The professional development of mathematics teachers needs to support teachers in orchestrating the mathematics classroom in ways that enable them to respond flexibly and productively to the unexpected. When a situation arises in the classroom which is not connected in an obvious way to the mathematical learning intentions of the lesson, it can be challenging for the teacher to improvise so as to craft this situation into an opportunity for doing and learning mathematics. In this study, as teacher-researcher I maintained a record of unexpected situations as they arose in my own secondary mathematics classroom. Details are given of four unexpected situations which I found ways to exploit mathematically, and these are analysed to highlight factors which may enhance a mathematics teacher’s preparedness for dealing with the unexpected. The results of this study indicate that deviating from the intended lesson to exploit an unexpected situation in which students have shown some interest can lead them into enjoyable and worthwhile mathematical engagement.
Armstrong, P. (2003). Teaching as stand-up comedy: The metaphor of scripted and improvised performance of teaching. In I. Davidson, D. Murphy & B. Piette (Eds.) Speaking in tongues: Languages of lifelong learning, Proceedings of the 33rd Annual Conference on University Teaching and Research in the Education of Adults. Bangor: University of Wales Bangor/SCUTREA. Available at www.leeds.ac.uk/educol/documents/00003086.htm.
Atkinson, T. & Claxton, G. (2003). The intuitive practitioner: On the value of not always knowing what one is doing. Maidenhead: The Open University.
Berliner, D. C. (2001). Learning about and learning from expert teachers. International Journal of Educational Research, 35(5), 463–482.
Brookfield, S. D. (2006). The skillful teacher: On technique, trust, and responsiveness in the classroom (2nd ed.). San Francisco: Wiley.
Bryant, J. & Sangwin, C. (2008). How round is your circle?: Where engineering and mathematics meet. Oxford: Princeton University Press.
Chick, H. & Stacey, K. (2013). Teachers of mathematics as problem-solving applied mathematicians. Canadian Journal of Science, Mathematics, and Technology Education, 13(2), 121–136.
Claxton, G. (2003). The anatomy of intuition. In T. Atkinson & G. Claxton (Eds.), The intuitive practitioner: On the value of not always knowing what one is doing (pp. 32–52). Maidenhead: The Open University.
Coker, J. (1964). Improvising jazz. Englewood Cliffs: Prentice-Hall.
Cryer, B. (2009). Butterfly brain. London: Orion Books Ltd.
Csikszentmihalyi, M. (1988). The flow experience and its significance for human psychology. In M. Csikszentmihalyi & I. S. Csikszentmihalyi (Eds.), Optimal experience: Psychological studies of flow in consciousness (pp. 15–35). Cambridge: CUP.
Csikszentmihalyi, M. (2002). Flow: The classic work on how to achieve happiness. London: Rider.
Csikszentmihalyi, M. & Csikszentmihalyi, I. S. (1988). Optimal experience: Psychological studies of flow in consciousness. Cambridge: CUP.
Davis, B. (2009). Inventions of teaching: A genealogy. London: Routledge.
Davis, B. & Simmt, E. (2003). Understanding learning systems: Mathematics education and complexity science. Journal for Research in Mathematics Education, 34(2), 137–167.
Davis, B. & Sumara, D. (2004). Becoming more curious about learning. Journal of Curriculum and Pedagogy, 1(1), 26–30.
Davis, B. & Sumara, D. (2005). Complexity science and educational action research: Toward a pragmatics of transformation. Educational Action Research, 13(3), 453–466.
Davis, B., Sumara, D. & Luce-Kapler, R. (2008). Engaging minds: Changing teaching in complex times (2nd ed.). London: Routledge.
Fernandez, C. (2004). Lesson study: A Japanese approach to improving mathematics teaching and learning. London: Lawrence Erlbaum.
Foster, C. (2007). Mathematical behaviour. Mathematics Teaching, 202, 12–13.
Foster, C. (2013a). Resisting reductionism in mathematics pedagogy. Curriculum Journal, 24(4), 563–585.
Foster, C. (2013b). Mathematical études: Embedding opportunities for developing procedural fluency within rich mathematical contexts. International Journal of Mathematical Education in Science and Technology, 44(5), 765–774.
Geertz, C. (1994). Thick description: Toward an interpretive theory of culture. In M. Martin & L. C. McIntyre (Eds.), Readings in the philosophy of social science (pp. 213–231). London: MIT Press.
George, M. (2012). How mathematics teaching can be like improv theater. MathAMATYC Educator, 3(2), 21–23.
Griffiths, J. (2007). Improvisando. Mathematics Teaching Incorporating Micromath, 205, 31.
Hoftstadter, D. (2007). Thoughts on geometrical thinking. Mathematics in School, 36(4), 27.
LeCompte, M. D., Preissle, J. & Tesch, R. (1993). Ethnography and qualitative design in educational research. San Diego: Academic Press.
Leinhardt, G. (1990). Capturing craft knowledge in teaching. Educational Researcher, 19(2), 18–25.
Mason, J. (2002). Researching your own practice: The discipline of noticing. London: RoutledgeFalmer.
Mason, J. & Davis, B. (2013). The importance of teachers’ mathematical awareness for in-the-moment pedagogy. Canadian Journal of Science, Mathematics, and Technology Education, 13(2), 182–197.
Mason, J. & Spence, M. (1999). Beyond mere knowledge of mathematics: The importance of knowing-to act in the moment. Educational Studies in Mathematics, 38, 135–161.
McMahon, A. (2003). The development of professional intuition. In T. Atkinson & G. Claxton (Eds.), The intuitive practitioner: On the value of not always knowing what one is doing (pp. 137–148). Maidenhead: The Open University.
Middleton, J. A. & Spanias, P. A. (1999). Motivation for achievement in mathematics: Findings, generalizations, and criticisms of the research. Journal for Research in Mathematics Education, 30(1), 65–88.
Pelletier, L. G. & Sharp, E. (2008). Persuasive communication and proenvironmental behaviours: How message tailoring and message framing can improve the integration of behaviours through self-determined motivation. Canadian Psychology, 49(3), 210–217.
Polanyi, M. (2009). The tacit dimension. Chicago: University of Chicago Press.
Remillard, J. T. (1997). Mathematics teaching as improvisation: A problem for policy implementation. Chicago: Paper presented at the annual meeting of the American Educational Research Association.
Rothenberg, J. J. (1994). Memories of schooling. Teaching and Teacher Education, 10(4), 369–379.
Rowland, T. & Zazkis, R. (2013). Contingency in the mathematics classroom: Opportunities taken and opportunities missed. Canadian Journal of Science, Mathematics, and Technology Education, 13(2), 137–153.
Rowland, T., Huckstep, P. & Thwaites, A. (2005). Elementary teachers’ mathematics subject knowledge: The knowledge quartet and the case of Naomi. Journal of Mathematics Teacher Education, 8(3), 255–281.
Sawyer, R. K. (2004). Creative teaching: Collaborative discussion as disciplined improvisation. Educational researcher, 33(2), 12–20.
Sedig, K. (2007). Toward operationalization of ‘flow’ in mathematics learnware. Computers in Human Behavior, 23(4), 2064–2092.
Skovsmose, O. (2011). An invitation to critical mathematics education. Rotterdam: Sense.
Tanner, H., Jones, S., Beauchamp, G. & Kennewell, S. (2010). Interactive whiteboards and all that jazz: Analysing classroom activity with interactive technologies. In L. Sparrow, B. Kissane & C. Hurst (Eds.), Shaping the future of mathematics education. Proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia, Freemantle (Vol. 2, pp. 547–554). Adelaide: MERGA.
Towers, J. & Davis, B. (2002). Structuring occasions. Educational Studies in Mathematics, 49(3), 313–340.
von Glasersfeld, E. (1995). Radical constructivism: A way of learning (studies in mathematics education). London: RoutledgeFalmer.
Walls, R. T., Sperling, R. A. & Weber, K. D. (2001). Autobiographical memory of school. The Journal of Educational Research, 95(2), 116–127.
Ward-Penny, R. (2010). Context or con? How might we better represent the “real-world” in the classroom? Mathematics in School, 39(1), 10–12.
Williams, G. (2002). Associations between mathematically insightful collaborative behaviour and positive affect. In A. Cockburn & E. Nardi (Eds.), Proceedings of the 26th conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 402–409). Norwich: PME.
Zodik, I. & Zaslavsky, O. (2008). Characteristics of teachers’ choice of examples in and for the mathematics classroom. Educational Studies in Mathematics, 69(2), 165–182.
About this article
Cite this article
Foster, C. EXPLOITING UNEXPECTED SITUATIONS IN THE MATHEMATICS CLASSROOM. Int J of Sci and Math Educ 13, 1065–1088 (2015). https://doi.org/10.1007/s10763-014-9515-3
- discipline of noticing
- mathematics teaching
- researching own practice
- unexpected situations