Abstract
In this chapter we draw on our research with mathematics students and recent graduates to investigate the tertiary mathematics curriculum. We present an argument for a particular vision of such a curriculum, which we refer to as a ‘broad’ as opposed to a ‘narrow’ curriculum. A narrow curriculum looks inwards and focuses primarily on the mathematics itself – the mathematical techniques that will be used by students of mathematics in specific situation. Traditional courses in mathematics have relied on such a curriculum for a long time. A broad curriculum looks outwards and focuses on the uses of mathematics as a way of investigating, understanding, and even changing the world. Such a curriculum positions students as citizens of the world first, future professionals in a variety of areas second, and mathematicians or users of mathematics third. Fewer mathematics courses are built on such an approach. Our arguments are based firmly on our students’ and recent graduates’ voices, as shown in transcripts of research interviews, and are consistent with ideas advocated by mathematics educators, in groups such as critical mathematics education and calculus reform, and with more general views of curriculum. Research into graduates’ early professional experiences and their views of their previous mathematics education reinforces these ideas and grounds them in the reality of the professional workplace. Such research indicates that a curriculum acknowledging and incorporating students’ and graduates’ ideas can assist in increasing their effectiveness as future professionals – as mathematicians or expert users of mathematics. Further, a curriculum that incorporates such views can include important aspects of professional formation such as communication and interpersonal skills, appreciation of a creative approach to problems, awareness of issues of sustainability and ethical considerations.
Note: Some of the material in this chapter was previously published in
Petocz, P., & Reid, A. (2005). Re-thinking the tertiary mathematics curriculum. Cambridge Journal of Education, 35(1), 89–106.
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References
American Statistical Association. (2010). Guidelines for assessment and instruction in statistics education: College report. Alexandria: American Statistical Association. Available online at http://www.amstat.org/education/gaise/
Artigue, M. (2010). The future of teaching and learning mathematics with digital technologies. In C. Hoyles & J. B. Lagrange (Eds.), Mathematics education and technology – Rethinking the terrain: The 17th ICMI study (pp. 463–475). New York: Springer.
Barton, B. (2008). The language of mathematics: Telling mathematical tales. New York: Springer.
Barton, B., Oliveras, M., Hollenstein, A., Emori, H., & Nakahara, T. (2004). WGA9: Communication and language in mathematics education. In H. Fujita, Y. Hashimoto, B. Hodgson, P. Y. Lee, S. Lerman, & T. Sawada (Eds.), Proceedings of the Ninth International Congress on Mathematical Education (pp. 264–269). Dordrecht: Kluwer.
Bowden, J., & Marton, F. (1998). The university of learning: Beyond quality and competence in higher education. London: Kogan Page.
Burton, L. (2004). Mathematicians as enquirers – Learning about learning mathematics. Dordrecht: Kluwer.
Burton, L., & Haines, C. (1997). Innovation in teaching and assessing mathematics at university level. Teaching in Higher Education, 2(3), 272–293.
Cater-Steel, A., & Cater, E. (2010). Women in engineering, science and technology: Education and career challenges. Hershey: IGI Global.
D’Ambrosio, U. (1985). Ethnomathematics and its place in the history and pedagogy of mathematics. For the Learning of Mathematics, 5(1), 44–48.
D’Ambrosio, U. (1998). Mathematics and peace: Our responsibilities. Zentralblatt für Didaktik der Mathematik, 30(3), 67–73. Online at http://www.emis.de/journals/ZDM/zdm983a2.pdf
D’Souza, S., & Wood, L. N. (2003). Rationale for establishing collaborative learning methods in first year mathematics learning. New Zealand Journal of Mathematics, 32(Suppl.), 47–56.
de la Harpe, B., & Radloff, A. (2000). Helping academic staff to integrate professional skills. In S. Fallows & C. Steven (Eds.), Integrating key skills in higher education: Employability, transferable skills and learning for life (pp. 165–174). London: Kogan Page.
Fallows, S., & Steven, C. (2000). Integrating key skills in higher education: Employability, transferable skills and learning for life. London: Page.
Gable, S. (2002). Some conceptual problems with critical pedagogy. Curriculum Inquiry, 32(2), 177–201.
Ganter, S., & Barker, W. (2004). The curriculum foundations project: Chapter 1, A collective vision. Washington, DC: Mathematical Association of America. Available online at www.maa.org/cupm/crafty/cf_project.html
Garfield, J., Hogg, R., Schau, C., & Whittinghill, D. (2002) First courses in statistical science: The status of educational reform efforts. Journal of Statistics Education, 10(2). Online at http://www.amstat.org/publications/jse/v10n2/garfield.html
Hanna, G. (Ed.). (2002). Towards gender equity in mathematics education: An ICMI study (pp. 9–26). Dordrecht: Kluwer.
Hoyles, C., & Lagrange, J. B. (2010). Mathematics education and technology – Rethinking the terrain: The 17th ICMI study. New York: Springer.
Keitel, C., & Vithal, R. (2008). Mathematical power as political power – the politics of mathematics education. In P. Clarkson and N. Presmeg (Eds.), Critical Issues in Mathematics Education, Springer, New York, 167–188.
Lesser, L. (2007) Critical values and transforming data: Teaching statistics with social justice. Journal of Statistics Education, 15(1). Online at http://www.amstat.org/publications/JSE/v15n1/lesser.pdf
Maindonald, J., & Richardson, A. (2004) This passionate study – A dialogue with Florence Nightingale. Journal of Statistics Education, 12(1). Online at http://www.amstat.org/publications/jse/v12n1/maindonald.html
Mathematical Association of America. (2004). Undergraduate programs and courses in the mathematical sciences: CUPM curriculum guide 2004. Washington, DC: Mathematical Association of America. Online at www.maa.org/cupm
Petocz, P., & Reid, A. (2003). What on earth is sustainability in mathematics? New Zealand Journal of Mathematics, 32(Suppl. Issue), 135–144.
Petocz, P., & Reid, A. (2008). Evaluating the internationalised curriculum. In M. Hellstén & A. Reid (Eds.), Researching international pedagogies: Sustainable practice for teaching and learning in higher education (pp. 27–43). Dordrecht: Springer.
Petocz, P., Reid, A., & Taylor, P. (2009). Thinking outside the square: Business students’ conceptions of creativity. Creativity Research Journal, 21(4), 1–8.
Prvan, T., Reid, A., & Petocz, P. (2002). Statistical laboratories using Minitab, SPSS and Excel: A practical comparison. Teaching Statistics, 24(2), 68–75.
Reid, A. (2000). Self and peer assessment in a course on instrumental pedagogy. In D. Hunter & M. Russ (Eds.), Peer learning in music (pp. 56–62). Belfast: University of Ulster.
Reid, A., & Petocz, P. (2002). Students’ conceptions of statistics: A phenomenographic study. Journal of Statistics Education, 10(2). Online at http://www.amstat.org/publications/jse/v10n2/reid.html
Reid, A., & Petocz, P. (2004). Learning domains and the process of creativity. Australian Educational Researcher, 31(2), 45–62. Online at www.aare.edu.au/aer/online/40020d.pdf
Reid, A., & Petocz, P. (2006). University lecturers’ understanding of sustainability. Higher Education, 51(1), 105–123.
Reid, A., Petocz, P., & Taylor, P. (2009). Business students’ conceptions of sustainability. Sustainability, 1(3), 662–673. Online at http://www.mdpi.com/2071-1050/1/3/662
Reid, A., Abrandt Dahlgren, M., Petocz, P., & Dahlgren, L. O. (2011). From expert student to novice professional. Dordrecht: Springer.
Skovsmose, O. (1994). Towards a critical mathematics education. Educational Studies in Mathematics, 27(1), 35–57.
Skovsmose, O. (2009). Towards a critical professionalism in university science and mathematics education. In O. Skovsmose, P. Valero, & O. Christensen (Eds.), University science and mathematics education in transition (pp. 325–346). New York: Springer.
Thomas, M., & Holton, D. (2003). Technology as a tool for teaching undergraduate mathematics. In A. Bishop, M. Clements, C. Keitel, J. Kilpatrick, & F. Leung (Eds.), Second international handbook in mathematics education (pp. 351–394). Dordrecht: Kluwer.
Toohey, S. (1999). Designing courses for higher education. Buckingham: Open University Press.
UNESCO. (2011). Education for sustainable development website. Paris: UNESCO. Online at http://www.unesco.org/new/en/education/themes/leading-the-international-agenda/education-for-sustainable-development/
Watts, C. (2000). Issues of professionalism in higher education. In T. Bourner, T. Katz, & D. Watson (Eds.), New directions in professional higher education (pp. 11–18). Buckingham: SRHE/Open University Press.
Wood, L. N., & Perrett, G. (1997). Advanced mathematical discourse. Sydney: University of Technology.
Wood, L. N., & Petocz, P. (2003). Reading statistics. Sydney: University of Technology.
Wood, L. N., Petocz, P., & Smith, G. H. (2000) Terror, tragedy and vibrations – Using mathematical models in engineering. Video (26 mins), booklet of exercises. Sydney: University of Technology.
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Wood, L.N., Petocz, P., Reid, A. (2012). What University Curriculum Best Helps Students to Become Mathematicians?. In: Becoming a Mathematician. Mathematics Education Library, vol 56. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2984-1_8
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