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The Theory of Mathematical Working Spaces—Theoretical Characteristics

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Mathematical Work in Educational Context

Part of the book series: Mathematics Education in the Digital Era ((MEDE,volume 18))

Abstract

The theory of Mathematical Working Spaces (MWS) is introduced in this chapter. Presenting epistemological and cognitive aspects, we see how the theory of MWS aims to provide tools—theoretical and methodological—for the specific study of mathematical work in which students and teachers effectively engage during mathematics lessons. Some of the main key constructs of the theory are introduced: the notion of mathematical work in relation to Mathematical Working Spaces; the semiotic, instrumental and discursive geneses associated with MWS diagrams; the different levels of MWS associated with reference, suitable and personal work, etc. We then demonstrate how these different tools enable the description, characterization and formation of mathematical work. Finally, emphasis is placed on the originality of this theory in the field of mathematics education theories.

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Notes

  1. 1.

    This topic is further developed in Chap. 7 (Kuzniak, Montoya and Vivier).

  2. 2.

    The material component of mathematical artifacts alone is often not enough to identify them, and it is important to know their symbolic valence: Indeed, the artifact is often recognized through observation of the technique implemented, Chap. 9 (Lagrange & Richard).

  3. 3.

    For a discussion on the different types of discourses in the theory of MWS, see Pizarro (2018) who introduces three kind of discourse in relation to each genesis.

  4. 4.

    A cognitive unit encompasses the different elements of knowledge about the mathematical entity.

  5. 5.

    We can see here that the point is part of the circle in its cognitive unit, whereas from a mathematical point of view, it is not.

  6. 6.

    This point is discussed in further detail in Chap. 7 (Kuzniak, Montoya-Delgadillo & Vivier).

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Authors and Affiliations

  1. LDAR, Université de Paris, Paris, France

    Alain Kuzniak

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  1. Alain Kuzniak
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Correspondence to Alain Kuzniak .

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  1. LDAR, Département de Mathématiques, Université de Paris, Paris, France

    Alain Kuzniak

  2. Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile

    Elizabeth Montoya-Delgadillo

  3. Département de Didactique, Université de Montréal, Montreal, QC, Canada

    Philippe R. Richard

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Kuzniak, A. (2022). The Theory of Mathematical Working Spaces—Theoretical Characteristics. In: Kuzniak, A., Montoya-Delgadillo, E., Richard, P.R. (eds) Mathematical Work in Educational Context. Mathematics Education in the Digital Era, vol 18. Springer, Cham. https://doi.org/10.1007/978-3-030-90850-8_1

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  • DOI: https://doi.org/10.1007/978-3-030-90850-8_1

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