# Undergraduate Students’ Conceptions of Mathematics: An International Study

## Abstract

In this paper, we report on an international study of undergraduate mathematics students’ conceptions of mathematics. Almost 1,200 students in five countries completed a short survey including three open-ended questions asking about their views of mathematics and its role in their future studies and planned professions. Responses were analysed starting from a previously-developed phenomenographic framework (Reid et al., 2003) which required only minor modification. Students’ conceptions of mathematics ranged from the narrowest view as a focus on calculations with numbers, through a notion of mathematics as a focus on models or abstract structures, to the broadest view of mathematics as an approach to life and a way of thinking. Broader conceptions of mathematics were more likely to be found in later-year students (*p*<0.001) and there were significant differences between universities (*p*<0.001). The information obtained from the study not only confirms previous research, but also provides a basis for future development of a monitoring questionnaire.

## Key words

conceptions of mathematics mathematics in careers mathematics in tertiary study## Preview

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## References

- Agresti, A. (1996).
*An introduction to categorical data analysis*. New York: Wiley.Google Scholar - Bowden, J. & Green, P. (Eds.) (2005).
*Doing Developmental Phenomenography*. Melbourne: RMIT University Press.Google Scholar - Breiman, L., Friedman, J., Olshen, R. & Stone, C. (1984).
*Classification and regression trees*. Belmont CA: Wadsworth.Google Scholar - Burton, L. (2004).
*Mathematicians as enquirers – Learning about learning mathematics*. Dordrecht, The Netherlands: Kluwer.Google Scholar - Crawford, K., Gordon, S., Nicholas, J. & Prosser, M. (1994). Conceptions of mathematics and how it is learned: The perspectives of students entering university.
*Learning and Instruction, 4*, 331–345.CrossRefGoogle Scholar - Coutis, P. & Wood, L.N. (2002). Teaching statistics and academic language in culturally diverse classrooms. In M. Boezi (Ed.),
*2nd International Conference on the Teaching of Mathematics*. Crete, July. John Wiley and Sons.Google Scholar - Criner, O.H. (2003).
*Technological labor shortage requires re-engineering educational systems*. Online at http:www.nbufront.org/html/FRONTalView/ArticlesPapers/TechLaborShortage.html [accessed 25/8/2006]. - Dahlgren, L.O., Abrandt Dahlgren, M., Hult, H., Hård af Segerstad, H., Johansson, K., Handal, G., Karseth, B., Hofgaard Lycke, K., Dyrdal Solbrekke, T., Bayer, M., Labadibi, T., Krumpholz, P., Szkudlarek, T., Cackowska, M., Kopciewicz, L., Mendel, M., Meczkowska, A. & Struzynska, A. (2005).
*Students as journeymen between communities of higher education and work*. Final Report, The European Commission Fifth Framework Programme. Online at http://www.hewl.net/HPSE_CT-2001-0068__final_ju.pdf [accessed 25/8/2006]. - Engelbrecht, J. & Harding, A. (2003). Is mathematics running out of numbers?
*South African Journal of Science, 99*(1/2), 17–20.Google Scholar - Gardiner, T. (2003).
*Maths has to be hard to be interesting*. Online at http://www.arts.telegraph.co.uk/education/main.jhtml?xml=/education/2003/09/10/tefmath10.xml [accessed 25/8/2006]. - Grigutsch, S. & Törner, G. (1998).
*World views of mathematics held by university teachers of mathematics science*. Schriftenreihe des Fachbereichs Matematik, Preprint 420, Gerhard Mercator University, Duisburg. Online at http://www.ub.uni-duisburg.de/ETD-db/theses/available/duett-05272002-102811/unrestricted/mathe121998.pdf [accessed 25/6/2006]. - Hersh, R. (1997).
*What is mathematics, really?*Oxford: Oxford University Press.Google Scholar - Hillel, J. (2001). Trends in curriculum: a working group report. In D. Holton (Ed.),
*The teaching and learning of mathematics at university level: An ICMI study*(pp. 59–70). Dordrecht, The Netherlands: Kluwer.Google Scholar - Houston, K. (1997). M’s and R’s in post-16 mathematics.
*Teaching Mathematics and its Application, 16*, 192–195.CrossRefGoogle Scholar - Houston, K. (2001). Teaching modelling as a way of life.
*Quaestiones Mathematicae*, Supplement 1, 105–113.Google Scholar - Jackson, A. (2000). Declining student numbers worry German mathematics departments
*. Notices of the American Mathematical Society, 47*(3), 364–368.Google Scholar - Kent, P. & Noss, R. (2003).
*Mathematics in the university education of engineers*. Ove Arup Foundation Report, Ove Arup Foundation, London. Online at http://k1.ioe.ac.uk/rnoss/REMIT/Kent-Noss-report.pdf [accessed 25/8/2006]. - Krantz, S. (1999).
*How to teach mathematics*(2nd edition). Providence, Rhode Island: American Mathematical Society.Google Scholar - Leitze, A.R. (1996). To major or not major in mathematics? Affective factors in the choice-of-major decision.
*CBMS Issues in Mathematics Education, 6*, 83–99.Google Scholar - Marton, F. & Booth, S. (1997).
*Learning and awareness*. New Jersey: Lawrence Erlbaum.Google Scholar - Mura, R. (1993). Images of mathematics held by university teachers of mathematical sciences.
*Educational Studies in Mathematics, 25*, 375–385.CrossRefGoogle Scholar - Mura, R. (1995). Images of mathematics held by university teachers of mathematics education.
*Educational Studies in Mathematics, 28*, 385–399.CrossRefGoogle Scholar - Perrett, G., Wood, L.N. & Smith, G.H. (2002) Advanced mathematical discourse: A case study.
*Literacy and Numeracy Studies, 12*(1), 63–76.Google Scholar - Petocz, P., Griffiths, D. & Wright, P. (1996).
*Statistics for quality – Using statistics in Australian industry*. Multimedia Package, Summer Hill Films, University of Technology, Sydney and University of Wollongong.Google Scholar - Petocz, P. & Reid, A. (2003). Relationships between students’ experience of learning statistics and teaching statistics.
*Statistics Education Research Journal*, 2(1), 39–53. Online at http://www.stat.auckland.ac.nz/~iase/serj/SERJ2(1).pdf [accessed 25/8/2006]. - Ponte, J.P., Matos, J.F., Guimarães, H., Canavarro, P. & Leal, L.C. (1994). Teachers’ and students’ views and attitudes towards a new mathematics curriculum.
*Educational Studies in Mathematics, 26*(4), 347–365.CrossRefGoogle Scholar - Reid, A. & Petocz, P. (2002a). Students’ conceptions of statistics: A phenomenographic study.
*Journal of Statistics Education*, 10(2). Online at http://www.amstat.org/publications/jse/v10n2/reid.html [accessed 25/8/2006]. - Reid, A. & Petocz, P. (2002b). Learning about statistics and statistics learning.
*Australian Association for Research in Education*2002*Conference Papers*. Compiled by Jeffery, P. L., AARE, Melbourne. Online at http://www.aare.edu.au/02pap/rei02280.htm [accessed 25/8/2006]. - Reid, A. & Petocz, P. (2003). Completing the circle: Researchers of practice in statistics education.
*Mathematics Education Research Journal, 15*(3), 288–300.Google Scholar - Reid, A., Petocz, P, Smith, G. Wood, L. & Dortins, E. (2003). Mathematics students’ conceptions of mathematics.
*New Zealand Journal of Mathematics, 32*(Supplement), 163–172.Google Scholar - Reid, A., Wood, L., Smith, G. & Petocz, P. (2005). Intention, approach and outcome: University mathematics students’ conceptions of learning mathematics.
*International Journal of Science and Mathematics Education, 3*(4), 567–586.CrossRefGoogle Scholar - Salford Systems (2006). CART version 6. Online at http://www.salford-systems.com [accessed 25/8/2006].
- Smith, G.H. & Wood, L.N. (2000). Assessment of learning in university mathematics.
*International Journal of Mathematical Education in Science and Technology, 31*, 125–132.CrossRefGoogle Scholar - Wood, L.N. & Petocz, P. (1999). Video in mathematics learning at the secondary-tertiary interface. In W. Spunde, S. Cretchley and R. Hubbard, (Eds.),
*The challenge of diversity: Proceedings of the Δ’99 Symposium on Undergraduate Mathematics*, Rockhampton, Queensland. Online at http://www.sci.usq.edu.au/staff/spunde/delta99/Papers/wood_p.pdf [accessed 25/8/2006]. - Wood, L.N. & Petocz, P. (2003).
*Reading statistics*. Sydney: University of Technology.Google Scholar - Wood, L.N., Petocz, P. & Smith, G.H. (2000).
*Terror, tragedy and vibration – Using mathematical models in engineering*. Sydney: Multimedia package, UTS.Google Scholar - Wood, L.N., Smith, G.H., Mather, G., Harding, A., Engelbrecht, J., Houston, K., Perrett, G., Hillel, J., Petocz, P. & Reid, A. (2006,
*in press*). Student voices: Implications for teaching mathematics.*Proceedings of the**3rd**International Conference on the Teaching of Mathematics at the Undergraduate Level*, Istanbul, Turkey. Online at http://www.tmd.org.tr/ictm3/ [accessed 25/8/2006].