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Justifications-on-Demand as a Device to Promote Shifts of Attention Associated With Relational Thinking in Elementary Arithmetic

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Abstract

Student responses to arithmetical questions that can be solved by using arithmetical structure can serve to reveal the extent and nature of relational, as opposed to computational thinking. Student responses to probes which require them to justify-on-demand are analysed using a conceptual framework which highlights distinctions between different forms of attention. We analyse a number of actions observed in students in terms of forms of attention and shifts between them: in the shortterm (the moment), medium-term (over several tasks), and long-term (over a year). The main factors conditioning students_ attention and its movement are identified and some didactical consequences are proposed.

Résumé

Les réponses des étudiants aux questions qui peuvent être résolues par structure arithmétique sont parfois utiles pour déterminer la portée et la nature de la pensée relationnelle, par opposition à la pensée computationnelle. Les réponses des étudiants aux questions qui requièrent une justification sur demande sont analysées au moyen d’un cadre conceptuel qui met en relief les distinctions entre différents niveaux d’attention. Nous analysons certaines actions observées chez des étudiants en termes de niveaux d’attention, ainsi que les passages d’un niveau à l’autre: à court terme (sur le moment), à moyen terme (au cours d’un certain nombre de tâches) et à long terme (sur une année). Les facteurs principaux qui conditionnent l’attention des étudiants et les différents passages d’un niveau l’autre sont identifiés et certaines conséquences didactiques sont proposées.

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Authors and Affiliations

  1. Diáctica de la Matemática, Facultad de Ciencias de la Educación, University of Granada, Campus de Cartuja s/n, Granada, 18071, Spain

    Marta Molina

  2. University of Oxford, Oxford, United Kingdom

    John Mason

  3. Open University, Milton Keynes, United Kingdom

    John Mason

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  1. Marta Molina
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  2. John Mason
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Correspondence to Marta Molina.

Additional information

This research was made possible by grant #891/03 from the Israel Science Foundation.

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Molina, M., Mason, J. Justifications-on-Demand as a Device to Promote Shifts of Attention Associated With Relational Thinking in Elementary Arithmetic. Can J Sci Math Techn 9, 224–242 (2009). https://doi.org/10.1080/14926150903191885

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