### Abstract

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.

Original language | English (US) |
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Pages (from-to) | 1-21 |

Number of pages | 21 |

Journal | International Journal of Mathematical Education in Science and Technology |

DOIs | |

State | Accepted/In press - Jan 1 2017 |

### Fingerprint

### Keywords

- hypothetical learning trajectory
- Linear algebra
- linear transformation

### ASJC Scopus subject areas

- Mathematics (miscellaneous)
- Education
- Applied Mathematics

### Cite this

*International Journal of Mathematical Education in Science and Technology*, 1-21. https://doi.org/10.1080/0020739X.2016.1276225

**A hypothetical learning trajectory for conceptualizing matrices as linear transformations.** / Andrews-Larson, Christine; Wawro, Megan; Zandieh, Michelle.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - A hypothetical learning trajectory for conceptualizing matrices as linear transformations

AU - Andrews-Larson, Christine

AU - Wawro, Megan

AU - Zandieh, Michelle

PY - 2017/1/1

Y1 - 2017/1/1

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 - hypothetical learning trajectory

KW - Linear algebra

KW - linear transformation

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U2 - 10.1080/0020739X.2016.1276225

DO - 10.1080/0020739X.2016.1276225

M3 - Article

SP - 1

EP - 21

JO - International Journal of Mathematical Education in Science and Technology

JF - International Journal of Mathematical Education in Science and Technology

SN - 0020-739X

ER -