Abstract
Research in mathematics education is a discursive process: It entails the analysis and production of texts, whether in the analysis of what learners say, the use of transcripts, or the publication of research reports. Much research in mathematics education is concerned with various aspects of mathematical thinking, including mathematical knowing, understanding and learning. In this paper, using ideas from discursive psychology, I examine the discursive construction of mathematical thinking in the research process. I focus, in particular, on the role of researchers’ descriptions. Specifically, I examine discursive features of two well-known research papers on mathematical thinking. These features include the use of contrast structures, categorisation and the construction of facts. Based on this analysis, I argue that researchers’ descriptions of learners’ or researchers’ behaviour and interaction make possible subsequent accounts of mathematical thinking.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
This observation derives from a similar one originally made in sociology in the 1960s by Garfinkel (1967), which led to the development of ethnomethodology:
[...] Garfinkel demonstrates that social knowledge cannot be adequately characterized in the form of statistically countable, abstract categories such as scalar ratings of role, status or personality characteristics. He argues that social knowledge is revealed in the process of interaction itself and that interactants create their own social world by the way in which they behave. He then goes on to suggest that sociology should concentrate on describing the mechanisms by which this is done in what he calls ‘naturally organized activities’, rather than in staged experiments or interview elicitations. (Gumperz, 1982, p. 158)
Discursive psychology can be seen as the application of ethnomethodology to psychological questions.
References
Barwell, R. (2008). Discourse, mathematics and mathematics education. In M. Martin-Jones, A.-M. de Mejia & N. Hornberger (Eds.), Encyclopedia of language and education, vol. 3: Discourse and education (2nd ed., pp. 317–328). New York: Springer.
Edwards, D. (1993). But what do children really think? Discourse analysis and conceptual content in children’s talk. Cognition and Instruction, 11(3&4), 207–225.
Edwards, D. (1997). Discourse and cognition. London: Sage.
Edwards, D. (2006). Discourse, cognition and social practices: The rich surface of language and social interaction. Discourse Studies, 8(1), 41–49.
Edwards, D., & Potter, J. (1992). Discursive psychology. London: Sage.
Garfinkel, H. (1967). Studies in ethnomethodology. Englewood Cliffs: Prentice Hall.
Gumperz, J. J. (1982). Discourse strategies. Cambridge: Cambridge University Press.
Gray, E. M. (1991). An analysis of diverging approaches to simple arithmetic: Preference and its consequences. Educational Studies in Mathematics, 22, 551–574.
Gray, E. M., & Tall, D. O. (1994). Duality, ambiguity, and flexibility: A ‘proceptual’ view of simple arithmetic. Journal for Research in Mathematics Education, 25(2), 116–140.
Kieran, C., Forman, E., & Sfard, A. (2001). Learning discourse: Discursive approaches to research in mathematics education. Dordrecht: Kluwer.
Lerman, S. (2001). Cultural, discursive psychology: A sociocultural approach to studying the teaching and learning of mathematics. Educational Studies in Mathematics, 46(1–3), 87–113.
Moschkovich, J. (2003). Examining mathematical discourse practices. For the Learning of Mathematics, 27(1), 24–30.
Ochs, E. (1979). Transcription as theory. In E. Ochs & B. B. Schiffelin (Eds.), Developmental pragmatics (pp. 43–72). New York: Academic.
Potter, J. (2003). Discursive psychology: between method and paradigm. Discourse and Society, 14(6), 783–794.
Sfard, A. (2001). There is more to discourse than meets the ears: Looking at thinking as communicating to learn more about mathematical learning. Educational Studies in Mathematics, 46(1–3), 13–57.
Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. Cambridge: Cambridge University Press.
Smith, D. E. (1978). ‘K is mentally ill’: The anatomy of a factual account. Sociology, 12(1), 23–53.
Te Molder, H., & Potter, J. (2005). Conversation and cognition. Cambridge: Cambridge University Press.
Walkerdine, V. (1988). The mastery of reason. Cognitive development and the production of rationality. London: Routledge.
Wertsch, J. V. (1991). Voices of the mind. A sociocultural approach to mediated action. Cambridge: Harvard University Press.
Wetherell, M. (2007). A step too far: Discursive psychology, linguistic ethnography and questions of identity. Journal of Sociolinguistics, 11(5), 661–681.
Wetherell, M., & Potter, J. (1992). Mapping the language of racism: Discourse and the legitimation of exploitation. London: Harvester Wheatsheaf.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Barwell, R. Researchers’ descriptions and the construction of mathematical thinking. Educ Stud Math 72, 255–269 (2009). https://doi.org/10.1007/s10649-009-9202-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10649-009-9202-4