Mathematical modelling and the learning trajectory: tools to support the teaching of linear algebra |
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| Authors: | Andrea Dorila Cárcamo Bahamonde Josep Maria Fortuny Aymemí Joan Vicenç Gómez i Urgellés |
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| Institution: | 1. Centro de Docencia de Ciencias Básicas para Ingeniería, Universidad Austral de Chile, Valdivia, Chile;2. Departamento de Didáctica de la Matemática y las Ciencias Experimentales, Universidad Autónoma de Barcelona, Barcelona, Espa?aandrea.carcamo@uach.cl;4. Departamento de Didáctica de la Matemática y las Ciencias Experimentales, Universidad Autónoma de Barcelona, Barcelona, Espa?a;5. Departamento de Matemáticas, Universidad Politécnica de Catalu?a, Barcelona, Espa?a |
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| Abstract: | In this article we present a didactic proposal for teaching linear algebra based on two compatible theoretical models: emergent models and mathematical modelling. This proposal begins with a problematic situation related to the creation and use of secure passwords, which leads students toward the construction of the concepts of spanning set and span. The objective is to evaluate this didactic proposal by determining the level of match between the hypothetical learning trajectory (HLT) designed in this study with the actual learning trajectory in the second experimental cycle of an investigation design-based research more extensive. The results show a high level of match between the trajectories in more than half of the conjectures, which gives evidence that the HLT has supported, in many cases, the achievement of the learning objective, and that additionally mathematical modelling contributes to the construction of these linear algebra concepts. |
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| Keywords: | Hypothetical learning trajectory actual learning trajectory emergent models heuristic mathematical modelling design-based research spanning set span |
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