11858-014-0579-x

Abstract

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.

Keywords

Linear algebra Adjacency matrices Collective activity

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Megan Wawro
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1.Department of MathematicsVirginia TechBlacksburgUSA

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Student reasoning about the invertible matrix theorem in linear algebra

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