Mathematical modelling and the learning trajectory: tools to support the teaching of linear algebra

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 co...

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Detalles Bibliográficos
Autores: Cárcamo Bahamonde, Andrea, Fortuny Aymemí, Josep Maria, Gómez Urgellés, Joan Vicenç|||0000-0002-9974-0425
Tipo de recurso: artículo
Fecha de publicación:2017
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/167813
Acceso en línea:https://hdl.handle.net/2117/167813
https://dx.doi.org/10.1080/0020739X.2016.1241436
Access Level:acceso abierto
Palabra clave:Algebras, Linear
Hypothetical learning trajectory
Actual learning trajectory
Emergent models heuristic
Mathematical modelling
Design-based research
Spanning set
Span
Àlgebra lineal
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Àlgebra lineal i multilineal
Descripción
Sumario: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.