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The Role of Representation in Solving Addition Problems
Project team: Chronoula (Charis) Voutsina; Keith Jones
The aim of this project was to examine the role of mental representation when young pupils (aged 6-around 6 years old) are solving addition problems. Karmiloff-Smith’s model of Representational Re-description (RR), which predicts that higher conceptualisation and control of an employed strategy develops after the achievement of a successful solution, was used as a basis for the analysis of the changes observed. A number of cases were studied at a micro-developmental level. Through an analysis of these cases, the findings of the study support certain predictions of the model regarding problem solving behaviour after success, such as the introduction of qualitative changes. Other findings of the study diverge from the predictions of the RR model.
This project was supported by ESRC award R00429934454.
Publications
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
Click here for
the extended abstract 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.
Click here for
full article in pdf format.
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.
Click here for
full paper in pdf format.
Conference Presentations
3rd Mediterranean Conference on Mathematical Education. Athens, January 2003.
Conference of the International Group for the Psychology of Mathematics Education, Utrecht University, The Netherlands, 2001.
Conference of the British Society for Research into Learning Mathematics, University of Surrey at Roehampton, 2000.
Related CRME Projects
Children
Moving Beyond Initial Success in Problem Solving
This project was supported by ESRC research award PTA-026-27-0697
Selected Bibliography
Baroody, A. J., & Ginsburg, H. P.: 1986, The relationships between initial meaningful and mechanical knowledge of arithmetic. In J. Hiebert (Ed.), Conceptual and Procedural Knowledge: The case of mathematics. (pp. 75-112). Hillsdale, N. Jersey: Lawrence Erlbaum Associates.
Bisanz, J., & LeFevre, J. A.: 1990, Strategic and non-strategic processing in the development of mathematical cognition. In D.F. Bjorklund (Ed.), Children's strategies: Contemporary views of Cognitive Development. (pp. 213-244). Hillsdale, New 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, N. Jersey: Lawrence Erlbaum Associates.
Karmiloff-Smith, A.: 1992, Beyond Modularity: a developmental perspective on cognitive science. London: Bradford Book/MIT Press.
Karmiloff-Smith, A.: 1994, Précis of Beyond Modularity: a developmental perspective on cognitive science. Behavioral and Brain Sciences, 17, 696-745.
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.
Page updated 08 September 2006
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