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Didactics of Mathematics as a Field of Mathematical Research: The Anthropological Approach

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Mathematicians' Reflections on Teaching

Part of the book series: Advances in Mathematics Education ((AME))

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Abstract

We develop the thesis that mathematics is an essentially didactical field of human activity, and that, therefore, Didactics of Mathematics is (or should be) a central part of mathematics itself. The basic ideas of the anthropological theory of the didactic are invested in this argument, as are some personal experiences from 25 years of research in von Neumann algebra theory, as well as in the didactics of analysis at university level.

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References

  • Archives Bourbaki. (n.d.). Mode d’emploi de ce traité. Manuscript, located April 2, 2019, on: http://sites.mathdoc.fr/archives-bourbaki/PDF/031ter_delr_007bis.pdf

  • Bosch, M., & Winsløw, C. (2016). Linking problem solving and mathematical contents: the challenge of sustainable study and research processes. Recherches en Didactique des Mathématiques 35(3), 357–401.

    Google Scholar 

  • Bouligand, G. (1957). L’activité mathématique et son dualisme. Dialectica, 11, 121–139.

    Article  Google Scholar 

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

    Google Scholar 

  • CBMS. (2012). The Mathematical Education of Teachers II. American Mathematical Society and Mathematical Association of America.

    Google Scholar 

  • Chevallard, Y. (1991). La transposition didactique – du savoir savant au savoir enseigné (first edition, 1985). La Pensée Sauvage.

    Google Scholar 

  • Chevallard, Y. (1992). Fundamental concepts in didactics: Perspectives provided by an anthropological approach. In R. Douady & A. Mercier (Eds.), Research in didactique of mathematics, selected papers (pp. 131–167). La Pensée Sauvage.

    Google Scholar 

  • Chevallard, Y. (1999). Didactique? Is it a plaisanterie? You must be joking! A critical comment on terminology. Instructional Science, 27(1), 5–7.

    Article  Google Scholar 

  • Cuban, L. (1999). How scholars trumped teachers - Change without reform in university curriculum, teaching, and research, 1890-1990. Teachers College Press.

    Google Scholar 

  • Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Kluwer.

    Google Scholar 

  • Halmos, P. (1985). I want to be a mathematician. An automathography. Springer.

    Book  Google Scholar 

  • Kilpatrick, J. (1981). The reasonable ineffectiveness of research in mathematics education. For the Learning of Mathematics, 2(2), 22–28.

    Google Scholar 

  • Klein, F. (1908/2016). Fundamental mathematics from a higher standpoint, I–III (G. Schubring, Trans.). Springer.

    Google Scholar 

  • Kondratieva, M., & Winsløw, C. (2018). Klein’s Plan B in the early teaching of analysis: Two theoretical cases of exploring mathematical links. International Journal of Research in Undergraduate Mathematics Education, 4(1), 119–138.

    Article  Google Scholar 

  • Madsen, L., & Winsløw, C. (2009). Relations between teaching and research in physical geography and mathematics at research intensive universities. International Journal of Science and Mathematics Education, 7, 741–763.

    Article  Google Scholar 

  • Moslehian, M. E., Størmer, M., Thorbjørnsen, S., & Winsløw, C. (2017). Uffe Haagerup - His life and mathematics. Advances in Operator Theory, 3(1), 295–325.

    Google Scholar 

  • National Research Council. (2013). The mathematical sciences in 2025. The National Academies Press.

    Google Scholar 

  • Philips, C. (2015). The new math – A political history. University of Chicago Press.

    Google Scholar 

  • Schoenfeld, A. (2008). The math wars. Educational Policy, 18(1), 253–286.

    Article  Google Scholar 

  • Verret, M. (1975). Le temps des études. Paris.

    Google Scholar 

  • Wilson, N. (2006). Encyclopedia of ancient Greece. Routledge.

    Google Scholar 

  • Winsløw. (1993). Strongly free actions on subfactors. International Journal of Mathematics, 4, 675–688.

    Article  Google Scholar 

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Authors and Affiliations

  1. University of Copenhagen, Copenhagen, Denmark

    Carl Winsløw

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  1. Carl Winsløw
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Correspondence to Carl Winsløw .

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Editors and Affiliations

  1. David and Judi Proctor Department of Mathematics, University of Oklahoma, Norman, OK, USA

    Sepideh Stewart

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Winsløw, C. (2023). Didactics of Mathematics as a Field of Mathematical Research: The Anthropological Approach. In: Stewart, S. (eds) Mathematicians' Reflections on Teaching. Advances in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-031-34295-0_7

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  • DOI: https://doi.org/10.1007/978-3-031-34295-0_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-34294-3

  • Online ISBN: 978-3-031-34295-0

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