The Mathematical Crisis in Secondary–Tertiary Transition
Abstract
Tertiary transition in mathematics appears to be an insurmountable struggle for many students, including for high achievers in secondary school. The high dropout rates in many Western Countries represent a big issue from an individual and social point of view. It appears particularly significant to analyse this phenomenon in the context of the degree course in Mathematics, studying students’ cognitive and affective reactions to the (often unexpected and severe) difficulties encountered in the tertiary transition. With this aim, we developed a narrative study in a specific context in Italy—that involves excellent students from secondary school—to investigate how successful and dropout students describe their experience in transition. Implications for the educational practice are discussed.
Keywords
Mathematical failure at tertiary level High achievers Narrative research Tertiary transition in mathematics Affective factorsReferences
- Alcock, L., & Simpson, A. (2002). Definitions: Dealing with categories mathematically. For the Learning of Mathematics, 22(2), 28–34.Google Scholar
- Artigue, M. (1999). The teaching and learning of mathematics at the university level crucial questions for contemporary research in education. Notices of the AMS, 46, 1377–1385.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, The Netherlands: Kluwer.Google Scholar
- Artigue, M. (2016). Mathematics education research at university level: Achievements and challenges. In E. Nardi, C. Winslow, & T. Hausberger (Eds.), Proc. 1 st Conf. Of INDRUM (pp. 11–27). Montpellier, France: INDRUM.Google Scholar
- Bardelle, C., & Di Martino, P. (2012). E-learning in secondary-tertiary transition in mathematics: For what purpose? ZDM – International Journal on Mathematics Education, 44(6), 787–800.CrossRefGoogle Scholar
- Bruner, J. (1990). Acts of meaning. Cambridge, MA: Harvard University Press.Google Scholar
- Clark, M., & Lovric, M. (2008). Suggestion for a theoretical model for secondary–tertiary transition in mathematics. Mathematics Education Research Journal, 20(2), 25–37.CrossRefGoogle Scholar
- Cohen, L., Manion, L., & Morrison, K. (2007). Research methods in education. London, England: Routledge.Google Scholar
- Connelly, F. M., & Clandinin, D. J. (1990). Stories of experience and narrative inquiry. Educational Researcher, 19(5), 2–14.CrossRefGoogle Scholar
- Demazière, D., & Dubar, C. (1997). Analyser les entretiens biographiques [Analyze biographical interviews]. Paris, France: Èditions Nathan.Google Scholar
- De Bellis, V., & Goldin, G. (2006). Affect and meta-affect in mathematical problem solving: A representational perspective. Educational Studies in Mathematics, 63(2), 131–147.CrossRefGoogle Scholar
- De Guzmán, M., Hodgson, B., Robert, A., & Villani, V. (1998). Difficulties in the passage from secondary to tertiary education. In A. Louis, U. Rehmann & P. Schneider (Eds.), Proc. of the ICM (Vol. 3, pp. 747–762). Berlin, Germany: ICM.Google Scholar
- Di Martino, P., & Zan, R. (2010). ‘Me and maths’: Towards a definition of attitude grounded on students’ narratives. Journal of Mathematics Teacher Education, 13(1), 27–48.CrossRefGoogle Scholar
- Di Martino, P., & Zan, R. (2011). Attitude towards mathematics: A bridge between beliefs and emotions. ZDM – The International Journal on Mathematics Education, 43(4), 471–482.CrossRefGoogle Scholar
- Dorier, J.-L., & Sierpinska, A. (2001). Research into the teaching and learning of linear algebra. In D. Holton (Ed.), The teaching and learning of mathematics at university level. An ICMI study (pp. 255–274). Dordrecht, The Netherlands: Kluwer Academic Publishers.Google Scholar
- Ferrari, P. L. (2004). Mathematical language and advanced mathematics learning. In M. Johnsen Høines & A. Berit Fuglestad (Eds.), Proc. of the 28 th Conference of the IGPME (Vol. 2, pp. 383–390). Bergen, Norway: PME.Google Scholar
- Goldin, G., Hannula, M., Heyd-Metzuyanim, E., Jansen, A., Kaasila, R., Lutovac, S., . . . Zhang, Q. (2016). Attitudes, beliefs, motivation, and identity in mathematics education. An overview of the field and future directions. Hamburg, Germany: Springer.Google Scholar
- Gueudet, G. (2008). Investigating the secondary–tertiary transition. Educational Studies in Mathematics, 67(3), 237–254.CrossRefGoogle Scholar
- Hefendehl-Hebeker, L., Ableitinger, C., & Herrmann, A. (2010). Mathematik Besser Verstehen [Mathematics better understanding]. In A. Lindmeier & S. Ufer (Eds.), Beiträge zum Mathematikunterricht (pp. 93–94). Münster, Germany: WTM-Verlag Stein.Google Scholar
- Hernandez-Martinez, P., Williams, J., Black, L., Davis, P., Pampaka, M., & Wake, G. (2011). Students’ views on their transition from school to college mathematics: Rethinking ‘transition’ as an issue of identity. Research in Mathematics Education, 13(2), 119–130.CrossRefGoogle Scholar
- Kaasila, R. (2007). Using narrative inquiry for investigating the becoming of a mathematics teacher. ZDM – International Journal on Mathematics Education, 39(3), 205–213.CrossRefGoogle Scholar
- Marsh, H., Trautwein, U., Lüdtke, O., Baumert, J., & Köller, O. (2007). The big-fish-little-pond effect: Persistent negative effects of selective high schools on self-concept after graduation. American Educational Research Journal, 44(3), 631–669.CrossRefGoogle Scholar
- Mitchell, M., & Jolley, J. (2010). Research design explained. Belmont: WCL.Google Scholar
- Nardi, E. (2008). Amongst mathematicians: Teaching and learning mathematics at university level. New York, NY: Springer.Google Scholar
- Niss, M. (2003). Mathematical competencies and the learning of mathematics: The Danish KOM project. In A. Gagatsis & S. Papastavridis (Eds.), Proc. of the 3rd Mediterranean Conf. on Math. Ed. (pp. 115–124). Athens, Greece: Hellenic MS.Google Scholar
- Perkins, M. (2005). If you could teach the world just one thing... Newsletter of the London Mathematical Society, 339, 31–32.Google Scholar
- Rach, S., & Heinze, A. (2016). The transition from school to university in mathematics: Which influence do School-related variables have? International Journal of Science and Mathematics Education, 15(7), 1–21.Google Scholar
- Rasmussen, C. & Ellis, J. (2013). Who is switching out of calculus and why. In A. M. Lindmeier & A. Heinze (Eds.), Proc. of the 37 th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 73–80). Kiel, Germany: PME.Google Scholar
- Selden, A. (2005). New developments and trends in tertiary mathematics education: Or, more of the same? International Journal of Mathematical Education in Science and Technology, 36(2/3), 131–147.CrossRefGoogle Scholar
- Selden, A., & Selden, J. (2001). Tertiary mathematics education research and its future. In D. Holton (Ed.), The teaching and learning of mathematics at university level (pp. 237–254). Dordrecht, The Netherlands: Kluwer.Google Scholar
- Tall, D. (1991). Advanced mathematical thinking. Dordrecht, The Netherlands: Kluwer.Google Scholar
- Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151–169.CrossRefGoogle Scholar
- Weiner, B. (1986). An attributional theory of motivation and emotion. New York, NY: Springer-Verlag.Google Scholar
- Zan, R. (2013). Solid findings on students’ attitudes to mathematics. EMS Newsletter, (September), 51–53.Google Scholar