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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.

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