References
- Becker , H. 2000 . The etiquette of improvisation . Mind, Culture, and Activity , 7 ( 3 ) : 171 – 6 .
- Berliner , P. 1994 . Thinking in jazz: The infinite art of improvisation , Chicago : University of Chicago Press .
- Bowers , J.S. and Nickerson , S. 2001 . Identifying cyclic patterns of interaction to study individual and collective learning . Mathematical Thinking and Learning , 3 ( 1 ) : 1 – 28 .
- Cobb , P. 1998 . Learning from distributed theories of intelligence . Mind, Culture, and Activity , 5 ( 3 ) : 187 – 204 .
- Cobb , P. 1999 . Individual and collective mathematical development: The case of statistical data analysis . Mathematical Thinking and Learning , 11 : 5 – 43 .
- Cobb , P. and Yackel , E. 1996 . Constructivist, emergent, and sociocultural perspectives in the context of developmental research . Educational Psychologist , 31 ( 3–4 ) : 175 – 90 .
- Cobb , P. , Yackel , E. and Wood , T. 1992 . Interaction and learning in mathematics classroom situations . Educational Studies in Mathematics , 23 : 99 – 122 .
- Crawford , K. 1999 . “ Hierarchies, networks and learning ” . In Learning mathematics: From hierarchies to networks , Edited by: Burton , L. 108 – 18 . London : Falmer .
- Davis , B. 1996 . Teaching mathematics: Toward a sound alternative , New York : Garland .
- Davis , B. and Simmt , E. 2003 . Understanding learning systems: Mathematics education and complexity science . Journal for Research in Mathematics Education , 34 ( 2 ) : 137 – 67 .
- Gordon-Calvert , L. 2001 . Mathematical conversations within the practice of mathematics , New York : Peter Lang .
- Kieren , T. , Pirie , S. and Gordon-Calvert , L. 1999 . “ Growing minds, growing mathematical understanding: Mathematical understanding, abstraction and interaction ” . In Learning mathematics: From hierarchies to networks , Edited by: Burton , L. 209 – 231 . London : Falmer Press .
- Lave , J. 1996 . “ The practice of learning ” . In Understanding practice – Perspectives on activity and context , Edited by: Chaiklin , S. and Lave , J. 3 – 32 . Cambridge : Cambridge University Press .
- Lave , J. 1997 . “ The culture of acquisition and the practice of understanding ” . In Situated cognition: Social, semiotic, and psychological perspectives , Edited by: Kirshner , D. and Whitson , J. 17 – 35 . Mahwah, NJ : Lawrence Erlbaum Associates .
- Lave , J. and Wenger , E. 1991 . Situated learning: Legitimate peripheral participation , Cambridge : Cambridge University Press .
- 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 .
- Martin , L.C. , Towers , J. and Pirie , S.E.B. 2006 . Collective mathematical understanding as improvisation . Mathematical Thinking and Learning , 8 ( 2 ) : 149 – 83 .
- Monson , I. 1996 . Saying something – Jazz improvisation and interaction , Chicago : University of Chicago Press .
- Pirie , S.E.B. and Kieren , T. 1989 . A recursive theory of mathematical understanding . For the Learning of Mathematics , 14 ( 1 ) : 7 – 11 .
- Pirie , S.E.B. and Kieren , T. 1994 . Growth in mathematical understanding: How can we characterise it and how can we represent it? . Educational Studies in Mathematics , 26 ( 2–3 ) : 165 – 190 .
- Powell , A.B. , Francisco , J.M. and Maher , C.A. 2003 . An analytical model for studying the development of learners’ mathematical ideas and reasoning using videotape data . Journal of Mathematical Behavior , 22 : 405 – 35 .
- Rafal , C.T. 1996 . From co-construction to takeovers: Science talk in a group of four girls . The Journal of the Learning Sciences , 5 ( 3 ) : 279 – 293 .
- Rogoff , B. 1995 . “ Observing sociocultural activity on three planes: Participatory appropriation, guided participation, and apprenticeship ” . In Sociocultural studies of mind , Edited by: Wertsch , J.V. , del Rio , P. and Alvarez , A. 139 – 64 . New York : Cambridge University Press .
- Ruhleder , K. and Stoltzfus , F. 2000 . The etiquette of the master class: Improvisation on a theme by Howard Becker. Mind . Culture and Activity , 7 ( 3 ) : 186 – 196 .
- Sawyer , R. K. 2001 . Creating conversations: Improvisation in everyday discourse , Cresskill, NJ : Hampton Press .
- Sawyer , R. K. 2003 . Group creativity: Music, theatre, collaboration , Mahwah, NJ : Lawrence Erlbaum Associates .
- Sawyer , R. K. 2004 . Creative teaching: Collaborative discussion as disciplined improvisation . Educational Researcher , 23 ( 2 ) : 12 – 20 .
- Saxe , G. 2002 . Children's developing mathematics in collective practices: A framework for analysis . The Journal of the Learning Sciences , 11 ( 2–3 ) : 275 – 300 .
- Sfard , A. and Kieran , C. 2001 . Cognition as communication: Rethinking learning-by-talking through multi-faceted analysis of students’ mathematical interactions . Mind, Culture, and Activity , 8 ( 1 ) : 42 – 76 .
- Stahl , G. 2006 . Group Cognition , Cambridge, MA : Massachusetts Institute of Technology .
- Stephan , M. , Cobb , P. and Gravemeijer , K. 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 .
- Teacher Training Agency . 1998 . Assessing your needs in mathematics: Diagnostic tasks , London, , UK : TTA .
- Teasley , S. D. and Roschelle , J. 1993 . “ Constructing a joint problem space: The computer as a tool for sharing knowledge ” . In Computers as cognitive tools , Edited by: Lajoie , S.P. and Derry , S.J. 229 – 258 . Hillsdale, NJ : Lawrence Erlbaum Associates .
- 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 .
- 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 , Edited by: van Linden , J.A. 125 – 143 . Dordrecht : Kluwer .
- Von Glasersfeld , E. 1987 . “ Learning as a constructive activity ” . In Problems of representation in the learning and teaching of mathematics , Edited by: Janvier , C. 3 – 18 . Hillsdale, NJ : Lawrence Erlbaum Associates, Inc .
- Yackel , E. 2002 . What can we learn from analyzing the teacher's role in collective argumentation . Journal of Mathematical Behavior , 21 : 423 – 40 .