Uso de representaciones y generalizaciones de la regla del producto

• Autores: María Consuelo Cañadas Santiago , Lourdes Figueiras Ocaña
• Localización: Journal for the Study of Education and Development, Infancia y Aprendizaje, ISSN-e 1578-4126, ISSN 0210-3702, Vol. 34, Nº 4, 2011, págs. 409-425
• Idioma: español
• DOI: 10.1174/021037011797898449
• Títulos paralelos:
  • Use of representations and generalization of the multiplication principie
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• Dialnet Métricas: 3 Citas
• Resumen
  • español

    Analizamos los protocolos de resolución de problemas de 50 estudiantes con el objetivo de profundizar en la construcción de la regla del producto como esquema básico de resolución de problemas de conteo. En particular, indagamos en el uso que se hace de la inducción y de diferentes representaciones para pasar de la enumeración exhaustiva y el recuento total de posibilidades a la generalización de dicha regla. El análisis ha puesto de manifiesto la existencia de dos procesos de generalización: sobre la dimensión del problema y sobre el número de elementos que intervienen en cada factor. Mostramos cómo ambos procesos se relacionan con el uso efectivo de los diagramas de árbol que los estudiantes generan de manera espontánea y apuntamos posibles implicaciones para la instrucción. Por otra parte, el análisis de los datos ha generado la necesidad de indagar en la conexión entre las representaciones textuales y otros tipos de representaciones, evaluando su funcionalidad.

  • English

    We have examined the problem-solving protocols of 50 students with the goal of analysing the construction of the multiplication principle as a basic scheme for solving counting problems. In particular, we investigated how induction and different representations are used to move from exhaustive enumeration to the generalisation of this principle. The analysis revealed the existence of two processes of generalisation: 1) on the dimension of the problem, and 2) the number of elements involved in each factor. We show how both processes are related to the effective use of tree diagrams that students generated spontaneously, and suggest possible educational implications. Moreover, the analysis of our data has generated the need to investigate the connection between textual representations and other types of representations, evaluating its functionality.

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