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Investigating the secondary–tertiary transition

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Abstract

The secondary–tertiary transition has been studied in a great amount of research in mathematics education, adopting different focuses and theoretical approaches. I present here how these focuses led the authors to identify and study different students’ difficulties and to develop different means of didactical action. Individual, social, but also institutional phenomena are considered with different perspectives. Each perspective yields a particular view of transition. The association and comparison of these views makes it possible to build an organized outline of this complex object, combining several kinds of ruptures and long-term evolutions.

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References

  • Alcock, L., & Simpson, A. (2001). The Warwick analysis project: Practice and theory, In D. Holton (Ed.), The teaching and learning of mathematics at university level (pp. 99–112). Dordrecht: Kluwer.

    Google Scholar 

  • Artigue, M. (2001). What can we learn from educational research at the university level? In D. Holton (Ed.), The teaching and learning of mathematics at university level (pp. 207–220). Dordrecht: Kluwer.

    Google Scholar 

  • Artigue, M. (2004). Le défi de la transition secondaire-supérieur. Que peuvent nous apporter les recherches en didactique des mathématiques? (The secondary–tertiary challenge. What do we learn from mathematics didactics research?) Paper presented at the first French-Canadian Congress of Mathematical Sciences, Toulouse.

  • Battie, V. (2003). Spécificités et potentialités de l’arithmétique élémentaire pour l’apprentissage du raisonnement mathématique (Specificity and potential of elementary number theory for the learning of mathematical reasoning), Thèse de doctorat de l’Université Paris VII.

  • Berger, M. (2004). The functional use of a mathematical sign. Educational Studies in Mathematics, 55, 81–102.

    Article  Google Scholar 

  • Bloch, I. (2003). Teaching functions in a graphic milieu: What forms of knowledge enable students to conjecture and prove. Educational Studies in Mathematics, 52, 3–28.

    Article  Google Scholar 

  • Bloch, I., & Ghedamsi, I. (2004). The teaching of calculus at the transition between upper secondary school and university. Paper presented at the 10th International Congress on Mathematical Education (ICME10), Copenhague, Denmark.

  • Bookman, J., & Malone, D. (2003). The nature of learning in interactive technological environments. A proposal for a research agenda based on grounded theory. Research in Collegiate Mathematics Education V, 182–204.

  • Bosch, M., Fonseca, C., & Gascon, J. (2004). Incompletud de las organizaciones matematicas locales en las instituciones escolares (Incompleteness of the mathematical organizations in the educational institutions). Recherches en Didactique des Mathématiques, 24(2–3), 205–250.

    Google Scholar 

  • Brousseau, G. (1997). Theory of didactical situations in mathematics 1970–1990. Dordrecht: Kluwer.

    Google Scholar 

  • Castela, C. (2004). Institutions influencing mathematics students’ private work: A factor of academic achievement, Educational Studies in Mathematics, 57, 33–63.

    Article  Google Scholar 

  • Cazes, C., Gueudet, G., Hersant, M., & Vandebrouck, F. (2007). Using e-exercise bases in mathematics: Case studies at university. International Journal of Computers for Mathematical Learning, 11(3), 327–350.

    Article  Google Scholar 

  • Chellougui, F. (2004a). Articulation between logic, mathematics, and language in mathematical practice, Paper presented at the 10th International Congress on Mathematical Education (ICME10), Copenhague Denmark.

  • Chellougui, F. (2004b). L’utilisation des quantificateurs universel et existentiel en première année universitaire entre l’explicite et l’implicite (Between explicit and implicit use of the “for all” and “exists” quantifiers in the first university year), Thèse de doctorat, Université Claude Bernard Lyon 1 et Université de Tunis.

  • Chevallard, Y. (1992). Concepts fondamentaux de la didactique: Perspectives apportées par une approche anthropologique (Fundamental concepts of didactics: Perspectives opened by an anthropological approach). Recherches en Didactique des Mathématiques, 12(1), 77–111.

    Google Scholar 

  • Crawford, K., Gordon, S., Nicholas, J., & Prosser, M. (1998). Qualitatively different experiences of learning mathematics at university. Learning and Instruction, 8(5), 455–468.

    Article  Google Scholar 

  • De Guzman, M., Hodgson, B. R., Robert, A., & Villani, V. (1998). Difficulties in the passage from secondary to tertiary education, Proceedings of the International Congress of Mathematicians, Berlin, Documenta mathematica, extra volume ICM 1998, 747–762.

  • Douady, R. (1992). Des apports de la didactique des mathématiques à l’enseignement (Contribution of mathematics didactics to teaching). Repères Irem, 6, 132–158.

    Google Scholar 

  • Dreyfus, T. (1999). Why Johnny can’t prove. Educational Studies in Mathematics, 38, 85–109.

    Article  Google Scholar 

  • Durand-Guerrier, V., & Arsac, G. (2003). Méthodes de raisonnement et leurs modélisations logiques. Spécificité de l’analyse. Quelles implications didactiques? (Reasoning methods and their logical models. Specificity of calculus. Which didactical implications?). Recherches en Didactique des Mathématiques, 23(3), 295–342.

    Google Scholar 

  • Duval, R. (2006). A cognitive analysis of problems of comprehension in the learning of mathematics. Educational Studies in Mathematics, 61, 103–131.

    Article  Google Scholar 

  • Edwards, B. E., Dubinsky, E., & Mc Donald, M. A. (2005). Advanced mathematical thinking. Mathematical Thinking and Learning, 7(1), 15–25.

    Article  Google Scholar 

  • Epp, S. (2003). The role of logic in teaching proof. The Mathematical Association of America Monthly, 886–899.

  • Gray, E., Pinto, M., Pitta, D., & Tall, D. (1999). Knowledge construction and diverging thinking in elementary and advanced mathematics. Educational Studies in Mathematics, 38, 111–133.

    Article  Google Scholar 

  • Grønbǽk, N., & Winsløw, C. (2006). Developing and assessing specific competencies in a first course on real analysis. Research in Collegiate Mathematics Education VI, 99–138.

    Google Scholar 

  • Gueudet, G. (2004). Rôle du géométrique dans l’enseignement de l’algèbre linéaire (Resorting to geometrical aspects in the teaching of linear algebra). Recherches en Didactique des Mathématiques, 24(1), 81–114.

    Google Scholar 

  • Gueudet, G. (2006). Using geometry to teach and learn linear algebra. Research in Collegiate Mathematics Education VI, 171–195.

  • Haines, C., & Houston, K. (2001). Assessing student project work, In D. Holton (Ed.), The teaching and learning of mathematics at university level (pp. 431–442). Dordrecht: Kluwer.

    Google Scholar 

  • Harel, G., & Sowder, L. (1998) Students’ proof schemes: Results from exploratory study, Research in Collegiate Mathematics Education II, 234–283.

  • Iannone, P., & Nardi, E. (2008) The interplay between syntactic and semantic knowledge in proof production: Mathematicians’ perspectives, Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education (CERME 5), Larnaca, Cyprus (in press).

  • Legrand, M. (2001). Scientific debate in mathematics courses, In D. Holton (Ed.), The teaching and learning of mathematics at university level (pp. 127–136). Dordrecht: Kluwer.

    Google Scholar 

  • Lithner, J. (2000). Mathematical reasoning in task solving. Educational Studies in Mathematics, 41, 165–190.

    Article  Google Scholar 

  • Lithner, J. (2003). Students’ mathematical reasoning in university textbook exercises. Educational Studies in Mathematics, 52, 29–55.

    Article  Google Scholar 

  • Mamona-Downs, J., & Downs, M. (2004). Realisation of techniques in problem solving: The construction of bijections for enumerations tasks. Educational Studies in Mathematics, 56, 235–253.

    Article  Google Scholar 

  • Maschietto, M. (2001). Fonctionnalités des représentations graphiques dans la résolution de problèmes d’analyse à l’université (Functionality of graphical representations for problem solving at university). Recherches en Didactique des Mathématiques, 21(1.2), 123–156.

    Google Scholar 

  • Moore, R. C. (1994). Making the transition to formal proof, Educational Studies in Mathematics, 27, 249–266.

    Article  Google Scholar 

  • Nardi, E., & Iannone, P. (2005) To appear and to be: Acquiring the « genre speech » of university mathematics. Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education (CERME 4), San Feliu de Guixols, Spain.

  • Niss, M. (2001). University mathematics based on problem-oriented student projects: 25 years of experience with the Roskilde model. In D. Holton (Ed.), The teaching and learning of mathematics at university level (pp. 153–164). Dordrecht: Kluwer.

    Google Scholar 

  • Praslon, F. (2000). Continuités et ruptures dans la transition Terminale S / DEUG Sciences en analyse. Le cas de la notion de dérivée et son environnement (Ruptures and continuity in the Terminale S / first scientific university year in calculus. The case of the derivative and its environment), Thèse de doctorat de l’Université Paris 7.

  • Rey, B., Caffieaux, C., Compere, D., Lamme, A., Persenaire, E., Philippe, J. et al. (2003). Les caractéristiques des savoirs enseignés dans les universités et les hautes écoles (Characteristics of the knowledge taught at universities and colleges), Université Libre de Bruxelles – Service des Sciences de l'Education.

  • Ridgway, J., Swan, M., & Burkhardt, H. (2001). Assessing mathematical thinking via FLAG. In D. Holton (Ed.), The teaching and learning of mathematics at university level (pp. 423–430). Dordrecht: Kluwer.

    Google Scholar 

  • Robert, A. (1998). Outils d’analyse des contenus mathématiques à enseigner au lycée et à l’université (Tools for the analysis of the mathematical content taught at high school and university). Recherches en Didactique des Mathématiques, 18(2), 139–190.

    Google Scholar 

  • Robert, A., & Schwartzenberger, R. (1991). Research in teaching and learning mathematics at an advanced level. In D. Tall (Ed.), Advanced mathematical thinking (pp. 127–139). Dordrecht: Kluwer.

    Google Scholar 

  • Sackur, C., Assude, T., Maurel, M., Drouhard, J.-P., & Paquelier, Y. (2005). L’expérience de la nécessité épistémique (Experiencing the intrinsic necessity). Recherches en Didactique des Mathématiques, 25(1), 57–90.

    Google Scholar 

  • Santos-Trigo, M. (1998). On the implementation of mathematical problem solving instruction: Qualities of some learning activities. Research in Collegiate Mathematics Education III, 71–80.

  • Schneider, M. (2001). Praxéologies didactiques et praxéologies mathématiques. A propos d’un enseignement des limites au secondaire (Didactic and mathematical praxeologies. A teaching design for limits at secondary school). Recherches en Didactique des Mathématiques, 21(1.2), 7–56.

    Google Scholar 

  • Schoenfeld, A. H. (1998). Reflections on a course in mathematical problem solving. Research in Collegiate Mathematics Education III, 81–113.

  • Segal, J. (2000). Learning about mathematical proof: Conviction and validity. Journal of Mathematical Behavior, 18(2), 191–210.

    Article  Google Scholar 

  • Selden, A., & Selden, J. (2005). Perspectives on advanced mathematical thinking. Mathematical Thinking and Learning, 7(1), 1–13.

    Article  Google Scholar 

  • Sierpinska, A. (2000). On some aspects of students’ thinking in linear algebra, In J.-L. Dorier (Ed.), On the teaching of linear algebra (pp. 209–246). Dordrecht: Kluwer.

    Google Scholar 

  • Straesser, R. (2008). A propos de la transition du secondaire vers le monde du travail (About transition from secondary school to the workplace), In A. Rouchier, et al. (Eds.), Actes de la XIIIième école d’été de didactique des mathématiques, La Pensée Sauvage Editions Grenoble France (in press).

  • Tall, D. (1991). Advanced Mathematical Thinking. Kluwer, Dordrecht.

    Google Scholar 

  • Weber, K., & Alcock, L. (2004). Semantic and syntactic proof productions. Educational Studies in Mathematics, 56, 209–234.

    Article  Google Scholar 

  • Weller, K., Clark, J., Dubinsky, E., Loch, S., McDonald, M., & Merkovsky, R. (2003). Students performance and attitudes in courses based on APOS theory and the ACE teaching cycle. Research in Collegiate Mathematics Education V, 97–131.

  • Winsløw, C. (2003). Semiotic and discursive variables in CAS-based didactical engineering. Educational Studies in Mathematics, 52, 271–288.

    Article  Google Scholar 

  • Winsløw, C. (2008). Transformer la théorie en tâches: La transition du concret à l’abstrait en analyse réelle (Turning theory into tasks: Transition from concrete to abstract in calculus), In Rouchier, A. et al. (Eds.), Actes de la XIIIième école d’été de didactique des mathématiques, La Pensée Sauvage Editions Grenoble France (in press).

  • Wood, L. (2001). The secondary–tertiary interface. In D. Holton (Ed.), The teaching and learning of mathematics at university level (pp. 87–98). Dordrecht: Kluwer Academic Publishers.

    Google Scholar 

  • Yosof, Y. M., & Tall, D. (1999). Changing attitudes to university mathematics through problem solving. Educational Studies in Mathematics, 37, 67–82.

    Article  Google Scholar 

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Correspondence to Ghislaine Gueudet.

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Gueudet, G. Investigating the secondary–tertiary transition. Educ Stud Math 67, 237–254 (2008). https://doi.org/10.1007/s10649-007-9100-6

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