Back to CRME Home PageCollaborative Group for Research in Mathematics Education
Team included: Chronoula (Charis) Voutsina, Jill Bourne, Keith Jones
This project built on an earlier study, "The Role of Representation in Solving Addition Problems", which showed that children can move beyond success, and introduce qualitative changes and modifications to their successful successful problem-solving strategies. These changes indicate a movement from success-oriented behaviour to an organisation-oriented phase in problem solving during which children, as problem solvers, acquire better control and increasing conscious access to knowledge that they already have. The aim of this project was both to test the theoretical model and to refine an innovative methodology that is proving suitable for studying dynamic changes in young pupils' problem solving behaviour.
The project was supported by the award of an ESRC post-doc Fellowship (award PTA-026-27-0697).
Publications to date
Voutsina, C. and Jones, K. (2005), The Process of Knowledge Re-description as
Underlying Mechanism for the Development of Children’s Problem-solving
Strategies: an example from arithmetic. Paper presented to the European
Association for Research on Learning and Instruction conference 2005
(EARLI2005), Nicosia, Cyprus, August 23-27, 2005.
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full paper in pdf format.
Voutsina, C. and Jones, K. (2005), Children Building on Success: mathematical
problem solving in the early years. Paper presented to the British
Educational Research Association conference 2005 (BERA 2005), University of
Glamorgan, Wales, 14-17 September 2005.
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full paper in pdf format.
Voutsina, C. and Jones, K. (2004), Studying Change Processes in Primary
School Arithmetic Problem Solving: issues in combining methodologies,
Proceedings of the British Society for Research into Learning Mathematics,
24(3), 57-62.
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full paper in pdf format.
Voutsina, C. and Jones, K.(2003), Moving Beyond Success: changes in young
children’s successful problem solving behaviour. In: A. Gagatis and S.
Papastravridis (Eds), Proceedings of the 3rd Mediterranean Conference on
Mathematical Education. Athens: University of Athens. pp717-724. ISBN:
960-7341-25-2
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the extended abstract in pdf format.
Conference Presentations
European Association for Research on Learning and Instruction conference 2005 (EARLI2005), Nicosia, Cyprus, August 23-27, 2005
British Educational Research Association conference 2005 (BERA 2005)
Related CRME Projects
The
Role of Representation in Solving Addition Problems
This project was supported by ESRC research award R00429934454
Indicative bibliography
Aubrey, C. (1997), Children's early learning of number in school and out. In I. Thompson. (Ed.), Teaching and learning early number (pp. 20-29), Buckingham: Open University Press.
Aubrey, C. (1999), A developmental approach to early numeracy. Birmingham, The Questions Publishing Company.
Aubrey, C. (2003), "When we were very young": the foundations for mathematics. In I. Thompson. (Ed.), Enhancing primary mathematics teaching (pp. 43-53), Maidenhead: Open University Press.
Baroody, A.J. (1985), Mastery of basic number combinations: internalization of relationships or facts? Journal for Research in Mathematics Education, 16(2), 83-98.
Bottle, G., and Alfrey, C. (1999), Making sense of early mathematics. In T. David (Ed.), Teaching young children (pp. 52-67). London: PCP Ltd.
Carpenter, T.P., Fennema, E., Peterson, P.L., Chiang, C.P. and Loef, M. (1989). Using knowledge of children&'s mathematics thinking in classroom teaching: an experimental study. American Educational Research Journal, 26, 499-531.
Cobb, P., Wood, T., Yackel, E., Nicholls, J., Wheatley, G., Trigatti, B., & Perlwitz, M. (1991). Assessment of a problem-centered second-grade mathematics project. Journal for Research in Mathematics Education, 22(1), 3-29.
Cobb, P., Boufi, A., McClain, K., & Whitenack, J. (1997). Reflective discourse and collective reflection. Journal for Research in Mathematics Education, 28, 3, 258-277.
Doise, W., & Mugny, G.(1984). The social development of the intellect. Oxford: Pergamon Press.
Dwyer, M. C., Chait, R. and McKee, P. (2000), Building Strong Foundations for Early Learning: Guide to High-Quality Early Childhood Education Programs. Washington, DC: U.S. Department of Education, Planning and Evaluation Service.
English, L.D., & Halford, G.S. (1995). Mathematics Education. Models and Processes. N. Jersey: Lawrence Erlbaum Associates.
Halford, G.S. (1993). Children's Understanding. The Development of Mental Models. Hillsdale, N. Jersey: Lawrence Erlbaum Associates.
Hiebert, J., & Lefevre, P. (1986).Conceptual and procedural knowledge in mathematics: an introductory analysis. In J. Hiebert (Ed.), Conceptual and Procedural Knowledge: the Case of Mathematics (pp. 1-27). Hillsdale, NJ: LEA.
Karmiloff-Smith, A. (1984). Children's problem solving. In M.E. Lamb, A.L. Brown, & B. Rogoff (Eds.), Advances in Developmental Psychology, vol.3 (pp.39-90). Hillsdale, N. Jersey: Lawrence Erlbaum Associates.
Karmiloff-Smith, A. (1992). Beyond modularity: a developmental perspective on cognitive science. London: A Bradford Book. The MIT Press
Karmiloff-Smith, A. (1994). Précis of Beyond modularity: a developmental perspective on cognitive science. Behavioral and Brain Sciences, 17, 696-745.
Mandler, J.M. (1983). Representation. In J.H. Flavell, & E.M. Markman (volume Eds.), P.H. Mussen (series Ed.), Handbook of Child Psychology: Cognitive Development, vol. 3 (pp. 420-494). N. York: John Wiley & Sons.
Mandler, J.M. (1988). How to build a baby: on the development of an accessible representational system. Cognitive Development, 3, 113-136.
Meadows, S. (1996). The Child as Thinker. The Development and Acquisition of Cognition in Childhood. London: Routledge.
Miller, P. H., & Aloise-Young, P. A. (1995). Preschoolers' strategic behavior and performance on a same-different task. Journal of Experimental Child Psychology, 60, 284-303.
Siegler, R.S. (1996). Emerging Minds. The process of change in children's thinking. Oxford: Oxford University Press.
Siegler, R.S. (1997). Concepts and methods for studying cognitive change. In E. Amsel and K.A. Reninger (Eds.), Change and Development. Issues of Theory, Method, and Application (pp. 77-97). N. Jersey: Lawrence Erlbaum Associates.
Siegler, R.S. (2000). The rebirth of children's learning. Child Development, 71, 1, 26-35.
Siegler, R.S. (2003). The rebirth of children's learning. In Desforges, C. and Fox, R. (Eds.), Teaching and learning: the essential readings. Oxford: Blackwell Publishing.
Siegler, R.S., & Jenkins, E. (1989). How Children Discover New Strategies. Hillsdale, N. Jersey: Lawrence Erlbaum Associates.
Siegler, R.S., & Stern, E. (1998). Conscious and unconscious strategy discoveries: a microgenetic analysis. Journal of Experimental Psychology: General, 127, 4, 377-397.
Siraj-Blatchford, I., Sylva, K, Muttock, S., Gilden, R., and Bell, D. (2002). Researching effective pedagogy in the early years. DfES Research report RR356.
Underwood, G., & Bright, E.H. (1996). Cognition with and without awareness. In G. Underwood (Ed.), Implicit Cognition (pp. 1-40). Oxford: Oxford University Press.
Voutsina, C. and Jones, K. (2000), Changes in young children's strategies
when solving addition tasks, Proceedings of the British Society for Research
into Learning Mathematics, 20(3), 97-102.
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full article in pdf format.
Voutsina, C. and Jones, K. (2001), The Micro-development of Young Children's
Problem Solving Strategies when Tackling Addition Tasks, In: Marja van den
Heuvel-Panhuizen (Ed), Proceedings of the 25th Conference of the
International Group for the Psychology of Mathematics Education. Utrecht,
volume 4, 391-398.
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full article in pdf format.
Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458-477.
Page updated 08 September 2006
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