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ERIC Number: EJ1143710
Record Type: Journal
Publication Date: 2017
Pages: 21
Abstractor: As Provided
ISSN: ISSN-0020-739X
A Hypothetical Learning Trajectory for Conceptualizing Matrices as Linear Transformations
Andrews-Larson, Christine; Wawro, Megan; Zandieh, Michelle
International Journal of Mathematical Education in Science and Technology, v48 n6 p809-829 2017
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.
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Publication Type: Journal Articles; Reports - Research
Education Level: Higher Education; Postsecondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A