The object-tool duality in mathematical modelling. A framework to analyze students’ appropriation of Sankey diagrams to model dynamic processes

Pauline Vos; Peter Freyd

Ayuda

The object-tool duality in mathematical modelling. A framework to analyze students’ appropriation of Sankey diagrams to model dynamic processes

Pauline Vos ^[1] ; Peter Frejd ^[2]
1. [1] University of Agder
  
  University of Agder
  
  Noruega
2. [2] Linköping University
  
  Linköping University
  
  Linköpings S:t Lars, Suecia
Localización: Avances de investigación en educación matemática, ISSN-e 2254-4313, Nº. 17, 2020, págs. 52-66
Idioma: inglés
DOI: 10.35763/aiem.v0i17.305
Títulos paralelos:
- La dualidad objeto-herramienta en la modelización matemática. Un marco de análisis de la apropiación de los estudiantes de diagramas Sankey para modelar procesos dinámicos
Enlaces
- Texto completo (pdf)
Resumen
- español
  A menudo los estudiantes no perciben la relevancia de las matemáticas y de su aprendizaje. Este artículo presenta un análisis exploratorio de un caso de estudio, en el cual se introducen los diagramas de Sankey para estudiantes de octavo grado. El objetivo fue explorar hasta qué punto estos estudiantes se apropiaron de los diagramas Sankey, es decir, si los describían como objetos en sí mismos y si eran capaces de utilizarlos para modelizar y visualizar fenómenos relevantes para ellos. Con base en la Teoría Cultural-Histórica de la Actividad, desarrollamos un constructo analítico definido como la dualidad objeto-herramienta, que coordinan las matemáticas como conjunto de objetos y conjunto de herramientas. El análisis de respuestas de los estudiantes mostró cómo usaron estos diagramas a modo de herramientas para visualizar ciertos fenómenos. Cuando se les pidió que describieran el objeto, todos mencionaron los aspectos como herramienta. Así, en su proceso de apropiación la interpretación como herramienta se antepuso a la de objeto. Nuestra contribución es que el trabajo con la vertiente herramienta de las matemáticas antes que con la de objeto puede aumentar la relevancia que los estudiantes dan a las matemáticas, resultando ser una línea a desarrollar en futuras investigaciones.
- English
  Students often do not experience the relevance of learning mathematics. This paper reports on an exploratory case study, in which a class of grade 8 students (n=35) was introduced to Sankey diagrams.
  
  The aim was to explore to what extent these students could appropriate Sankey diagrams, meaning: they could describe these as objects in themselves and they could use them to model and visualize phenomena relevant to them. Based on Cultural-Historical Activity Theory, we developed an analytical construct defined as the object-tool duality, coordinating mathematics as a set of objects and as a set of tools. The analysis of students’ answers showed that they could use these diagrams as tools to visualize phenomena. When asked to describe the object, all mentioned the tool-side. So, in their appropriation the tool-side came before the object-side. Our contribution is that teaching the tool-side of mathematics before the object-side may increase students’ sense of the relevance of mathematics, which is a topic to develop for future research.
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