Skip to main content
Log in

Interaction and learning in mathematics classroom situations

  • Published:
Educational Studies in Mathematics Aims and scope Submit manuscript

Abstract

An analysis of one ten minute episode in which three seven year-old students engage in collaborative small group activity is presented to explore the relationship between individual learning and group development. Particular attention is given to the establishment of a taken-as-shared basis for mathematical activity and to the attainment of intersubjectivity. From a perspective which treats communication as a process of active interpretation and mutual adaptation, learning as it occurs in the course of social interaction is characterized as a circular, self-referential sequence of events rather than a linear cause-effect chain. In addition, the relationship between individual learning and group development is such that the students can be said to have participated in the establishment of the situations in which they learned.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Bakhurst, D.: 1988, ‘Activity, consciousness, and communication’, Quarterly Newsletter of the Laboratory of Comparative Human Cognition 10, 31–39.

    Google Scholar 

  • Balacheff, N.: 1990, ‘Towards a problematique for research on mathematics teaching’, Journal for Research in Mathematics Education 21, 258–272.

    Google Scholar 

  • Barnes, B.: 1982, T.S. Kuhn and Social Science, Columbia University Press, New York.

    Google Scholar 

  • Bateson, G.: 1973, Steps to an Ecology of Mind, Paladin, London.

    Google Scholar 

  • Bauersfeld, H.: 1980, ‘Hidden dimensions in the so-called reality of a mathematics classroom’, Educational Studies in Mathematics 11, 23–41.

    Google Scholar 

  • Bauersfeld, H.: 1988, ‘Interaction, construction, and knowledge: Alternative perspectives for mathematics education’, in T.Cooney and D.Grouws (eds.), Effective Mathematics Teaching, National Council of Teachers of Mathematics, Reston, VA, 27–46.

    Google Scholar 

  • Bauersfeld, H., Krummheuer, G., and Voigt, J.: 1988, ‘Interactional theory of learning and teaching mathematics and related microethnographical studies’, in H. G. Steiner and A. Vermandel (eds.), Foundations and Methodology of the Discipline of Mathematics Education, Proceedings of the TME Conference, Antwerp, 174–188.

  • Berstein, R. J.: 1983, Beyond Objectivism and Relativism: Science Hermeneutic, and Praxis, University of Pennsylvania Press, Philadelphia.

    Google Scholar 

  • Billing, M.: 1987, Arguing and Thinking: A Rhetorical Approach to Social Psychology, Cambridge University Press, Cambridge.

    Google Scholar 

  • Bishop, A.: 1985, ‘The social construction of meaning — a significant development for mathematics education?’, For the Learning of Mathematics 5(1), 24–28.

    Google Scholar 

  • Bloor, D.: 1983, Wittgenstein: A Social Theory of Knowledge, Columbia University Press, New York.

    Google Scholar 

  • Blumer, H.: 1969, Symbolic Interactionism, Prentice-Hall, Englewood Cliffs, NJ.

    Google Scholar 

  • Brousseau, G.: 1984, ‘The crucial role of the didactical contract in the analysis and construction of situations in teaching and learning mathematics’, in H. G. Steiner (ed.), Theory of Mathematics Education, Occasional paper 54, Institut fur Didaktik der Mathematik, University of Bielefeld, 110–119.

  • Bruner, H.: 1986, Actual Minds, Possible Worlds, Harvard University Press, Cambridge.

    Google Scholar 

  • Cobb, P.: 1988, ‘The tension between theories of learning and theories of instruction in mathematics education’, Educational Psychologist, 23, 87–104.

    Google Scholar 

  • Cobb, P.: 1989, ‘Experiential, cognitive, and anthropological perspectives in mathematics education’, For the Learning of Mathematics 9(2), 32–42.

    Google Scholar 

  • Cobb, P. and Merkel, G.: 1989, ‘Thinking strategies as an example of teaching arithmetic through problem solving’, in P.Trafton (ed.), 1989 Yearbook of the National Council of Teachers of Mathematics, National Council of Teachers of Mathematics, Reston, VA, 70–81.

    Google Scholar 

  • Cobb, P., Wood, T., and Yackel, E. 1990, ‘Classrooms as learning environments for teachers and researchers’, in R. B.Davis, C. A.Maher, and N.Noddings (eds.), Constructivist Views on the Teaching and Learning of Mathematics, Journal for Research in Mathematics Education Monograph No. 4; National Council of Teachers of Mathematics, Reston, VA, 125–146.

    Google Scholar 

  • Cobb, P., Wood, T., and Yackel, E.: 1991, ‘Learning through problem solving: A constructivist approach to second grade mathematics’, in E.vonGlasersfeld (ed.), Radical Constructivism in Mathematics Education, Kluwer, Dordrecht, Netherlands, 157–176.

    Google Scholar 

  • Cobb, P., Wood, T., and Yackel, E.: 1991, ‘Analogies from the philosophy and sociology of science for understanding classroom life’, Science Education 75, 23–44.

    Google Scholar 

  • Cobb, P., Wood, T., and Yackel, E.: (in press), ‘Characteristics of classroom mathematics traditions: An interactional analysis’, in C. A. Maher and R. B. Davis (eds.), Relating Schools to Reality in Mathematics Learning, Prentice Hall, Englewood Cliffs, NJ.

  • Cobb, P., Wood, T., Yackel, E., Nicholls, J., Wheatley, G., Trigatti, B., and Perlwitz, M.: 1991, ‘Assessment of a problem-centered second grade mathematics project’, Journal for Research in Mathematics Education 22, 3–29.

    Google Scholar 

  • Cobb, P., Yackel, E., and Wood, T.: 1989, ‘Young children's emotional acts while doing mathematical problem solving’, in D. B.McCleod and V. M.Adams (eds.), Affect and Mathematical Problem Solving: A New Perspective, Springer-Verlag, New York, 117–148.

    Google Scholar 

  • Cole, M.: 1986, ‘The zone of proximal development: Where culture and cognition create each other’, in J. V.Wertsch (ed.), Culture, Communication, and Cognition: Vygotskian Perspectives, Cambridge University Press, New York, 141–161.

    Google Scholar 

  • Comaroff, J. L.: 1982, ‘Dialectical systems, history and anthroplogy: Units of study and questions of theory’, Journal of South African Studies 8(2), 143–172.

    Google Scholar 

  • Dewey, J.: 1973, The Need for a Recovery of Philosophy, University of Chicago Press, Chicago.

    Google Scholar 

  • Dilthey, W.: 1978, ‘The rise of hermeneutics’, New Literature History 3, 229–244.

    Google Scholar 

  • Doise, W. and Mugny, G.: 1979, ‘Individual and collective conflicts of centrations in cognitive development’, European Journal of Psychology 9, 105–108.

    Google Scholar 

  • Eisenhart, M. A.: 1988, ‘The ethnographic research tradition and mathematics education research’, Journal for Research in Mathematics Education 19, 99–114.

    Google Scholar 

  • Erickson, F.: 1986, ‘Qualitative methods in research on teaching’, in M. C.Wittrock (ed.), Handbook of Research on Teaching (3rd ed.), Macmillan, New York, 119–161.

    Google Scholar 

  • Gadamer, H-G.: 1986, Truth and Method, Crossroad, New York.

    Google Scholar 

  • Geertz, C.: 1983, Local Knowledge, Basic Books, New York.

    Google Scholar 

  • Habermas, J.: 1979, Communication and the Evaluation of Society, Beacon Press, Boston.

    Google Scholar 

  • Kaput, J.: 1991, ‘Notations and representations as mediators of constructive processes’, in E.vonGlasersfeld (ed.), Constructivism in Mathematics Education, Kluwer, Dordrecht, Netherlands, 53–74.

    Google Scholar 

  • Krummheuer, G.: 1983, ‘Das Arbeitsinterim im Mathematikunterricht’, in H.Bauersfeld (ed.), Lernen und Lernen von Mathematik, Aulis, Koln, 57–106.

    Google Scholar 

  • Laborde, C.: 1982, Langue Naturelle et Ecriture Symbolique, These d'Etat, Universite Joseph Fourier, Grenoble.

  • Laborde, L.: 1989, ‘Audacity and reason: French research in mathematics education’, For the Learning of Mathematics 9(3), 31–36.

    Google Scholar 

  • Laborde, C.: 1990, ‘Language and mathematics’, in P.Nesher and J.Kilpatrick (eds.), Psychology of Mathematics Education, Cambridge University Press, Cambridge, 53–69.

    Google Scholar 

  • Lewin, K.: 1951, Field Theory in Social Science, Harper Torchbooks, New York.

    Google Scholar 

  • Maturana, H. R.: 1980, ‘Man and society’, in F.Benseler, P. M.Hejl, and W. K.Kock (eds.), Autopoiesis, Communication, and Society, Campus Verlag, Frankfurt, Germany, 11–32.

    Google Scholar 

  • Mead, G. H.: 1934, Mind, Self and Society, University of Chicago Press, Chicago.

    Google Scholar 

  • Mehan, H.: 1979, Learning Lessons, Harvard University Press, Cambridge, MA.

    Google Scholar 

  • Mehan, H. and Wood, H.: 1975, The Reality of Ethnomethodology, John Wiley, New York.

    Google Scholar 

  • Mishler, E. G.: 1986, Research Interviewing: Context and Narrative, Harvard University Press, Cambridge.

    Google Scholar 

  • Richards, J.: 1991, ‘Mathematical discussions’, in E.vonGlasersfeld (ed.), Radical Constructivism in Mathematics Education, Kluwer, Dordrecht, Netherlands, 13–52.

    Google Scholar 

  • Rommetveit, R.: 1985, ‘Language acquisition as increasing in linguistic structuring of experience and symbolic behavior control’, in J. V.Wertsch (ed.), Culture, Communication, and Cognition, Cambridge University Press, Cambridge, 183–205.

    Google Scholar 

  • Rorty, R.: 1979, Philosophy and the Mirror of Nature, Princeton University Press, Princeton.

    Google Scholar 

  • Sawada, D., Kieren, T., and Olson, A.: 1990 ‘The qualitative-quantitative distinction: Logic, paradigms, play and metaphor’, Paper presented at the annual meeting of the American Educational Research Association, Boston, April.

  • Schutz, A.: 1962, The Problem of Social Reality, Martinus Nijhoff, The Hague.

    Google Scholar 

  • Scribner, S.: 1990, ‘Reflections on a model’, Quarterly Newsletter of the Laboratory of Comparative Human Cognition 12, 90–94.

    Google Scholar 

  • Skemp, R.: 1976, ‘Relational understanding and instrumental understanding’, Mathematics Teacher 77, 20–26.

    Google Scholar 

  • Solomon, Y.: 1989, The Practice of Mathematics, Routledge, London.

    Google Scholar 

  • Steffe, L. P., Cobb, P., and vonGlasersfeld, E.: 1988, Construction of Arithmetical Meanings and Strategies, Springer-Verlag, New York.

    Google Scholar 

  • Steffe, L. P., vonGlasersfeld, E., Richards, J., and Cobb, P.: 1983, Children's Counting Types: Philosophy, Theory, and Application, Praeger Scientific, New York.

    Google Scholar 

  • Voigt, J.: 1985, ‘Patterns and routines in classroom interaction’, Recherches en Didactique des Mathematiques 6, 69–118.

    Google Scholar 

  • Voigt, J.: 1989, ‘The social constitution of the mathematics province—a microethnographical study in classroom interaction’, The Quarterly Newsletter of the Laboratory of Comparative Human Cognition 11(1&2), 27–34.

    Google Scholar 

  • vonGlasersfeld, E.: 1983, ‘On the concept of interpretation’, Poetics 12, 207–218.

    Google Scholar 

  • vonGlasersfeld, E.: 1984, ‘An introduction to radical constructivism’, in P.Watzlawick (ed.), The Invented Reality, Norton, New York, 17–40.

    Google Scholar 

  • vonGlasersfeld, E.: 1990, ‘Environment and communication’, in L. P.Steffe and T.Wood (eds.), Transforming Children's Mathematics Education: International Perspectives, Lawrence Erlbaum Associates, Hillsdale, NJ, 30–38.

    Google Scholar 

  • Walkerdine, V.: 1988, The Mastery of Reason: Cognitive Development and the Production of Rationality, Routledge, London.

    Google Scholar 

  • Winograd, T. and Flores, F.: 1986, Understanding Computers and Cognition: A New Foundation for Design, Ablex, Norwood, NJ.

    Google Scholar 

  • Wittgenstein, L.: 1964, Remarks on the Foundations of Mathematics, Blackwell, Oxford.

    Google Scholar 

  • Wood, T., Cobb, P., and Yackel, E.: 1990, ‘The contextual nature of teaching: Mathematics and reading instruction in one second-grade classroom’, Elementary School Journal 90(5), 497–514.

    Google Scholar 

  • Wood, T. and Yackel, E.: 1990, ‘The development of collaborative dialogue in small group interactions’, in L. P.Steffe and T.Wood (eds), Transforming Children's Mathematics Education: International Perspectives, Lawrence Erlbaum Associates, Hillsdale, NJ, 244–252.

    Google Scholar 

  • Yackel, E., Cobb, P., and Wood, T.: in press, ‘Small group interactions as a source of learning opportunities in second grade mathematics’, Journal for Research in Mathematics Education.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cobb, P., Yackel, E. & Wood, T. Interaction and learning in mathematics classroom situations. Educ Stud Math 23, 99–122 (1992). https://doi.org/10.1007/BF00302315

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00302315

Keywords

Navigation