Coordinated topics as transitional enablers towards higher-level conceptualisations of the range concept

Abstract

This paper discusses findings from an ongoing study investigating mental mechanisms involved in the conceptualisation of linear transformations from the perspective of Action (A), Process (P), Object (O), and Schema (S) (APOS) theory. Data reported in this paper came from 44 first-year linear algebra students’ responses on a task regarding the range of a linear transformation. Our analysis revealed parallels between Levels/Stages of the range concept and the use of representations of matrix multiplications. More importantly, these representations appeared to have been the enablers of transitions from lower to higher APOS Stages for the range. Conversely, mental mechanisms employing other means showed little to no progressions, some, furthermore, revealed faulty knowledge structures.

KEYWORDS:

• Linear transformations
• range
• APOS theory
• mental mechanisms
• transitional points
• coordinated topics

Acknowledgements

We thank the Editors and the reviewers for their valuable input towards the improvement of the earlier versions of the paper.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This material is based upon work supported by a grant from the University of Texas System and the Consejo Nacional de Ciencia y Tecnología de México (CONACYT). The opinions expressed are those of the authors and do not necessarily represent the views of these funding agencies.