A spectrum of possibilities: levels of improvisational behaviour in middle school mathematics

References

• Askew, M. (2011). Unscripted maths: Emergence and improvisation. In J. Clark, B. Kissane, J. Mousely, T. Spencer, & S. Thornton (Eds.), Mathematics traditions and [new] practices: Proceedings of the 34th annual conference of the mathematics education research group of australasia (MERGA) (pp. 59–67). Adelaide: MERGA.
   Google Scholar
• Barber, K. (1998). The Canadian Oxford dictionary. Toronto, ON: Oxford University Press.
   Google Scholar
• Barrett, F. J. (2002). Creativity and improvisation in jazz and organizations. Implications for organizational learning. In K. N. Kamoche, M. P. E. Cunha, & J. V. D. Cunha (Eds.), Organizational improvisation (pp. 135–162). London: Routledge.
   Google Scholar
• Bateson, M. C. (2001). Composing a life. New York, NY: Grove Press.
   Google Scholar
• Becker, H. S. (2000). The etiquette of improvisation. Mind, Culture and Activity, 7(3), 171–176.
   Google Scholar
• Berliner, P. (1994). Thinking in jazz. Chicago: University of Chicago Press.
   Google Scholar
• Borko, H., & Livingston, C. (1989). Cognition and improvisation: Differences in mathematical instruction by expert and novice teachers. American Educational Research Journal, 26(4), 473–498.
   Web of Science ®Google Scholar
• Campbell, D. T. (1974). “Downward causation” in hierarchically organized biological systems. In F. J. Ayala, & T. Dobzhansky (Eds.), Studies in the philosophy of biology: Reduction and related problems (pp. 179–186). Berkeley: University of California Press.
   Google Scholar
• Cobb, P., Yackel, E., & Wood, T. (1992). Interaction and learning in mathematics classroom situations. Educational Studies in Mathematics, 23(1), 99–122.
   Google Scholar
• Cook, S. D. N., & Brown, J. S. (1999). Bridging epistemologies: The generative dance between organizational knowledge and organizational knowing. Organization Science, 10(4), 381–400.
   Web of Science ®Google Scholar
• Engeström, Y. (1994). Teachers as collaborative thinkers: Activity-theoretical study of an innovative teacher team. In I. Cargren, G. Handal, & S. Vaage (Eds.), Teachers’ minds and actions: Research on teachers’ thinking and practice (pp. 43–61). London: Farmer.
   Google Scholar
• Francisco, J. M. (2013). Learning in collaborative settings: Students building on each other's ideas to promote their mathematical understand. Educational Studies in Mathematics, 82, 417–438.
   Web of Science ®Google Scholar
• Franke, M. L., Kazemi, E., & Bailey, D. (2007). Understanding teaching and classroom practice in mathematics. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 225–256). Reston, VA: NCTM.
   Google Scholar
• Gerofsky, S. (2004). A man left Albuquerque heading east: Word problems as genre in mathematics education. New York, NY: Peter Lang.
   Google Scholar
• Glaser, B. G., & Strauss, A. L. (1967). The discovery of grounded theory: Strategies for qualitative research (1st ed.). London: Aldine.
   Google Scholar
• Hargreaves, D. J., Cork, A. C., & Setton, T. (1991). Cognitive strategies in jazz improvisation: An exploratory study. Canadian Journal of Research in Music Education, 33, 47–54.
   Google Scholar
• Hewitt, D. (1996). Mathematical fluency: The nature of practice and the role of subordination. For the Learning of Mathematics, 16(2), 28–35.
   Google Scholar
• Hiebert, J. (1990). The role of routine procedures in the development of mathematical competence. In T. J. Cooney (Ed.), Teaching and learning mathematics in the 1990s: 1990 NCTM yearbook (pp. 31–40). Reston, VA: National Council of Teachers of Mathematics.
   Google Scholar
• Humphreys, M., & Hyland, T. (2002). Theory, practice and performance in teaching: Professionalism, intuition and jazz. Educational Studies, 28(1), 5–15.
   Web of Science ®Google Scholar
• King, K. D. (2001). Conceptually-orientated mathematics teacher development: Improvisation as a metaphor. For the Learning of Mathematics, 21(3), 9–15.
   Google Scholar
• Maheux, J.-F., & Lajoie, C. (2010). On improvisation in teaching and teacher education. Complicity: An International Journal of Complexity and Education, 8(2), 86–92.
   Google Scholar
• Mark, J., Cuoco, A., Goldenberg, E. P., & Sword, S. (2010). Contemporary curriculum issues: Developing mathematical habits of mind. Mathematics Teaching in the Middle School, 15(9), 505–509.
   Google Scholar
• Martin, L., Towers, J., & Pirie, S. (2006). Collective mathematical understanding as improvisation. Mathematical Thinking and Learning, 8(2), 149–183.
   Google Scholar
• Martin, L. C., & Towers, J. (2009). Improvisational coactions and the growth of collective mathematical understanding. Research in Mathematics Education, 11(1), 1–19.
   Google Scholar
• National Research Council. (2001). Adding it up: Helping children learn mathematics. J. Kilpatrick, J. Swafford, & B. Findell (Eds.). Washington, DC: National Academy Press.
   Google Scholar
• Neyland, J. (2004). Playing outside: An introduction to the jazz metaphor in mathematics education. Australian Senior Mathematics Journal, 18(2), 8–16.
   Google Scholar
• Pirie, S. E. B. (1996). Classroom video-recording: When, why and how does it offer a valuable data sourse for qualitative research? (Report No. SE-059-195). Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education.
   Google Scholar
• Powell, A. B., Francisco, J. M., & Maher, C. A. (2003). An analytical model for studying the development of learners’ mathematical ideas and reasoning using videotape data. The Journal of Mathematical Behavior, 22, 405–435.
   Google Scholar
• Remillard, J. T. (1999). Curriculum materials in mathematics education reform: A framework for examining teachers’ curriculum development. Curriculum Inquiry, 29, 315–342.
   Web of Science ®Google Scholar
• Romberg, T. A. (1992). Perspectives on scholarship and research methods. In D. A. Grouws (Ed.), Handbook of research on teaching and learning (pp. 49–64). Old Tappan, NJ: Macmillan.
   Google Scholar
• Ryle, G. (1979). On thinking. Totowa, NJ: Rowman and Littlefield.
   Google Scholar
• Sassi, A. M., & Goldsmith, L. T. (1995). Beyond recipes and behind the magic: Mathematics teaching as improvisation. Paper presented at the North American Chapter of the International Group for the Psychology of Mathematics education, Columbus, OH.
   Google Scholar
• Sawyer, R. K. (2003). Group creativity. Music, theater, collaboration. Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
   Google Scholar
• Simmt, E. (2001). Citizenship education in the context of school mathematics. Canadian Social Studies, 35(3), Retrieved from http://www2.education.ualberta.ca/css/css_35_3/ARcitizenship_education.htm)
   Google Scholar
• Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20–26.
   Google Scholar
• Small, M. (2009). Making math meaningful to Canadian students, K-8. Toronto, ON: Nelson Education Ltd.
   Google Scholar
• Smith, M. S., & Stein, M. K. (1998). Reflections on practice: Selecting and creating mathematical tasks: From research to practice. Mathematics Teaching in the Middle School, 3(5), 344–350.
   Google Scholar
• Stahl, G. G. (2006). Group cognition: Computer support for building collaborative knowledge. Cambridge, MA: MIT Press.
   Google Scholar
• Towers, J., & Martin, L. (2009). The emergence of a “better” idea: Preservice teachers’ growing understanding of mathematics for teaching. For the Learning of Mathematics, 29(3), 44–48.
   Google Scholar
• Van de Walle, J. A., Karp, K. S., Bay-Williams, J. M., McGarvey, L. M., & Folk, S. (2015). Elementary and middle school mathematics. Teaching developmentally (4th Canadian ed.). Toronto, ON: Pearson Canada.
   Google Scholar
• Vera, D., & Crossan, M. (2004). Theatrical improvisation: Lessons for organizations. Organization Studies, 25(5), 727–749.
   Web of Science ®Google Scholar
• Vera, D., & Crossan, M. (2005). Improvisation and innovative performance in teams. Organization Science, 16(3), 203–224.
   Web of Science ®Google Scholar
• Weick, K. E. (2002). Improvisation as a mindset for organizational analysis. In K. N. Kamoche, M. P. Cunha, & J. V. Cunha (Eds.), Organizational improvisation (pp. 49–70). London, UK: Routledge.
   Google Scholar
• Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458–477.
   Web of Science ®Google Scholar
• Zazkis, R., Sinclair, N., & Liljedahl, P. (2013). Lesson play in mathematics education. A tool for research and professional development. New York, NY: Springer.
   Google Scholar