Improvisational coactions and the growth of collective mathematical understanding

Research in Mathematics Education

Volumn 11, Issue 1, 2009, Pages 1-19

  Martin, Lyndon C ^a   Towers, Jo ^b  

^a UNIVERSITY OF EAST ANGLIA   (United Kingdom)

^b UNIVERSITY OF CALGARY   (Canada)

Author keywords

Interaction; Learning; Understanding

Indexed keywords

EID: 84879136373     PISSN: 14794802     EISSN: 17540178     Source Type: Journal    
DOI: 10.1080/14794800902732191     Document Type: Article

References (37)

1. Becker, H. 2000. The etiquette of improvisation. Mind, Culture, and Activity 7, no. 3: 171-176.
2. Berliner, P. 1994. Thinking in jazz: The infinite art of improvisation. Chicago: University of Chicago Press.
3. Bowers, J.S., and S. Nickerson. 2001. Identifying cyclic patterns of interaction to study individual and collective learning. Mathematical Thinking and Learning 3, no. 1: 1-28.
4. Cobb, P. 1998. Learning from distributed theories of intelligence. Mind, Culture, and Activity 5, no. 3: 187-204.
5. Cobb, P. 1999. Individual and collective mathematical development: The case of statistical data analysis. Mathematical Thinking and Learning 11: 5-43.
6. Cobb, P., and E. Yackel. 1996. Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational Psychologist 31, no. 3-4: 175-190.
7. Cobb, P., E. Yackel, and T. Wood. 1992. Interaction and learning in mathematics classroom situations. Educational Studies in Mathematics 23: 99-122.
8. Crawford, K. 1999. Hierarchies, networks and learning. In Learning mathematics: From hierarchies to networks, ed. L. Burton, 108-18. London: Falmer.
9. Davis, B. 1996. Teaching mathematics: Toward a sound alternative. New York: Garland.
10. Davis, B., and E. Simmt. 2003. Understanding learning systems: Mathematics education and complexity science. Journal for Research in Mathematics Education 34, no. 2: 137-67.
11. Gordon-Calvert, L. 2001. Mathematical conversations within the practice of mathematics. New York: Peter Lang.
12. Kieren, T., S. Pirie, and L. Gordon-Calvert. 1999. Growing minds, growing mathematical understanding: Mathematical understanding, abstraction and interaction. In Learning mathematics: From hierarchies to networks, ed. L. Burton, 209-231. London: Falmer Press.
13. Lave, J. 1996. The practice of learning. In Understanding practice - Perspectives on activity and context, ed. S. Chaiklin and J. Lave, 3-32. Cambridge: Cambridge University Press.
14. Lave, J. 1997. The culture of acquisition and the practice of understanding. In Situated cognition: Social, semiotic, and psychological perspectives, ed. D. Kirshner and J. Whitson, 17-35. Mahwah, NJ: Lawrence Erlbaum Associates.
15. Lave, J., and E. Wenger. 1991. Situated learning: Legitimate peripheral participation. Cambridge: Cambridge University Press.
16. Martin, L.C. 1999. The nature of the folding back phenomenon within the Pirie-Kieren Theory for the growth of mathematical understanding and the associated implications for teachers and learners of mathematics. PhD diss., Oxford University.
17. Martin, L.C., J. Towers, and S.E.B. Pirie. 2006. Collective mathematical understanding as improvisation. Mathematical Thinking and Learning 8, no. 2: 149-183.
18. Monson, I. 1996. Saying something - Jazz improvisation and interaction. Chicago: University of Chicago Press.
19. Pirie, S.E.B., and T. Kieren. 1989. A recursive theory of mathematical understanding. For the Learning of Mathematics 14, no. 1: 7-11.
20. Pirie, S.E.B., and T. Kieren. 1994. Growth in mathematical understanding: How can we characterise it and how can we represent it? Educational Studies in Mathematics 26, no. 2-3: 165-190.
21. Powell, A.B., J.M. Francisco, and C.A. Maher. 2003. An analytical model for studying the development of learners’ mathematical ideas and reasoning using videotape data. Journal of Mathematical Behavior 22: 405-435.
22. Rafal, C.T. 1996. From co-construction to takeovers: Science talk in a group of four girls. The Journal of the Learning Sciences 5, no. 3: 279-293.
23. Rogoff, B. 1995. Observing sociocultural activity on three planes: Participatory appropriation, guided participation, and apprenticeship. In Sociocultural studies of mind, ed. J.V. Wertsch, P. del Rio, and A. Alvarez, 139-64. New York: Cambridge University Press.
24. Ruhleder, K., and F. Stoltzfus. 2000. The etiquette of the master class: Improvisation on a theme by Howard Becker. Mind. Culture and Activity 7, no. 3: 186-196.
25. Sawyer, R.K. 2001. Creating conversations: Improvisation in everyday discourse. Cresskill, NJ: Hampton Press.
26. Sawyer, R.K. 2003. Group creativity: Music, theatre, collaboration. Mahwah, NJ: Lawrence Erlbaum Associates.
27. Sawyer, R.K. 2004. Creative teaching: Collaborative discussion as disciplined improvisation. Educational Researcher 23, no. 2: 12-20.
28. Saxe, G. 2002. Children’s developing mathematics in collective practices: A framework for analysis. The Journal of the Learning Sciences 11, no. 2-3: 275-300.
29. Sfard, A., and C. Kieran. 2001. Cognition as communication: Rethinking learning-by-talking through multi-faceted analysis of students’ mathematical interactions. Mind, Culture, and Activity 8, no. 1: 42-76.
30. Stahl, G. 2006. Group Cognition. Cambridge, MA: Massachusetts Institute of Technology.
31. Stephan, M., P. Cobb, and K. Gravemeijer. 2003. Coordinating social and individual analyses: Learning as participation in mathematical practices. Monograph of the Journal for Research in Mathematics Education: Supporting Students’ Development of Measuring Conceptions: Analyzing Students. Learning in Social Context 12: 67-102.
32. Teacher Training Agency 1998. Assessing your needs in mathematics: Diagnostic tasks. London, UK: TTA.
33. Teasley, S.D., and J. Roschelle. 1993. Constructing a joint problem space: The computer as a tool for sharing knowledge. In Computers as cognitive tools, ed. S.P. Lajoie and S.J. Derry, 229-58. Hillsdale, NJ: Lawrence Erlbaum Associates.
34. Towers, J., and L.C. Martin. 2007. The emergence of a ‘better’ idea: Preservice teachers’ growing mathematical understanding. Paper presented at the annual meeting of the American Educational Research Association, April 2007 in Chicago, IL.
35. Von Boxtel, K. 2004. Studying peer interaction from three perspectives: The example of collaborative concept learning. In Dialogic learning: Shifting perspectives to learning, instruction and teaching, ed. J.A. van Linden, 125-143. Dordrecht: Kluwer.
36. Von Glasersfeld, E. 1987. Learning as a constructive activity. In Problems ofrepresentation in the learning and teaching of mathematics, ed. C. Janvier, 3-18. Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
37. Yackel, E. 2002. What can we learn from analyzing the teacher’s role in collective argumentation. Journal of Mathematical Behavior 21: 423-440.