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Emergence of Uncertainties and Mathematical Problems Through Collective Investigation on Routine Tasks

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Abstract

This article aims to illustrate how the collective resolution of routine mathematical tasks can give rise to uncertainties, fostering and supporting a rich and authentic mathematical activity. While solving routine tasks may not typically be classified as problem-solving, the research presented in this paper shows that, at the collective level, their resolution can give rise to new mathematical tasks to solve in the classroom and generate authentic problem-solving activity. Grounded in the enaction theory of cognition (e.g. Maturana & Varela in Shambhala, 1992), this research considers the class as a unit, as a collectivity, which brings forth a mathematical activity. In this article, examples derived from an experiment conducted in elementary-level mathematics classrooms are used to show the emergence of uncertainties, highlighting the mathematical potential resulting from the collective resolution of routine tasks. In conclusion, the article introduces the concept of collective mathematical problems.

Résumé

Cet article vise à illustrer le potentiel d’une exploitation collective de tâches routinières à faire émerger des incertitudes qui favorisent une activité mathématique riche et authentique en classe. Alors que la résolution de tâches routinières peine à se qualifier de résolution de problèmes, la recherche présentée dans cet article montre qu’au niveau collectif leur résolution peut donner lieu à de nouvelles tâches mathématiques à résoudre et générer une authentique activité de résolution de problèmes en classe. Prenant appui sur la théorie cognitive de l’enaction (e.g. Maturana et Varela dans Shambhala, 1992) cette recherche considère la classe comme une unité collective, soit une collectivité, qui, ensemble, fait émerger une activité mathématique. Dans cet article, des exemples tirés d’une expérimentation en classe du primaire sont utilisés pour montrer l’émergence d’incertitudes, illustrant le potentiel mathématique résultant d’une résolution collective de tâches routinières. En conclusion, l’article introduit la notion de problèmes mathématiques collectifs.

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Data Availability

The data (transcripts only) that support the findings of this study are available on request from the corresponding author [genevieve.barabe@umontreal.ca].

Notes

  1. Some make a distinction between a ‘task’ and a ‘problem’ in mathematics (see e.g. Hoshino et al., 2016). A task refers to a mathematical statement whereas a problem refers to what is solved, i.e. what is done for and during solving. This distinction is retained in this paper and will be discussed in more detail subsequently.

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Funding

This research was funded by the Fonds de Recherche du Québec Société et Culture.

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Authors and Affiliations

  1. Faculté des sciences de l’éducation, Département de didactique, Université de Montréal, Pavillon Marie-Victorin, 90 avenue Vincent d’Indy, Montréal, H2V 2S9, Canada

    Geneviève Barabé

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  1. Geneviève Barabé
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Correspondence to Geneviève Barabé.

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This study was approved by and conducted in accordance with the ethical standard of the Université du Québec à Montréal.

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Barabé, G. Emergence of Uncertainties and Mathematical Problems Through Collective Investigation on Routine Tasks. Can. J. Sci. Math. Techn. Educ. (2024). https://doi.org/10.1007/s42330-024-00308-2

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