A hypothetical learning trajectory for conceptualizing matrices as linear transformations
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Christine Andrews-Larson [1] ; Megan Wawro [3] ; Michelle Zandieh [2]
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[1] Florida State University
Florida State University
Estados Unidos
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[2] Arizona State University
Arizona State University
Estados Unidos
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[3] Virginia Polytechnic Institute and State University
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- Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 48, Nº. 6, 2017, págs. 809-829
- Idioma: inglés
- DOI: 10.1080/0020739x.2016.1276225
- Texto completo no disponible (Saber más ...)
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Resumen
In this paper, we present a hypothetical learning trajectory (HLT) aimed at supporting students in developing flexible ways of reasoning about matrices as linear transformations in the context of introductory linear algebra. In our HLT, we highlight the integral role of the instructor in this development. Our HLT is based on the ‘Italicizing N’ task sequence, in which students work to generate, compose, and invert matrices that correspond to geometric transformations specified within the problem context. In particular, we describe the ways in which the students develop local transformation views of matrix multiplication (focused on individual mappings of input vectors to output vectors) and extend these local views to more global views in which matrices are conceptualized in terms of how they transform a space in a coordinated way.
