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The Constitution of the « Milieu » During an Inquiry Process: An Analysis in Terms of Question-Answer and Media-Milieu Dialectics

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Part of the Trends in Mathematics book series (RPCRMB,volume 13)


This paper proposes to analyze the internal assessment within the standard level mathematics course in the International Baccalaureate (IB). This written and individual piece of work entitled “Mathematical Exploration” that each student must produce should involve an investigation in a field of mathematics. This analysis uses the tools of the Anthropological theory of didactics (ATD), in particular the Herbartian scheme and the dialectics of questions/answers and media/milieu. We make the hypothesis that these two dialectics play a crucial role in conducting this exploration and without these the work would be reduced to “copy-pasting” information from the media.


  • Anthropological theory of didactics
  • Media-milieu dialectic
  • Inquiry-based learning
  • International baccalaureate
  • Assessment

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    The objective of this conference that took place in April 1974 was to review the present state of the IB experiment in order to determine its viability, its long-term extension and consider its future developments and procedures.


  • Artigue, M., & Blomhøj, M. (2013). Conceptualizing inquiry-based education in mathematics. ZDM, 45(6), 797–810.

  • Bosch, M. (2018). Study and research paths: A model for inquiry. In Proceedings of the International Congress of Mathematicians (ICM 2018). World Scientfic, 1–0, 4015–4035.

  • Chevallard, Y. (2005). La place des mathématiques vivantes dans l’éducation secondaire: Transposition didactique des mathématiques et nouvelle épistémologie scolaire. La Place Des Mathématiques Vivantes Dans l’enseignement Secondaire. 3e Université d’été Animath, (Saint-Flour, 22–27 août 2004), Paris.

  • Chevallard, Y. (2009). Remarques sur la notion d’infrastructure didactique et sur le rôle des PER [Communication]. Journées Ampère, Lyon.

  • Chevallard, Y. (2008). Un concept en émergence: La dialectique des média et des milieux. In G. Gueudet & Y. Matheron (Eds.), Actes du Séminaire national de didactique des mathématiques. IREM.

    Google Scholar 

  • Florensa, I., Bosch, M., Gascón, J., & Mata, M. (2016, March). SRP design in an Elasticity course: The role of mathematic modelling. First Conference of International Network for Didactic Research in University Mathematics.

  • IB. (2015). Approaches to teaching and learning in the Diploma Programme. International Baccalaureate.

    Google Scholar 

  • IBO. (2012). Diploma Programme Mathematics SL guide. International Baccalaureate Organization.

    Google Scholar 

  • Lackova, J., & Dorier, J.-L. (2018). La démarche d’investigation dans le cadre du Baccalaureat International. Actes Du Colloque EMF 2018. Mathématique en scène - des ponts entre les disciplines. Paris : Gennevilliers.

    Google Scholar 

  • Rocard, M., Csermely, P., Jorde, D., Lenzen, D., Walberg-Henriksson, H., & Hemmo, V. (2007). Science Education Now: A Renewed Pedagogy for the Future of Europe. Commission européenne.

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Correspondence to Jana Lackova .

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Lackova, J. (2021). The Constitution of the « Milieu » During an Inquiry Process: An Analysis in Terms of Question-Answer and Media-Milieu Dialectics. In: Barquero, B., Florensa, I., Nicolás, P., Ruiz-Munzón, N. (eds) Extended Abstracts Spring 2019. Trends in Mathematics(), vol 13. Birkhäuser, Cham.

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