RUME 25
2023
Omaha, Nebraska
APOS Levels, Stages, and Coordinated Topics as Transitional Points: Case of Range of a Linear Transformation
Page: 262
This paper discusses findings from an ongoing study investigating mental mechanisms involved in the conceptualization of linear transformations from the perspective of 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 differences in APOS Levels, Stages, and Coordinated topics. Moreover, our findings pointed to connections between Levels/Stages of the range concept and mental mechanisms of representations of matrix multiplications. That is, our findings revealed that the absence of these representations from ones conceptualization process may result in irreversible misconceptions. More importantly, we identified more transitions occurring among Levels/Stages when linear combination expressions were considered as representations of matrix multiplications.