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.
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.
Balacheff, N.: 1990, ‘Towards a problematique for research on mathematics teaching’, Journal for Research in Mathematics Education 21, 258–272.
Barnes, B.: 1982, T.S. Kuhn and Social Science, Columbia University Press, New York.
Bateson, G.: 1973, Steps to an Ecology of Mind, Paladin, London.
Bauersfeld, H.: 1980, ‘Hidden dimensions in the so-called reality of a mathematics classroom’, Educational Studies in Mathematics 11, 23–41.
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.
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.
Billing, M.: 1987, Arguing and Thinking: A Rhetorical Approach to Social Psychology, Cambridge University Press, Cambridge.
Bishop, A.: 1985, ‘The social construction of meaning — a significant development for mathematics education?’, For the Learning of Mathematics 5(1), 24–28.
Bloor, D.: 1983, Wittgenstein: A Social Theory of Knowledge, Columbia University Press, New York.
Blumer, H.: 1969, Symbolic Interactionism, Prentice-Hall, Englewood Cliffs, NJ.
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.
Cobb, P.: 1988, ‘The tension between theories of learning and theories of instruction in mathematics education’, Educational Psychologist, 23, 87–104.
Cobb, P.: 1989, ‘Experiential, cognitive, and anthropological perspectives in mathematics education’, For the Learning of Mathematics 9(2), 32–42.
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.
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.
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.
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.
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.
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.
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.
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.
Dewey, J.: 1973, The Need for a Recovery of Philosophy, University of Chicago Press, Chicago.
Dilthey, W.: 1978, ‘The rise of hermeneutics’, New Literature History 3, 229–244.
Doise, W. and Mugny, G.: 1979, ‘Individual and collective conflicts of centrations in cognitive development’, European Journal of Psychology 9, 105–108.
Eisenhart, M. A.: 1988, ‘The ethnographic research tradition and mathematics education research’, Journal for Research in Mathematics Education 19, 99–114.
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.
Gadamer, H-G.: 1986, Truth and Method, Crossroad, New York.
Geertz, C.: 1983, Local Knowledge, Basic Books, New York.
Habermas, J.: 1979, Communication and the Evaluation of Society, Beacon Press, Boston.
Kaput, J.: 1991, ‘Notations and representations as mediators of constructive processes’, in E.vonGlasersfeld (ed.), Constructivism in Mathematics Education, Kluwer, Dordrecht, Netherlands, 53–74.
Krummheuer, G.: 1983, ‘Das Arbeitsinterim im Mathematikunterricht’, in H.Bauersfeld (ed.), Lernen und Lernen von Mathematik, Aulis, Koln, 57–106.
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.
Laborde, C.: 1990, ‘Language and mathematics’, in P.Nesher and J.Kilpatrick (eds.), Psychology of Mathematics Education, Cambridge University Press, Cambridge, 53–69.
Lewin, K.: 1951, Field Theory in Social Science, Harper Torchbooks, New York.
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.
Mead, G. H.: 1934, Mind, Self and Society, University of Chicago Press, Chicago.
Mehan, H.: 1979, Learning Lessons, Harvard University Press, Cambridge, MA.
Mehan, H. and Wood, H.: 1975, The Reality of Ethnomethodology, John Wiley, New York.
Mishler, E. G.: 1986, Research Interviewing: Context and Narrative, Harvard University Press, Cambridge.
Richards, J.: 1991, ‘Mathematical discussions’, in E.vonGlasersfeld (ed.), Radical Constructivism in Mathematics Education, Kluwer, Dordrecht, Netherlands, 13–52.
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.
Rorty, R.: 1979, Philosophy and the Mirror of Nature, Princeton University Press, Princeton.
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.
Scribner, S.: 1990, ‘Reflections on a model’, Quarterly Newsletter of the Laboratory of Comparative Human Cognition 12, 90–94.
Skemp, R.: 1976, ‘Relational understanding and instrumental understanding’, Mathematics Teacher 77, 20–26.
Solomon, Y.: 1989, The Practice of Mathematics, Routledge, London.
Steffe, L. P., Cobb, P., and vonGlasersfeld, E.: 1988, Construction of Arithmetical Meanings and Strategies, Springer-Verlag, New York.
Steffe, L. P., vonGlasersfeld, E., Richards, J., and Cobb, P.: 1983, Children's Counting Types: Philosophy, Theory, and Application, Praeger Scientific, New York.
Voigt, J.: 1985, ‘Patterns and routines in classroom interaction’, Recherches en Didactique des Mathematiques 6, 69–118.
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.
vonGlasersfeld, E.: 1983, ‘On the concept of interpretation’, Poetics 12, 207–218.
vonGlasersfeld, E.: 1984, ‘An introduction to radical constructivism’, in P.Watzlawick (ed.), The Invented Reality, Norton, New York, 17–40.
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.
Walkerdine, V.: 1988, The Mastery of Reason: Cognitive Development and the Production of Rationality, Routledge, London.
Winograd, T. and Flores, F.: 1986, Understanding Computers and Cognition: A New Foundation for Design, Ablex, Norwood, NJ.
Wittgenstein, L.: 1964, Remarks on the Foundations of Mathematics, Blackwell, Oxford.
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.
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.
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.
Author information
Authors and Affiliations
Rights 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
Issue Date:
DOI: https://doi.org/10.1007/BF00302315