Skip to main content
SpringerLink
Log in

The epistemic, the cognitive, the human: a commentary on the mathematical working space approach

  • Commentary Paper
  • Published:
ZDM Aims and scope Submit manuscript

Abstract

This article is a commentary on the mathematical working space (MWS) approach and draws on the articles contained in this ZDM issue. The article is divided into three parts. In the first part I discuss the place of the MWS approach among the French theories of didactique des mathématiques. In the second part I outline what I think are the central ideas of the MWS approach. I conclude the article with a sketch of what seems to me to be its accomplishments and challenges, focusing mainly on the epistemological and cognitive stances that the MWS approach conveys in order to elucidate the manner in which this approach theoretically assumes that things are known and learned.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Andler, D. (2004). Introduction aux sciences cognitives [Introduction to cognitive sciences]. Paris: Gallimard.

    Google Scholar 

  • Anghileri, J. (1989). An investigation of young children’s understanding of multiplication. Educational Studies in Mathematics, 20(4), 367–385.

    Article  Google Scholar 

  • Artigue, M. (1990). Épistémologie et didactique [Epistemology and didactics]. Recherches En Didactique Des Mathématiques, 10(2–3), 241–286.

    Google Scholar 

  • Artigue, M. (2013a). L’impact curriculaire des technologies sur l’éducation mathématique. Cuadernos de investigación y formación en Educación Matemática, 11, 313–323.

    Google Scholar 

  • Artigue, M. (2013b). Teaching and learning mathematics in the digital era: Challenges and perspectives. In Y. Baldwin (Ed.), Proceedings of HTEM, July 14th–19th, 2013. Brasil.

  • Brousseau, G. (1989). Les obstacles épistémologiques et la didactique des mathématiques [Epistemological obstacles and didactic of mathematics]. In N. Bednarz & C. Garnier (Eds.), Construction des savoirs, obstacles et conflits (pp. 41–64). Montréal: les éditions Agence d’Arc inc.

    Google Scholar 

  • Brousseau, G. (1997). Theory of didactical situations in mathematics. Dordrecht: Kluwer.

    Google Scholar 

  • Brousseau, G. (2006). Mathematics, didactical engineering and observation. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings of the 30th conference of the international group for the psychology of mathematics education (Vol. 1, pp. 3–18). Prague, Czech Republic.

  • Chevallard, Y. (1985). La transposition didactique [The didactical transposition] (p. 1991). France: La pensée sauvage éditions. Deuxième édition.

    Google Scholar 

  • Chevallard, Y. (1997). Familière et problématique, la figure du professeur [Familiar and enigmatic, the figure of the teacher]. Recherche en didactique des mathématiques, 17(3), 17–54.

    Google Scholar 

  • Chevallard, Y. (2006). Steps towards a new epistemology in mathematics education. In M. Bosch (Ed.), Proceedings of the 4th conference of the european society for research in mathematics education (CERME4) (pp. 21–30). Sant Feliu de Guíxols: CERME.

    Google Scholar 

  • Cobb, P. (1987). An investigation of young children’s academic arithmetic contexts. Educational Studies in Mathematics, 18(2), 109–124.

    Article  Google Scholar 

  • de Vega, M. (1986). Introduccion a la psicologia cognitive [Introduction to cognitive psychology]. Mexico: Alianza Editorial Mexicana.

    Google Scholar 

  • Descartes, R. (1637). Discours de la méthode. Texte et commentaire par Étienne Gilson, 4e édition. [Discourse on Method]. Paris: Librairie Philosophique Vrin.

  • Duval, R. (1995). Sémoisis et pensée humaine [Semiosis and human thinking]. Bern: Lang.

    Google Scholar 

  • Duval, R. (1998). Signe et objet, I et II. Annales De Didactique Et De Sciences Cognitives, IREM De Strasbourg, 6, 139–196.

    Google Scholar 

  • Duval, R. (2000). Basic issues for research in mathematics education. In T. Nakahara & M. Koyama (Eds.), Proceedings of the 24th conference of the international group for the psychology of mathematics education (PME-24) (Vol. 1, pp. 55–69). Hiroshima University, Japan.

  • Elia, I., Özel, S., Gagatsis, A., Panaoura, A., & Yetkiner Özel, Z. E. (2016). Students’ mathematical work on absolute value: Focusing on conceptions, errors and obstacles. ZDM Mathematics Education, 48(6), this issue. doi:10.1007/s11858-016-0780-1.

  • Elias, N. (1991). The society of individuals. Oxford: Basil Blackwell.

    Google Scholar 

  • Foucault, M. (2003). Society must be defended. Lectures at the Collège de France 1975–76. New York: Picador.

    Google Scholar 

  • Friedrich, P. (1970). Shape in grammar. Language, 46(2), 379–407.

    Article  Google Scholar 

  • Glaeser, G. (1999). Une introduction à la didactique expérimentale des mathématiques [An introduction to the experimental didactic of mathematics]. Grenoble: La pensée sauvage.

    Google Scholar 

  • Guin, D., & Trouche, L. (2004). Intégration des TICE: Concevoir, expérimenter et mutualiser des ressources pédagogiques. Repères, 55, 81–100.

    Google Scholar 

  • Harré, R., & Gillett, G. (1994). The discursive mind. London: Sage.

    Google Scholar 

  • Hitt, F., Saboya, M., & Cortés, C. (2016). An arithmetic-algebraic work space for the promotion of arithmetic and algebraic thinking: Triangular numbers. ZDM Mathematics Education, 48(6), this issue. doi:10.1007/s11858-015-0749-5.

  • Hume, D. (1921). An enquiry concerning human understanding and selections from A treatise of human nature. Chicago: The Open Court Publishing Co. (Original work published 1777).

  • Kahane, J. (2003). Est-il bien utile d’enseigner les mathématiques? [Is it useful to teach mathematics?]. Canadian School Mathematics Forum/Forum Canadien Sur L’enseignement Des Mathématiques. Montréal, May 16–18, 2003, pp. 1–9.

  • Kant, I. (2003). Critique of pure reason (N. K. Smith, Trans.). New York: Palgrave Macmillan (Original work published 1781).

  • Kotovsky, K., & Simon, H. A. (1990). What makes some problems really hard: Explorations in the problem space of difficulty. Cognitive Psychology, 22, 143–183.

    Article  Google Scholar 

  • Kuzniak, A., Nechache, A., & Drouhard, J.-P. (2016). Understanding the development of mathematical work in the context of the classroom. ZDM Mathematics Education, 48(6), this issue. doi:10.1007/s11858-016-0773-0.

  • Kuzniak, A., Tanguay, D., & Elia, I. (2016). Mathematical working spaces in schooling: an introduction. ZDM Mathematics Education. doi:10.1007/s11858-016-0812-x.

    Google Scholar 

  • Lakoff, G., & Núñez, R. (2000). Where mathematics comes from. New York: Basic Books.

    Google Scholar 

  • Leont’ev, A. N. (1978). Activity, consciousness, and personality. Englewood Cliffs, NJ: Prentice-Hall.

    Google Scholar 

  • Luria, A. R. (1976). Cognitive development, its cultural and social foundations. Cambridge, Ma London: Harvard University Press.

    Google Scholar 

  • Luria, A. R. (1979). The making of mind. Cambridge: Harvard University Press.

    Google Scholar 

  • Mikhailov, F. T. (1980). The riddle of the self. Moscow: Progress Publishers.

    Google Scholar 

  • Montoya Delgadillo, E., & Vivier, L. (2016). Mathematical working space and paradigms as an analysis tool for the teaching and learning of analysis. ZDM Mathematics Education, 48(6), this issue. doi:10.1007/s11858-016-0777-9.

  • Piaget, J. (1979). L’épistémologie génétique [Genetic epistemology]. Paris: Presses Universitaires de France.

    Google Scholar 

  • Radford, L. (2014). On teachers and students: An ethical cultural-historical perspective. In P. Liljedahl, C. Nicol, S. Oesterle, & D. Allan (Eds.), Proceedings of the joint meeting of PME 38 and PME-NA 36 (Vol. 1, pp. 1–20). Vancouver: PME.

    Google Scholar 

  • Radford, L. (in press). The theory of objectification and its place among sociocultural research in mathematics education. International Journal for Research in Mathematics Education.

  • Richard, P. R., Oller Marcén, A. M., & Meavilla Seguí, V. (2016). The concept of proof in the light of mathematical work. ZDM Mathematics Education, 48(6), this issue. doi:10.1007/s11858-016-0805-9.

  • Roth, W.-M., & Radford, L. (2011). A cultural historical perspective on teaching and learning. Rotterdam: Sense Publishers.

    Book  Google Scholar 

  • Salin, M.-H., Clanché, P., & Sarrazy, B. (2005). Sur la théorie des situations didactiques [On the theory of didactical situations]. Grenoble: La pensée sauvage.

    Google Scholar 

  • Santos-Trigo, M., Moreno-Armella, L., & Camacho-Machín, M. (2016). Problem solving and the use of digital technologies within the mathematical working space framework. ZDM Mathematics Education, 48(6), this issue. doi:10.1007/s11858-016-0757-0.

  • Shweder, R., & LeVine, R. (1984). Culture theory. Essays on mind, self, and emotion. Cambridge: Cambridge University Press.

    Google Scholar 

  • Sierpinska, A., & Lerman, S. (1996). Epistemologies of mathematics and of mathematics education. In B. Bishop, M. Clements, C. Keitel-Kreidt, J. Kilpatrick, C. Laborde (Eds.), International handbook of mathematics education (pp. 827–876). Kluwer Academic Publishers.

  • Trouche, L. (2003). From artifact to instrument: Mathematics teaching mediated by symbolic calculators. Interacting with Computers, 15(6), 783–800.

    Article  Google Scholar 

  • Vergnaud, G. (1985). Concepts et schèmes dans la théorie opératoire de la représentation [Concepts and schemas in the operational theory of representation]. Psychologie Française, 30(3–4), 245–252.

    Google Scholar 

  • Vergnaud, G. (1990). La théorie des champs conceptuels [The theory of conceptual fields]. Recherche En Didactique Des Mathématiques, 10, 133–170.

    Google Scholar 

  • Vergnaud, G. (2001). Forme opératoire et forme prédicative de la connaissance [Operational and predicative forms of knowledge]. In J. Portugais (Ed.), Actes du colloque GDM-2001 (pp. 1–22). Montréal: Université de Montréal.

Download references

Author information

Authors and Affiliations

  1. Université Laurentienne, Sudbury, Canada

    Luis Radford

Authors
  1. Luis Radford
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Luis Radford.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Radford, L. The epistemic, the cognitive, the human: a commentary on the mathematical working space approach. ZDM Mathematics Education 48, 925–933 (2016). https://doi.org/10.1007/s11858-016-0811-y

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11858-016-0811-y

Keywords

Search

Navigation