Balancing classroom management with mathematical learning: Using practice-based task design in mathematics teacher education
Keywords:prospective teachers, classroom management, mathematical learning, social and sociomathematical norms, teaching triad
In this paper we present the results from a study in which 21 mathematics trainee teachers engage with two practice-based tasks in which classroom management interferes with mathematical learning. We investigate the trainees’ considerations when they make decisions in classroom situations and how these tasks can trigger their reflections on the teaching and learning of mathematics. In our analysis we used the constructs of Social and Sociomathematical norms (Cobb & Yackel, 1996) and Teaching Triad (Jaworski, 1994). Results indicate commendable norms trainees aspire to establish in their classroom, such as peer respect, value of discussion and investigative mathematical learning. However, they often miss the opportunity to engage students with metacognitive discussions and mathematical challenge as they focus on behavioural issues or endorse dichotomous and simplistic views of mathematical learning. We credit these tasks with allowing insight into trainees’ considerations and we propose their further implementation in teacher education programmes.
Biza, I., Joel, G., & Nardi, E. (2015, in press). Transforming trainees’ aspirational thinking into solid practice. Mathematics Teaching, v(i), p-p.
Biza, I., Nardi, E., & Joel, G. (2014). What are prospective teachers’ considerations regarding their intended practice when management interferes with mathematical learning? In Adams, G. (Ed). Proceedings of the British Society for Research into Learning Mathematics, 34(2), 13-18.
Biza, I., Nardi, E., & Zachariades, T. (2007). Using tasks to explore teacher knowledge in situation-specific contexts. Journal of Mathematics Teacher Education, 10, 301-309.
Cobb, P., & Yackel, E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational Psychologist, 31(3/4), 175-190.
Freeman, J. B. (2005). Systematizing Toulmin’s warrants: An epistemic approach. Argumentation, 19(3), 331–346.
Goodell E. J. (2006). Using critical incident reflections: a self-study as a mathematics teacher educator. Journal of Mathematics Teacher Education, 9(3), 221-248.
Hill, H. C., & Ball, D. L. (2004). Learning mathematics for teaching: Results from California's mathematics professional development institutes. Journal for Research in Mathematics Education, 35(5), 330-351.
Jaworski, B. (1994). Investigating Mathematics Teaching: A Constructivist Enquiry. London: Routledge.
Kersting, N. (2008). Using video clips of mathematics classroom instruction as item prompts to measure teachers’ knowledge of teaching mathematics. Educational and Psychological Measurement, 68(5), 845–861.
Leatham, K. R., & Peterson, B. E. (2010a). Purposefully designing student teaching to focus on students’ mathematical thinking. In J. Luebeck, & J. W. Lott (Eds.), AMTE Monograph 7: Mathematics teaching: Putting research into practices at all levels (pp. 225-239). San Diego, CA: Association of Mathematics Teacher Educators.
Leatham, K. R., & Peterson, B. E. (2010b). Secondary mathematics cooperating teachers’ perceptions of the purpose of student teaching. Journal of Mathematics Teacher Education, 13, 99–119.
Levin, D. M., Hammer, D., & Coffey, J. E. (2009). Novice teachers’ attention to student thinking. Journal of Teacher Education, 60(2), 142–154.
Mitchell, N. R., & Marin, K. A. (2014). Examining the use of a structured analysis framework to support prospective teacher noticing. Journal of Mathematics Teacher Education. DOI: 10.1007/s10857-014-9294-3.
Nardi, E., Biza, I., & Zachariades, T. (2012) ‘Warrant’ revisited: Integrating mathematics teachers’ pedagogical and epistemological considerations into Toulmin’s model for argumentation. Educational Studies in Mathematics, 79(2), 157–173.
Potari, D. & Jaworski, B. (2002). Tackling complexity in mathematics teacher development: Using the teaching triad as a tool for reflection and enquiry. Journal of Mathematics Teacher Education, 5, 351-380.
Skemp, R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20–26.
Shulman, L. S. (1987). Knowledge and teaching: Foundations of the New Reform. Harvard Educational Review, 57(1), 1-22.
Thompson, A. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 122–127). New York: Macmillan.
Toulmin, S. (1958). The uses of argument. Cambridge, UK: Cambridge University Press.
Zaslavsky, O. & Leikin, R. (1999). Interweaving the training of mathematics teacher-educators and the professional development of mathematics teachers. In O. Zaslavsky (Ed.). Proceedings of the 23rd Conference of the International Group for the Psychology of Mathematics Education, Vol.1, pp. 143-158. Haifa, Israel: PME.
Zazkis, R., Sinclair, N., & Liljedahl, P. (2013). Lesson play in mathematics education a tool for research and professional development. London: Springer.