Characterising undergraduate mathematics teaching across settings and countries: an analytical framework

Authors

Angeliki Mali
Georgia Petropoulou

Abstract

This paper explores the characteristics of teaching of a sample of university mathematics teachers in two countries, Greece and Great Britain, and in two settings, lectures and tutorials, seeking to identify a common ground for undergraduate mathematics teaching. Our observations of teaching and our sociocultural perspectives enabled us to develop a framework for a detailed description of the observed teaching. The description reveals categories of teaching actions, and the associated tools teachers use in selecting tasks for their students, providing comprehensive explanations, extending students’ mathematical thinking, or evaluating students’ mathematical meaning. The findings are across settings and countries in the direction of a profound understanding of undergraduate mathematics teaching.

References

Anghileri, J. (2006). Scaffolding practices that enhance mathematics learning. Journal of Mathematics Teacher Education, 9, 33-52. https://doi.org/10.1007/s10857-006-9005-9

Baxter, A. J. & Williams, S. (2010). Social and analytic scaffolding in middle school mathematics: managing the dilemma of telling. Journal of Mathematics Teacher Education, 13, 7-26. https://doi.org/10.1007/s10857-009-9121-4

Ben-Zvi, D. & Arcavi, A. (2001). Junior high school students' construction of global views of data and data representations. Educational Studies in Mathematics, 45, 35-65. https://doi.org/10.1023/A:1013809201228

Biza, I., Giraldo, V., Hochmuth, R., Khakbaz, A. & Rasmussen, C. (2016). Research on teaching and learning mathematics at the tertiary level: state-of-the-art and looking ahead. Berlin: Springer. https://doi.org/10.1007/978-3-319-41814-8

Castela, C. (2004). Institutions influencing mathematics students' private work: a factor of academic achievement. Educational Studies in Mathematics, 57, 33-63. https://doi.org/10.1023/B:EDUC.0000047050.70008.59

Chazan, D. & Ball, D. (1999). Beyond being told not to tell. For the Learning of Mathematics, 19 (2), 2-10.

Cole, M. & Gajdamaschko, N. (2007). Vygotsky and culture. In H. Daniels, M. https://doi.org/10.1017/CCOL0521831040.009

Cole & J. V. Wertsch (Eds.), The Cambridge companion to Vygotsky, (pp. 193- 211). New York: Cambridge University Press.

Conner, A. M., Singletary, L., Smith, R., Wagner, P. A. & Francisco, R. (2014). Teacher support for collective argumentation: A framework for examining how teachers support students' engagement in mathematical activities. Educational Studies in Mathematics, 86, 401-429. https://doi.org/10.1007/s10649-014-9532-8

Drageset, O. G. (2014). Redirecting, progressing, and focusing actions - a framework for describing how teachers use students' comments to work with mathematics. Educational Studies in Mathematics, 85, 281-304. https://doi.org/10.1007/s10649-013-9515-1

Dunne, C. (2011). The place of the literature review in grounded theory research. International Journal of Social Research Methodology, 14 (2), 111-124. https://doi.org/10.1080/13645579.2010.494930

Fraivillig, J. L., Murphy, L. A. & Fuson, K. C. (1999). Advancing children's mathematical thinking in everyday mathematics classrooms. Journal for Research in Mathematics Education, 30 (2), 148-170. https://doi.org/10.2307/749608

Fukawa-Connelly, P. T. (2012). A case study of one instructor's lecture-based teaching of proof in abstract algebra: Making sense of her pedagogical moves. Educational Studies in Mathematics, 81, 325-345. https://doi.org/10.1007/s10649-012-9407-9

Cengiz, N., Kline, K. & Grant, T. J. (2011). Extending students' mathematical thinking during whole-group discussions. Journal of Mathematics Teacher Education, 14, 355-374. https://doi.org/10.1007/s10857-011-9179-7

Cranach, M. von & Valach, L. (1984). The social dimension of goal-directed action. In T. Tajfel (Ed.), The social dimension: European developments in social psychology, 1, (pp. 285-299). Cambridge: Cambridge University Press.

Giannakoulias, E., Mastorides, E., Potari, D. & Zachariades T. (2010). Studying teachers' mathematical argumentation in the context of refuting students' invalid claims. Journal of Mathematical Behavior, 29 (3), 160-168. https://doi.org/10.1016/j.jmathb.2010.07.001

Glaser, B. (1978). Theoretical sensitivity. Mill Valley: The Sociology Press.

Glaser, B. G. & Strauss A. L. (1967). The discovery of grounded theory. Piscataway: Aldine Transactions.

Grandi, C. & Rowland, T. (2013). Developing one-to-one teacher-student interaction in post-16 mathematics instruction. In A. M. Lindmeier & A. Heinze (Eds.), Proceedings of the 37th conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 385-392). Kiel: PME.

Jaworski, B. (2003). Sensitivity and challenge in university mathematics teaching. Educational Studies in Mathematics, 51, 71-94. https://doi.org/10.1023/A:1022491404298

Jaworski, B. & Didis, M. G. (2014). Relating student meaning-making in mathematics to the aims for and design of teaching in small group tutorials at university level. In P. Liljedahl, S. Oesterle, C. Nicol & D. Allan (Eds.), Proceedings of the 38th conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 377-384). Vancouver: PME.

Jaworski, B., Mali, A. & Petropoulou, G. (2016). Critical theorising from studies of undergraduate mathematics teaching for students' meaning making in mathematics. International Journal of Research in Undergraduate Mathematics Education, 3, 168-197. https://doi.org/10.1007/s40753-016-0044-z

Jaworski, B. & Potari, D. (2009). Bridging the macro-micro divide: using an activity theory model to capture complexity in mathematics teaching and its development. Educational Studies in Mathematics, 72, 219-236. https://doi.org/10.1007/s10649-009-9190-4

Larsson, M. (2015). Exploring a framework for classroom culture: a case study of the interaction patterns of mathematical whole-class discussions. In K. Krainer & N. Vondrová (Eds.), Proceedings of the 9th congress of the European Society for Research in Mathematics Education (pp. 3065-3071). Prague: ERME.

Leont'ev, A. N. (1979). The problem of activity in psychology. In J. V. Wertsch (Ed.), The concept of activity in Soviet psychology (pp. 37-71). New York: M. E. Sharpe.

Lobato, J., Clarke, D. & Ellis, A. B. (2005). Initiating and eliciting in teaching: a reformulation of telling. Journal for Research in Mathematics Education, 36 (2), 101-136.

Mali, A. (2015). Characterising university mathematics teaching. In K. Krainer & N. Vondrová (Eds.), Proceedings of the 9th congress of the European Society for Research in Mathematics Education (pp. 2187-2193). Prague: ERME.

Mali, A., Biza, I. & Jaworski, B. (2014). Characteristics of university mathematics teaching: use of generic examples in tutoring. In P. Liljedahl, S. Oesterle, C. Nicol & D. Allan (Eds.), Proceedings of the 38th conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 161-168). Vancouver: PME.

Morgan, C. (2014). Understanding practices in mathematics education: structure and text. Educational Studies in Mathematics, 87, 129-143. https://doi.org/10.1007/s10649-013-9482-6

Nardi, E. (1996). The novice mathematician's encounter with mathematical abstraction: tensions in concept-image construction and formalisation. (Doctoral dissertation). Oxford University.

Olson, J. C. & Knott, L. (2013). When a problem is more than a teacher's question. Educational Studies in Mathematics, 83, 27-36. https://doi.org/10.1007/s10649-012-9444-4

Petropoulou, G., Jaworski, B., Potari, D. & Zachariades, T. (2015). How do research mathematicians teach Calculus? In K. Krainer & N. Vondrová (Eds.), Proceedings of the 9th congress of the European Society for Research in Mathematics Education (pp. 2221-2227). Prague: ERME.

Petropoulou, G., Potari, D. & Zachariades, T. (2011). Inquiring mathematics teaching at the university level. In B. Ubuz (Ed.), Proceedings of the 35th conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 385-392). Ankara: PME.

Polya, G. (1971). How to solve it: a new aspect of mathematical method (2nd Ed.). Princeton University Press.

Ponte, J. P. & Quaresma, M. (2015). Conducting mathematical discussions as a feature of teachers' professional practice. In K. Krainer & N. Vondrová (Eds.), Proceedings of the 9th congress of the European Society for Research in Mathematics Education (pp. 3100-3106). Prague: ERME.

Pring, R. (2000). Philosophy of educational research. London: Continuum. https://doi.org/10.1111/1467-8527.t01-1-00129

Pritchard, D. (2010). Where learning starts? A framework for thinking about lectures in university mathematics. International Journal of Mathematical Education in Science and Technology, 41 (5), 609-623. https://doi.org/10.1080/00207391003605254

Sierpinska, A., Bobos, G. & Pruncut, A. (2011). Teaching absolute value in-equalities to mature students. Educational Studies in Mathematics, 78, 275-305. https://doi.org/10.1007/s10649-011-9325-2

Speer, N. M., Smith, J. P. & Horvath, A. (2010). Collegiate mathematics teaching: an unexamined practice. The Journal of Mathematical Behavior, 29 (2), 99-114. https://doi.org/10.1016/j.jmathb.2010.02.001

Treffert-Thomas, S. (2015). Conceptualising a university teaching practice in an activity theory perspective. Nordic Studies in Mathematics Education, 20 (2), 53-78.

Treffert-Thomas, S. & Jaworski, B. (2015). Developing mathematics teaching: What can we learn from the literature? In M. Grove, T. Croft, J. Kyle & D. Lawson (Eds.), Transitions in undergraduate mathematics (pp. 259-276). Higher Education Academy, University of Birmingham.

Viirman, O. (2014). The function concept and university mathematics teaching (Doctoral dissertation). Karlstad: Karlstad University.

Viirman, O. (2015). Explanation, motivation and question posing routines in university mathematics teachers' pedagogical discourse: a commognitive analysis. International Journal of Mathematical Education in Science and Technology, 46 (8), 1165-1181. https://doi.org/10.1080/0020739X.2015.1034206

Vygotsky, L. (1978). Mind in society: the development of higher psychological processes. Cambridge: Harvard University Press.

Weber, K. (2004). Traditional instruction in advanced mathematics courses: a case study of one professor's lectures and proofs in an introductory real analysis course. Journal of Mathematical Behavior, 23 (2), 115-133. https://doi.org/10.1016/j.jmathb.2004.03.001

Wellington, J. (2000). Educational research: contemporary issues and practical approaches. London: Continuum.

Weinberg, A., Wiesner, E. & Fukawa-Connelly, T. (2016). Mathematics lectures as narratives: insights from network graph methodology. Educational Studies in Mathematics, 91, 203-226. https://doi.org/10.1007/s10649-015-9663-6

Winsløw, C., Barquero, B., Vleeschouwer, M. de & Hardy, N. (2014). An institutional approach to university mathematics education: from dual vector spaces to questioning the world. Research in Mathematics Education, 16 (2), 95-111. https://doi.org/10.1080/14794802.2014.918345

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Published

2024-11-19

How to Cite

Mali, A., & Petropoulou, G. (2024). Characterising undergraduate mathematics teaching across settings and countries: an analytical framework. NOMAD Nordic Studies in Mathematics Education, 22(4), 23–42. Retrieved from https://tidsskrift.dk/NOMAD/article/view/148915