Educational Studies in Mathematics

, Volume 50, Issue 2, pp 212–237 | Cite as

Implication de l'analyse de productions d'élèves dans la formation des maîtres du primaire

  • Lucie DeBlois
  • Hassan Squalli

Abstract

Several studies have shown that pre-service teachers enter their pre-service training with already formed conceptions pertaining to teaching and learning. Pre-service teachers are considered as epistemologically complex beings with varying postures they adopt according to differing contexts. This article looks at the meanings pre-service teachers attribute to pupil errors and how these meanings evolved over the course of a 15 week course in mathematics education. Pre-service teachers were interviewed at two intervals during their first semester: at mid session and at the end. First, we identified the various kinds of analyses they brought to bear upon pupil errors as well as the interventions they suggested to rectify these errors. Then, we conducted a statistical analysis of the changes in the type of interventions suggested. Four trend indicators were created to help understand these changes. When analysing pupil's errors, pre-service teachers identified specific conceptual elements without situating them within a global context. This led to piecemeal interventions about how pupils ought to correct their errors. In conclusion, pre-service teachers' appear to base their analyses of pupils's errors upon an epistemological positioning ween title ‘former-pupil stance‘. This stance seems to create a resistance to changing their conceptions regarding the teaching and learning of mathematics.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. Antibi, A. et Brousseau, G.: 2000, ‘La détransposition de connaissances scolaires’, Recherches en Didactique des Mathématiques 20(1), 7–40.Google Scholar
  2. Astolfi, J-P. et Peterfalvi, B.: 1993, ‘Obstacles et construction de situations didactiques en sciences expérimentales’, Aster 16, 103–141.CrossRefGoogle Scholar
  3. Bednarz, N.: 2000, ‘Formation continue des enseignants en mathématiques: une nécessaire prise en compte du contexte’, in Pascale Blouin et Linda Gattuso (dir.), Didactique des mathématiques et formation des enseignants, Éditions Modulo. Collection Astroïde, Montréal, pp. 61–78.Google Scholar
  4. Bednarz, N., Gattuso, L. and Mary, C.: 1999, ‘Evolution of Pre-service Mathematics Teachers’ Representations during Training: a Case Study’, in F. Hitt, M. Santos (eds.) Proceedings of the 21st annual meeting, North American Chapter of the International Group for the Psychology of Mathematics Education Centro de Investigacion y de Estudios Avanzados - IPN. Universitad Autonoma del Estado de Morelos. Cuernavaca, Morelos, Mexico, 2, pp. 683–691.Google Scholar
  5. Bednarz, N., Gattuso, L. et Mary, C.: 1995, ‘Formation à l'intervention d'un futur enseignant en mathématiques au secondaire’, Bulletin AMQ XXXV(1), 17–30.Google Scholar
  6. Blanchard-Laville, Cl., Chevallard, Y. et Schubauer-Leoni, M.-L.: 1997. Regards croisés sur le didactique, Ed. La Pensée Sauvage, Grenoble.Google Scholar
  7. Borasi, R.: 1987, ‘Exploring mathematics through the Analysis of errors’, For the Learning of Mathematics 7(3), 2–8.Google Scholar
  8. Britzman, D.P.: 1991, ‘PracticeMakes Practice’, University of New York Press, New York.Google Scholar
  9. Civil, M.: 1993, ‘Prospective elementary teachers’ thinking about teaching mathematics’, Journal of Mathematical Behavior 12, 79–109.Google Scholar
  10. Chevallard, Y.: 1999, ‘L'analyse des pratiques enseignantes en théorie antrhopologique du didactique’, Recherches en Diudactique des Mathématiques 19(2), 221–266. La Pensée Sauvage, Grenoble.Google Scholar
  11. DeBlois, L. et Vézina, N.: 2001, ‘Conceptions des futurs maîtres du primaire relativement à des activités d'enseignement en mathématiques’, Canadian Journal of Higher Education 31(2), 103–134.Google Scholar
  12. DeBlois, L. et Uwimana, A.: 1998, ‘De nos pratiques d'enseignement vers une compréhension de l'enseignement des mathématiques’, in CD-Rom de la 4e Biennale sur la Formation et l'Éducation Paris, Sorbonne.Google Scholar
  13. DeBlois, L.: 1997a, ‘Quand additionner ou soustraire implique comparer’, Éducation et Francophonie, Québec, Association canadienne d'éducation en langue française, 25(1), pp. 102–120. http: //www.acelf.ca/revueGoogle Scholar
  14. DeBlois, L.: 1997b, ‘Trois élèves en difficulté devant des situations de réunion et de complément d'ensembles’, Educational Studies in Mathematics, 34 Dordrecht, Kluwer Academic Publishers, 67–96.Google Scholar
  15. DeBlois, L. et Squalli, H.: 1997, ‘L'analyse des erreurs des élèves en mathématiques par des étudiantes et des étudiants en formation initiale à l'enseignement’, La formation initiale continuités et ruptures, Presses de l'Université Laval, Québec, pp. 125–143.Google Scholar
  16. DeBlois, L.: 1996, ‘Une analyse conceptuelle de la numération de position au primaire’ Recherches en Didactique des Mathématiques 16(1), 71–128.Google Scholar
  17. Enemaker, C.E.: 1995, The Influence of a Problem-Solving Approach to Teaching Mathematics on Preservice Teacher's Mathematical Beliefs, Eric no. ED391657, Washington, DC.Google Scholar
  18. Favre, D. et Reynaud, C.: 2000, ‘Des représentations-obstacles à prendre en compte dans la formation aux métiers de l'enseignement’, Éducation et Francophonie, Québec: Association canadienne d'éducation en langue française. Volume XXVIII(2). http: //www.acelf.ca.Google Scholar
  19. Fayol, M.: 1990, L'enfant et le nombre, Delachaux et Niestlé, Genève.Google Scholar
  20. Fennema, E., Carpenter, T.P., Franke, L.M., Levi L., Jacobs, V.R. and Empson, S.B.: 1996, ‘A longitudinal study of learning to use children's thinking in mathematics instruction’, Journal for Research in Mathematics Education 27, 403–434.CrossRefGoogle Scholar
  21. Guba, E.G.: 1981, ‘Critera for assessing the trustworthiness of naturalistic inquiries’, Educational Communication and Technology. A Journal of Theory, Research and Development 29(2), 75–91.Google Scholar
  22. Herscovics, N. et Bergeron, J.: 1989, ‘Analyse épistémologique des débuts de l'addition’, Actes de la 41e rencontre de la Commission internationale pour l'étude et l'amélioration de l'enseignement des mathématiques Bruxelles, pp. 155–165.Google Scholar
  23. Johnston, M.: 1990, ‘Teacher's background and beliefs: Influences on learning to teach in the social studies’, Theory and Research in Social Education 18, 207–232.Google Scholar
  24. Margolinas, C. et Perrin-Glorian, M.-J.: 1997, ‘Des recherches visant à modéliser le rôle de l'enseignant’, Recherches en Didactique des Mathématiques 17(3), 7–16.Google Scholar
  25. McKinnon, A.M.: 1987, ‘Detecting reflection in-action among preservice elementary science teachers’, Teaching and Teacher Education 3, 135–145.CrossRefGoogle Scholar
  26. Portuguais, J. et Brun, J.: 1994, ‘De futurs instituteurs formés à la didactique des mathématiques? Une étude de cas’, in Vingt Ans de Didactique des Mathématiques en France, Les Éditions La Pensée sauvage, Grenoble, pp. 282–292.Google Scholar
  27. Raymond, A.: 1997, ‘Inconsistency between a beginning elementary school teacher's mathematics beliefs and teaching practice’, Journal for Research in Mathematics Education 28(5), 550–576.CrossRefGoogle Scholar
  28. Robert, A.: 1997, ‘Un essai d'analyse de pratiques effectives en classe de seconde ou comment un enseignant fait “fréquenter” les mathématiques à ses élèves pendant la classe ‘Recherches en Didactique des Mathématiques 17(3), 103–150.Google Scholar
  29. Rondeau, J.-C.: 1999, Les indicateurs en éducation. Le point de vue international et quelques indicateurs nationaux, http: //membres.point-net.com/~jerondea/indicateurs.htmlGoogle Scholar
  30. Ross, D.D.: 1989, ‘First steps in developing a reflexive approach’ Journal of Teacher Education 40(2), 22–30.Google Scholar
  31. Ross, W.: 1987, ‘Teachers’ perspective development: A study of preservice social studies teachers’, Theory and Research in Social Education 15, 225–243.Google Scholar
  32. Strauss, A.L. et Corbin, J.: 1990, Basics of Qualitatives Research. Grounded Theory Procedures and Techniques, Sage, London.Google Scholar
  33. Schram, P., Wilcox, S.K., Lanier, P. et Lappan, G.: 1988, Changing Mathematical Conceptions of Preservice Teachers: A Content and Pedagogical Intervention, National Center on Teacher Education Learning, Washington DC.Google Scholar
  34. Vacc Nesbitt, N. et Bright, G.W.: 1999, ‘Elementary preservice teachers’ changing beliefs and instructional use of children's mathematical thinking’, Journal for Research in Mathematics Education 30(1), 89–110.CrossRefGoogle Scholar
  35. Voyer, P.: 1994, Tableaux de bord de gestion: l'élaboration d'un support informationnel pour le suivi et le reportage des indicateurs de performance, Presses de l'Université du Québec, Sainte-Foy.Google Scholar
  36. Vergnaud, G.: 1981, L'enfant, la mathématique et la réalité, Peter Lang, Berne.Google Scholar
  37. Westerman, D.: 1991, ‘Expert and novice teacher decision-making’, Journal of Teacher Education 42(4), 292–305.Google Scholar
  38. Wilcox, S.K., Lanier, P., Schram, P. et Lappan, G.: 1992, Influencing Beginning Teachers’ Practice in Mathematics Education: Confronting Constraints of Knowledge, Beliefs, and Context, National Center on Teacher Education Learning, Washington DC.Google Scholar
  39. Wideen, M., Mayer-Smith, J. and Moon, B.: 1998, ‘A critical analysis of the research on learning to teach: Making the case of an ecological perspective on inquiry’, Review of Educational Research 68(2), 130–178.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Lucie DeBlois
    • 1
  • Hassan Squalli
    • 2
  1. 1.Université LavalCanada
  2. 2.Université de SherbrookeCanada

Personalised recommendations