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Suggestion for a theoretical model for secondary-tertiary transition in mathematics

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Abstract

One of most notable features of existing body of research in transition seems to be the absence of a theoretical model. The suggestion we present in this paper—to view and understand the high school to university transition in mathematics as a modern-day rite of passage—is an attempt at defining such framework. Although dominantly reflecting North-American reality, we believe that the model could be found useful in other countries as well. Let us emphasize that our model is not new in the sense that it recognizes the transition as such. In this paper, we try to determine whether (and, if so, how) the notion of a rite of passage—which is a well-understood concept in anthropology, as well as in some other disciplines (e.g. culture shock in cultural studies)—can help us understand mathematics transition issues better. Can it help us systematize existing body of research, and enhance our understanding of transition in mathematics; does it point at something new? We believe so, and by elaborating some traditional aspects of rites of passage, we hope to provide a useful lens through which we can examine the process of transition in mathematics, and make suggestions for improved management of some transitional issues.

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References

  • Alcock, L., & Simpson, A. (2002). Definitions: Dealing with categories mathematically.For the Learning of Mathematics, 22(2), 28–34.

    Google Scholar 

  • Appleby, J., & Cox, W. (2002). The transition to higher education. In P. Kahn & J. Kyle (Eds.)Effective learning and teaching in mathematics and its applications (pp. 3–19). Sterling, VA: Stylus Publishing Inc.

    Google Scholar 

  • Barnard, D. (2003). The transition to mathematics at university: Students’ views.New Zealand Journal of Mathematics, 32(supplementary issue), 1–8.

    Google Scholar 

  • Biza, I., Souyoul A., & Zachariades, T. (2005). Conceptual change in advanced mathematical thinking discussion paper.Fourth Congress of ERME, Sant Feliu de Guíxols, Spain.

    Google Scholar 

  • Clark, M. (1995). Raising achievement in mathematics for Pacific Island students in New Zealand. In R. Hunting, G. Fitzsimons, P. Clarkson, & A. Bishop (Eds.)Regional Collaboration in Mathematics Education (pp. 201–210). Melbourne: Monash University.

    Google Scholar 

  • Cohen, D. (1978). Maths in the sun.New Scientist, 3 August 1978.

  • Cooper, H., Nye, B., Charlton, K., Lindsay, J., & Greathouse, S. (1996). The effects of summer vacation on achievement test scores: A narrative and meta-analytic review.Review of Educational Research, 66(3), 227–268.

    Google Scholar 

  • Crawford, K., Gordon, S., Nicholas, J., & Posser, M. (1994). Conceptions of mathematics and how it is learned: The perspectives of students entering university.Learning and Instruction, 4, 331–345.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Davies, D. (1994). Introduction: Raising the Issues. In J. Holm, & J. Bowker (Eds.),Rites of Passage (pp. 1–9). London, UK: Pinter Publishers.

    Google Scholar 

  • Demana, F. (1990). Improving college readiness through school/university articulation. In N. Fisher, H. Keynes, & P. Weigreics (Eds.)Mathematicians and education reform: Proceedings of the 1998 workshop. CBMS Issues in Mathematics Education (Vol. 1, pp. 131–143). American Mathematical Society.

  • Easter, W. (1990). Ensuring minorities’ success in mathematics, engineering and science: The MESA program.Carnegie Quarterly, Vol. XXXV Summer/Fall 1990, 1–7.

    Google Scholar 

  • Gruenwald, N., Klymchuk, S., & Jovanoski, Z. (2003). Investigating the ways of reducing the gap between the school and university mathematics: An international study. In N. A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.),Proceedings of the 27tl annual conference of the International Group for the Psychology of mathematics Education (Vol. 1, pp. 238–244). Honolulu, HI: IGPME.

    Google Scholar 

  • Guzman, M. de, Hodgson B., Robert, A., & Villani, V. (1998). Difficulties in passage from secondary to tertiary education. In G. Fischer & U. Rehmann (Eds.),Proceedings of the International Congress of Mathematicians (Vol III: pp. 747–762). Berlin: Documenta Mathematica.

    Google Scholar 

  • Howe, R. (1998). The AMS and mathematics education: The revision of the ‘NCTM Standards.’Notices of the American Mathematical Society, 45, 243–247.

    Google Scholar 

  • Howitt, A. W. (1904).The native tribes of South-East Australia. London, U.K.: Macmillan.

    Google Scholar 

  • Howson, G. (1989). Maths problem: Can more pupils reach higher standards?Policy Studies No.102. London: Centre for Policy Studies.

    Google Scholar 

  • Institute of Mathematics and its Applications, London Mathematical Society and Royal Statistical Society (1995).Tackling the mathematics problem, Available from http://www.lms.ac.uk/policy/tackling_maths_prob.pdf.

  • Kajander, A., & Lovric, M. (2005). Transition from secondary to tertiary mathematics: McMaster University experience.International Journal of Mathematics Education in Science and Technology, 36(2–3), 149–160.

    Article  Google Scholar 

  • Kajander, A., & Lovric, M. (in press). Mathematics textbooks and their potential role in supporting misconceptions.International Journal of Mathematics Education in Science and Technology.

  • Leeman, T. (1972).The rites of passage in a student culture. New York: Teachers College Press, Columbia University.

    Google Scholar 

  • Maddern, E. (1990). What is it that fifteen year olds need? Notes on developing initiations appropriate to our times.Adventure Education, 17(1), 29–32.

    Google Scholar 

  • McInnes, C., James, R., & Hartley, R. (2000).Trends in the first year experience in Australian universities. Canberra: AGDS.

    Google Scholar 

  • Schoenfeld, A. H. (1994). What do we know about mathematics curricula?Journal of Mathematical Behavior, 13(1), 55–80.

    Article  Google Scholar 

  • Tall, D. O. (1991). Reflections. In D. O. Tall (Ed.)Advanced mathematical thinking (pp. 251–259). Holland: Kluwer Academic Publishers.

    Google Scholar 

  • Tall, D. O. (1992). The transition to advanced mathematical thinking: functions, limits, infinity and proof. In D. A. Grouws (Ed.)Handbook of research on mathematics teaching and learning (pp. 495–511). New York: Macmillan.

    Google Scholar 

  • Tall, D. O. (1997). From school to university: The effects of learning styles in the transition from elementary to advanced mathematical thinking. In M. O. J. Thomas (Ed.),Proceedings of The Seventh Annual Australasian Bridging Network Mathematics Conference (pp. 9–26). Auckland: University of Auckland.

    Google Scholar 

  • Tsamir, P. (2007). Should more than one theoretical approach be used for analyzing students’ errors? The case of areas, volumes and integration.For the Learning of Mathematics, 27(2), 28–33.

    Google Scholar 

  • van Gennep, A. (1960).The rites of passage. Chicago: The University of Chicago Press (translation of the 1908 edition).

    Google Scholar 

  • Vosniadou, S., & Verschaffel, L. (2004). Extending the conceptual change approach to mathematics learning and teaching.Learning and Instruction, 14, 445–451.

    Article  Google Scholar 

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

    Google Scholar 

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Clark, M., Lovric, M. Suggestion for a theoretical model for secondary-tertiary transition in mathematics. Math Ed Res J 20, 25–37 (2008). https://doi.org/10.1007/BF03217475

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