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Modeling Practices to Design Computer Simulators for Trainees’ and Mentors’ Education

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Mathematics Education in the Age of Artificial Intelligence

Part of the book series: Mathematics Education in the Digital Era ((MEDE,volume 17))

Abstract

How can AI be brought to support teaching and learning at a time when the uses of digital technologies remain fairly poor and teacher education is struggling to make an impact? The design of classroom computer simulators has led us to create models, based on ordinary practices in the use of digital technologies, and in particular the articulation between working with digital and paper space. This allows us to identify the knowledge needed by the teacher and educators to move from the usual workspaces to these new ones or to coordinate the two. This chapter therefore shows the design process of AI tools: computerized classroom and mentoring simulators (as expert systems). Our analysis will be based mainly on the teaching of proof in geometry for middle school students.

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Notes

  1. 1.

    Congress of the European Society for Research in Mathematics Education.

  2. 2.

    The HyPE-13 project—Hybridizing and Sharing Teachings funded by the National Research Agency (ANR) is led by the University of Pau and the Pays de l’Adour (UPPA).

  3. 3.

    See this simulator at https://fabien-emprin.pagesperso-orange.fr/actioninstr/.

References

  • Abboud-Blanchard, M., & Emprin, F. (2010). Pour mieux comprendre les pratiques des formateurs et de formations TICE. Recherche Et Formation, 62, 125–140.

    Google Scholar 

  • Arsac, G. (1987). L’origine de la démonstration: Essai d’épistémologie didactique [The origin of the demonstration: Essay on didactic epistemology]. Publications Mathématiques Et Informatique De Rennes, 5, 1–45.

    Google Scholar 

  • Arzarello, F., Micheletti, C., Olivero, F., Robutti, O., & Paola, D. (1998). A model for analysing the transition to formal proofs in geometry. In PME Conference (Vol. 2, pp. 2–24).

    Google Scholar 

  • Arzarello, F., Olivero, F., Paola, D., & Robutti, O. (2002). A cognitive analysis of dragging practises in Cabri environments. Zentralblatt Für Didaktik Der Mathematik, 34(3), 66–72.

    Article  Google Scholar 

  • Baccaglini-Frank, A., & Mariotti, M. A. (2010). Generating conjectures in dynamic geometry: The maintaining dragging model. International Journal of Computers for Mathematical Learning, 15(3), 225–253. https://doi.org/10.1007/s10758-010-9169-3

    Article  Google Scholar 

  • Balacheff, N. (1998). Contract and custom: Two registers of didactical interactions. The Mathematics Educator, 9(2).

    Google Scholar 

  • Bkouche, R. (1997). Epistémologie, histoire et enseignement des mathématiques. For the Learning of Mathematics, 17(1), 34–42.

    Google Scholar 

  • Brau-Antony, S., & Mieusset, C. (2013). Accompagner les enseignants stagiaires: Une activité sans véritables repères professionnels [Trainee teachers mentoring: An activity without real professional benchmarks]. Recherche Et Formation, 72, 27–40.

    Article  Google Scholar 

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

    Google Scholar 

  • Brousseau, G. (2006). Theory of didactical situations in mathematics: Didactique des mathématiques, 1970–1990 (Vol. 19). Springer Science & Business Media.

    Google Scholar 

  • Coulange, L. (2012). L’ordinaire dans l’enseignement des mathématiques. In Les pratiques enseignantes et leurs effets sur les apprentissages des élèves. Mémoire d’HDR, Université Paris-Diderot.

    Google Scholar 

  • Duval, R. (1993). Registres de représentation sémiotique et fonctionnement cognitif de la pensée. Annales De Didactique Et De Sciences Cognitives, 5(1), 37–65.

    Google Scholar 

  • Emprin, F., & Sabra, H. (2019). Les simulateurs informatiques, ressources pour la formation des enseignants de mathématiques [Computer simulators, a resource for training mathematics teachers]. Canadian Journal of Science, Mathematics and Technology Education, 19(2), 204–216. https://doi.org/10.1007/s42330-019-00046-w

    Article  Google Scholar 

  • Emprin, F. (2007). Formation initiale et continue pour l'enseignement des mathématiques avec les TICE: Cadre d'analyse des formations et ingénierie didactique. Doctoral dissertation, Université Paris-Diderot-Paris VII.

    Google Scholar 

  • Emprin, F. (2009). A didactic engineering for teachers education courses in mathematics using ICT. In Proceedings of the sixth congress of the European Society for Research in Mathematics Education (CERME6) (pp. 1290–1299).

    Google Scholar 

  • Emprin, F., & Petitfour, É. (2020). Using a simulator to help students with dyspraxia learn geometry. Digital Experiences in Mathematics Education, 1–23.

    Google Scholar 

  • Emprin, F., & Sabra, H. (2019). Les simulateurs informatiques, ressources pour la formation des enseignants de mathématiques. Canadian Journal of Science, Mathematics and Technology Education, 19(2), 204–216.

    Article  Google Scholar 

  • Emprin, F., Maschietto, M., & Soury-Lavergne, S. (2017). Technologies pour l’enseignement, l’apprentissage et la formation en geometrie au premier degre, in actes de la 19ème école d’été de didactique des mathématiques organisé par l’Association pour la Recherche en Didactique des Mathématiques (ARDM). Actes prochainement en ligne.

    Google Scholar 

  • Гaлиaкбepoвa, A. A., Гaлямoвa, Э. X. & C. H. Maтвee, Э. X. [Galiakberova, A. A., Galyamova E. K., & Matveev S. N.] (2020). Meтoдичecкиe ocнoвы пpoeктиpoвaния цифpoвoгo cимyлятopa пeдaгoгичecкoй дeятeльнocти [Methodological basis for designing a digital simulator of pedagogical activities]. Vestnik of Minin University, 8(3). https://doi.org/10.26795/2307-1281-2020-8-3-2

  • Haenlein, M., & Kaplan, A. (2019). A brief history of artificial intelligence: On the past, present, and future of artificial intelligence. California Management Review, 61(4), 5–14. https://doi.org/10.1177/0008125619864925

    Article  Google Scholar 

  • Hennissen, P., Beckers, H., & Moerkerke, G. (2017). Linking practice to theory in teacher education: A growth in cognitive structures. Teaching and Teacher Education, 63, 314–325.

    Article  Google Scholar 

  • Hennissen, P., Crasborn, F., Brouwer, N., Korthagen, F., & Bergen, T. (2008). Mapping mentor teachers’ roles in mentoring dialogues. Educational Research Review, 3(2), 168–186.

    Article  Google Scholar 

  • Hilbert, D. (1900). Les principes fondamentaux de la géométrie, traduit par L. Laugel, Gauthier-Villard (Eds.), Paris, Bureau des longitudes de l’école polytechnique (114 pp.). disponible à https://gallica.bnf.fr/ark:/12148/bpt6k996866.

  • Houdement, C., & Kuzniak, A. (2006). Paradigmes géométriques et enseignement de la géométrie. In Annales De Didactique Et De Sciences Cognitives, 11, 175–193.

    Google Scholar 

  • Jones, K. (2000). Providing a foundation for deductive reasoning: Students’ interpretations when using dynamic geometry software. Educational Studies in Mathematics, 44(1 & 2), 55–85.

    Article  Google Scholar 

  • Jones, K., Maschietto, M., & Mithalal-Le Doze, J. (2017). Introduction to the papers of TWG04: Geometry education. CERME 10, Feb 2017, Dublin, Ireland. hal-01925528.

    Google Scholar 

  • Krämer, N. C., & Bente, G. (2010). Personalizing e-learning. The social effects of pedagogical agents. Educational Psychology Review, 22(1), 71–87.

    Google Scholar 

  • Laborde, C. (1985). Quelques problèmes d’enseignement de la géométrie dans la scolarité obligatoire. For the Learning of Mathematics, 5(3), 27–34.

    Google Scholar 

  • Laborde, C. (2000). Dynamic geometry environments as a source of rich learning contexts for the complex activity of proving. Educational Studies in Mathematics, 44(1–2), 151–161.

    Article  Google Scholar 

  • Laborde, C. (2001). Integration of technology in the design of geometry tasks with cabri-geometry. International Journal of Computers for Mathematical Learning, 6(3), 283–317.

    Article  Google Scholar 

  • Mammana, C., & Villani, V. (1998). Perspectives on the teaching of geometry for the 21st century: An ICMI study. Kluwer.

    Book  Google Scholar 

  • Mariotti, M.-A. (2000). Introduction to Proof: The mediation of a dynamic software environment. Educational Studies in Mathematics, 44(1 & 2), 25–53.

    Article  Google Scholar 

  • Mattéï-Mieusset, C. (2013). Les dilemmes d’une pratique d’accompagnement et de conseil en formation. Analyze de l’activite reelle du maitre de stage dans l’enseignement secondaire [The dilemmas of a mentoring practice and training. Analysis of the actual activity of the professional supervisor in secondary education].(Doctoral dissertation, Université de Reims Champagne Ardenne).

    Google Scholar 

  • Mercier, A. (2018). Dessin, schéma, figure. Essais sur la formation des savoirs scientifiques. In Du mot au concept, PUG, 183-203.

    Google Scholar 

  • Pastré, P. (dir.) (2005). Apprendre par la simulation: de l'analyse du travail aux apprentissages professionnels. Toulouse: Octarès, 363 pp.

    Google Scholar 

  • Paris, C., & Gespass, S. (2001). Examining the mismatch between learner-centered teaching and teacher-centered supervision. Journal of Teacher Education, 52(5), 398–412.

    Article  Google Scholar 

  • Peyrard, F. (1804). Les éléments de géométrie d'Euclide, traduits littéralement et suivis d'un Traité du cercle, du cylindre, du cône et de la sphère, de la mesure des surfaces et des solides, avec des notes, F. Louis: Paris, 601 pp. Disponible à l'adresse http://gallica.bnf.fr/ark:/12148/bpt6k110982q

  • Rabardel, P. (2002). people and technology: A cognitive approach to contemporary instruments. Translated by Wood, H., université paris 8, pp.188, hal-01020705.

    Google Scholar 

  • Restrepo, A. M. (2008). Genèse instrumentale du déplacement en géométrie dynamique chez des élèves de 6ème [instrumental genesis of dragging in a dynamic geometry software in 6th grade] (Doctoral dissertation, Université Joseph-Fourier-Grenoble I).

    Google Scholar 

  • Richard, P. R. (2004). L’inférence figurale: Un pas de raisonnement discursivo-graphique [Figural inference: A step of discursive-graphic reasoning]. Educational Studies in Mathematics, 57(2), 229–263.

    Article  Google Scholar 

  • Robert, A., & Rogalski, J. (2005). A cross-analysis of the mathematics teacher’s activity. An example in a French 10th-grade class. Educational Studies in Mathematics, 59(1–3), 269–298.

    Google Scholar 

  • Sträßer, R. (2001). Cabri-geometre: Does dynamic geometry software (DGS) change geometry and its teaching and learning? International Journal of Computers for Mathematical Learning, 6(3), 319–333.

    Google Scholar 

  • Vergnaud, G. (1998). Towards a cognitive theory of practice. In Mathematics education as a research domain: A search for identity (pp. 227–240). Springer, Dordrecht.

    Google Scholar 

  • Sherard, W. H. (1981). Why is geometry a basic skill? The Mathematics Teacher, 74(1), 19–60.

    Article  Google Scholar 

  • Whitely, W. (1999). The decline and rise of geometry in 20th century North America. In Proceedings of the 1999 Conference of the Mathematics Education Study Group of Canada. St. Catharines, Ontario: Brock University.

    Google Scholar 

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Correspondence to Fabien Emprin .

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Emprin, F. (2022). Modeling Practices to Design Computer Simulators for Trainees’ and Mentors’ Education. In: Richard, P.R., Vélez, M.P., Van Vaerenbergh, S. (eds) Mathematics Education in the Age of Artificial Intelligence. Mathematics Education in the Digital Era, vol 17. Springer, Cham. https://doi.org/10.1007/978-3-030-86909-0_14

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  • DOI: https://doi.org/10.1007/978-3-030-86909-0_14

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