A hypothetical learning trajectory for linear combination of vectors in R2
Résumé
This paper presents the results of the first cycle of an ongoing design research. A Hypothetical Learning Trajectory (HLT) is proposed to introduce the concept of linear combination in a first linear algebra course. To evaluate the HLT, we conducted a teaching experiment with engineering students in a Mexican public university. In the analysis phase, the HLT was compared with the Real Learning Trajectory (RLT) to evaluate how university students' understanding progresses when they work with tasks designed under the practical action projects. We use emergent modelling as a theoretical framework for describing students' level of understanding achieved. Results showed some limitations of the HLT to achieve a formal level of understanding.
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