TY - JOUR
T1 - A hypothetical learning trajectory for conceptualizing matrices as linear transformations
AU - Andrews-Larson, Christine
AU - Wawro, Megan
AU - Zandieh, Michelle
N1 - Funding Information:
This work was supported by the Division of Undergraduate Education and Division of Research on Learning in Formal and Informal Settings, National Science Foundation [grant numbers DRL 0634099, 0634074, DUE 1245673, 1245796, 1246083, and 1431393].
Publisher Copyright:
© 2017 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2017/8/18
Y1 - 2017/8/18
N2 - 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.
AB - 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.
KW - Linear algebra
KW - hypothetical learning trajectory
KW - linear transformation
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U2 - 10.1080/0020739X.2016.1276225
DO - 10.1080/0020739X.2016.1276225
M3 - Article
AN - SCOPUS:85011271885
SN - 0020-739X
VL - 48
SP - 809
EP - 829
JO - International Journal of Mathematical Education in Science and Technology
JF - International Journal of Mathematical Education in Science and Technology
IS - 6
ER -