Advertisement

Introduction

  • Paul CobbEmail author
  • Erna Yackel
Chapter
  • 1.4k Downloads
Part of the Mathematics Education Library book series (MELI, volume 48)

Abstract

I completed my dissertation studies with Les Steffe and Ernst von Glasersfeld at the University of Georgia in 1983 and then accepted a faculty position at Purdue University in Indiana. The first study that I conducted at Purdue University was built on my dissertation work and focused on the psychological contexts within which young children interpret and attempt to solve arithmetical tasks in school (see Chapter 2). In this study, I interviewed approximately 40 first-grade students from two classrooms at the beginning, middle, and end of the school year. In the initial interviews, most of the children attempted to solve all types of arithmetical tasks presented by reasoning about quantities. However, in the interviews at the end of the school year, most of the same children attempted to solve all interview tasks that were similar to those in their school textbook by either using very elementary counting methods or by focusing on patterns in numerals regardless of whether they made sense in terms of relations between quantities. In this respect, the children’s solutions were reminiscent of those that Erlwanger (1973) had documented in his influential case of study of a fifth-grade student’s conception of mathematics.

Keywords

Mathematics Classroom Mathematical Learning Arithmetical Task School Textbook Mathematics Education Researcher 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Bateson, G. (1973). Steps to an ecology of mind. London: Paladin.Google Scholar
  2. Bauersfeld, H. (1980). Hidden dimensions in the so-called reality of a mathematics classroom. Educational Studies in Mathematics, 11, 23–41.CrossRefGoogle Scholar
  3. Blumer, H. (1969). Symbolic interactionism: Perspectives and method. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
  4. Cobb, P. (1986). Contexts, goals, beliefs, and learning mathematics. For the Learning of Mathematics, 6(2), 2–9.Google Scholar
  5. Cobb, P. (1998). Theorizing about mathematical conversations and learning from practice. For the Learning of Mathematics, 18(1), 46–48.Google Scholar
  6. Cobb, P., & Bauersfeld, H. (Eds.). (1995). Emergence of mathematical meaning: Interaction in classroom cultures. Hillsdale, NJ: Erlbaum.Google Scholar
  7. Cobb, P., & Yackel, E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational Psychologist, 31, 175–190.CrossRefGoogle Scholar
  8. Doise, W., & Mugny, G. (1979). Individual and collective conflicts of centrations in cognitive development. European Journal of Psychology, 9, 105–108.CrossRefGoogle Scholar
  9. Doise, W., Mugny, G., & Perret-Clermont, A. N. (1975). Social interaction and the development of cognitive operations. European Journal of Soviet Psychology, 5, 367–383.CrossRefGoogle Scholar
  10. Erickson, F. (1986). Qualitative methods in research on teaching. In M. C. Wittrock (Ed.), The handbook of research on teaching (3rd ed., pp. 119–161). New York: Macmillan.Google Scholar
  11. Erlwanger, S. H. (1973). Studies of children’s conceptions of mathematics – Part I. Journal of Children’s Mathematical Behavior, 1(3), 157–283.Google Scholar
  12. Harré, R. (Ed.). (1986). The social construction of emotions. Oxford: Blackwell.Google Scholar
  13. Maturana, H. R. (1980). Man and society. In F. Benseler, P. M. Hejl, & W. F. Kock (Eds.), Autopoiesis, communication, and society (pp. 11–32). Frankfurt, Germany: Campus Verlag.Google Scholar
  14. Mehan, H., & Wood, H. (1975). The reality of ethnomethodology. New York: John Wiley.Google Scholar
  15. Perret-Clermont, A. N. (1980). Social interaction and cognitive development in children. New York: Academic Press.Google Scholar
  16. Schoenfeld, A. H. (1983). Beyond the purely cognitive: Belief systems, social cognitions, and metacognitions as driving forces in intellectual performance. Cognitive Science, 7, 329–363.CrossRefGoogle Scholar
  17. Schutz, A. (1962). The problem of social reality. The Hague, The Netherlands: Martinus Nijhoff.Google Scholar
  18. Voigt, J. (1985). Patterns and routines in classroom interaction. Recherches en Didactique des Mathematiques, 6, 69–118.Google Scholar
  19. Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27, 458–477.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Vanderbilt UniversityNashvilleUSA
  2. 2.Purdue University CalumetHammondUSA

Personalised recommendations