Advertisement

Educational Studies in Mathematics

, Volume 49, Issue 2, pp 193–223 | Cite as

Socially mediated metacognition: creating collaborative zones of proximal development in small group problem solving

  • Merrilyn Goos
  • Peter Galbraith
  • Peter Renshaw
Article

Abstract

This paper reports on a three year study of patterns of student-student social interaction that mediated metacognitive activity in senior secondary school mathematics classrooms. Transcripts of small group problem solving were analysed to determine how a collaborative zone of proximal development could be created through interaction between peers of comparable expertise, and to investigate conditions under which such interaction led to successful or unsuccessful problem solving outcomes. Unsuccessful problem solving was characterised by students' poor metacognitive decisions exacerbated by lack of critical engagement with each other's thinking, while successful outcomes were favoured if students challenged and discarded unhelpful ideas and actively endorsed useful strategies. In reconceptualising metacognition as a social practice, the study contributes to the growing body of research applying sociocultural theories to understand learning in mathematics classrooms.

metacognition social interaction zone of proximal development 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. Artzt, A.F. and Armour-Thomas, E.: 1992, 'Development of a cognitive-metacognitive framework for protocol analysis of mathematical problem solving in small groups', Cognition and Instruction 9(2), 137–175.Google Scholar
  2. Abreu, G. de: 2000, 'Relationships between macro and micro socio-cultural contexts: Implications for the study of interactions in the mathematics classroom', Educational Studies in Mathematics 41, 1–29.CrossRefGoogle Scholar
  3. Australian Education Council: 1991, A National Statement on Mathematics for Australian Schools. Curriculum Corporation, Melbourne.Google Scholar
  4. Board of Senior Secondary School Studies: 1992, Senior Syllabus in Mathematics B. BSSSS, Brisbane.Google Scholar
  5. Board of Senior Secondary School Studies: 2000, Mathematics B Senior Syllabus 2001. BSSSS, Brisbane.Google Scholar
  6. Brown, A.L., Ash, D., Rutherford, M., Nakagawa, K., Gordon, A. and Campione, J.C.: 1993, 'Distributed expertise in the classroom', in G. Salomon (ed.), Distributed Cognitions, Cambridge University Press, Cambridge, pp. 188–228.Google Scholar
  7. Brown, A.L., Bransford, J.D., Ferrara, R.A. and Campione, J.C.: 1983, 'Learning, remembering, and understanding', in P. H. Mussen (ed.), Handbook of Child Psychology (4th ed.) Vol. 3, Wiley, New York, pp. 77–166.Google Scholar
  8. Bruner, J.: 1985, 'Vygotsky: A historical and conceptual perspective', in J.V. Wertsch (ed.), Culture, Communication, and Cognition: Vygotskian Perspectives, Cambridge University Press, Cambridge, pp. 21–34.Google Scholar
  9. Cobo, P. and Fortuny, J.M.: 2000, 'Social interactions and cognitive effects in contexts of area-comparison problem solving', Educational Studies in Mathematics 42, 115–140.CrossRefGoogle Scholar
  10. Curcio, F.R. and Artzt, A.F.: 1998, 'Students communicating in small groups: Making sense of data in graphical form', in H. Steinbring, M. Bartolini Bussi and A. Sierpinska (eds.), Language and Communication in the Mathematics Classroom, National Council of Teachers of Mathematics, Reston, VA, pp. 179–190.Google Scholar
  11. Damon, W. and Phelps, E.: 1989, 'Critical distinctions among three approaches to peer education', International Journal of Educational Research 13, 9–19.CrossRefGoogle Scholar
  12. Flavell, J.H.: 1976, 'Metacognitive aspects of problem solving', in L.R. Resnick (ed.), The Nature of Intelligence, Erlbaum, Hillsdale, NJ, pp. 231–235.Google Scholar
  13. Forman, E.A.: 1989, 'The role of peer interaction in the social construction of mathematical knowledge', International Journal of Educational Research 13, 55–70.CrossRefGoogle Scholar
  14. Forman, E.A. and McPhail, J.: 1993, 'Vygotskian perspective on children's collaborative problem-solving activities', in E.A. Forman, N. Minick and C.A. Stone (eds.), Contexts for Learning: Sociocultural Dynamics in Children's Development, Oxford University Press, New York, pp. 213–229.Google Scholar
  15. Garofalo, J. and Lester, F.K., Jr.: 1985, 'Metacognition, cognitive monitoring, and mathematical performance', Journal for Research in Mathematics Education 16, 163–176.Google Scholar
  16. Good, T.L., Mulryan, C. and McCaslin, M.: 1992, 'Grouping for instruction in mathematics: A call for programmatic research on small-group processes', in D.A. Grouws (ed.), Handbook of Research on Mathematics Teaching and Learning, Macmillan, New York, pp. 165–196.Google Scholar
  17. Goos, M.: 1994, 'Metacognitive decision making and social interactions during paired problem solving', Mathematics Education Research Journal 6, 144–165.Google Scholar
  18. Goos, M.: 1995, 'Metacognitive knowledge, beliefs, and classroom mathematics, in B. Atweh and S. Flavel (eds.), Galtha (Proceedings of the 18th annual conference of the Mathematics Education Research Group of Australasia), MERGA, Darwin, pp. 300–306.Google Scholar
  19. Goos, M.: 1999a, 'Metacognitive Self-Knowledge (MSK) Questionnaire and Interview', in R.J. Cameron and A.R. Reynolds (eds.), Psychology in Education Portfolio: Learning Style and Metacognition, NFER-Nelson, Windsor, pp. 39–54.Google Scholar
  20. Goos, M.: 1999b, 'Scaffolds for learning: A sociocultural approach to reforming mathematics teaching and teacher education', Mathematics Teacher Education and Development 1, 4–21.Google Scholar
  21. Goos, M.: 2000, Metacognition in Context: A Study of Collaborative Metacognitive Activity in a Classroom Community of Mathematical Inquiry, Unpublished doctoral dissertation, The University of Queensland, Brisbane.Google Scholar
  22. Goos, M. and Galbraith, P.: 1996, 'Do it this way! Metacognitive strategies in collaborative mathematical problem solving', Educational Studies in Mathematics 30, 229–260.CrossRefGoogle Scholar
  23. Goos, M., Galbraith, P. and Renshaw, P.: 1999, 'Establishing a community of practice in a secondary mathematics classroom', in L. Burton (ed.), Learning Mathematics: From Hierarchies to Networks, Falmer Press, London, pp. 36–61.Google Scholar
  24. Granott, N.: 1993, 'Co-construction of knowledge: Separate minds, joint effort, and weird creatures', in R.H. Wozniak and K.W. Fischer (eds.), Development in Context: Acting and Thinking in Specific Environments, Erlbaum, Hillsdale, NJ, pp. 183–207.Google Scholar
  25. Kruger, A.C.: 1993, 'Peer collaboration: Conflict, cooperation or both?', Social Development 2, 165–182.Google Scholar
  26. Lester, F.K., Jr.: 1994, 'Musings about mathematical problem-solving research: 1970- 1994, Journal for Research in Mathematics Education 25, 660–675.Google Scholar
  27. Lincoln, Y.S. and Guba, E.G.: 1985, Naturalistic Inquiry, Sage, Beverly Hills, CA.Google Scholar
  28. Minick, N.: 1987, 'The development of Vygotsky's thought: An introduction', in R.W. Rieber and A.S. Carton (eds.), The Collected Works of L. S. Vygotsky, Vol. 1: Problems of General Psychology, Plenum Press, New York, pp. 17–36.Google Scholar
  29. National Council of Teachers ofMathematics: 1989, Curriculum and Evaluation Standards for School Mathematics, NCTM, Reston, VA.Google Scholar
  30. National Council of Teachers of Mathematics: 2000, Principles and Standards for School Mathematics, NCTM, Reston, VA.Google Scholar
  31. Packer, M.: 1993, 'Away from internalisation', in E.A. Forman, N. Minick and C.A. Stone (eds.), Contexts for Learning: Sociocultural Dynamics in Children's Development, Oxford University Press, New York, pp. 254–265.Google Scholar
  32. Schoenfeld, A.H.: 1989, 'Ideas in the air: Speculations on small group learning, environmental and cultural influences on cognition, and epistemology', International Journal of Educational Research 13, 71–88.CrossRefGoogle Scholar
  33. Schoenfeld, A.H.: 1992, 'Learning to think mathematically: Problem solving, metacognition and sense making in mathematics', in D.A. Grouws (ed.), Handbook of Research on Mathematics Teaching and Learning, Macmillan, New York, pp. 334–370.Google Scholar
  34. Schoenfeld, A.H.: 1999, 'Looking toward the 21st century: Challenges of educational theory and practice', Educational Researcher 28(7), 4–14.Google Scholar
  35. Stacey, K.: 1992, 'Mathematical problem solving in groups: Are two heads better than one?' Journal of Mathematical Behavior 11, 261–275.Google Scholar
  36. Teasley, S.D.: 1997, 'Talking about reasoning: How important is the peer in peer collaboration?', in L.B. Resnick, R. Säljö, C. Pontecorvo and B. Burge (eds.), Discourse, Tools and Reasoning: Essays on Situated Cognition, Springer-Verlag, Berlin, pp. 361–384.Google Scholar
  37. Teasley, S.D. and Roschelle, J.: 1993, 'Constructing a Joint Problem Space: The computer as a tool for sharing knowledge', in S.P. Lajoie and S.J. Derry (eds.), Computers as Cognitive Tools, Erlbaum, Hillsdale, NJ, pp. 229–258.Google Scholar
  38. Vygotsky, L.S.: 1978, Mind in Society, Harvard University Press, Cambridge, MA.Google Scholar
  39. Wertsch, J.V.: 1984, 'The zone of proximal development: Some conceptual issues', in B. Rogoff and J.V. Wertsch (eds.), Children's Learning in the “Zone of Proximal Development” (New Directions for Child Development, No. 23), Jossey-Bass, San Francisco, pp. 7–18.Google Scholar
  40. Wertsch, J.V.: 1985, Vygotsky and the Social Formation of Mind, Harvard University Press, Cambridge, MA.Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Merrilyn Goos
    • 1
  • Peter Galbraith
    • 1
  • Peter Renshaw
    • 1
  1. 1.School of EducationThe University of QueenslandSt LuciaAustralia

Personalised recommendations