Advertisement

Mathematics Education Research Journal

, Volume 24, Issue 3, pp 323–346 | Cite as

“They’re gonna explain to us what makes a cube a cube?” Geometrical properties as contingent achievement of sequentially ordered child-centered mathematics lessons

  • Wolff-Michael Roth
  • Rod Gardener
Original Article
First Online:

Abstract

In mathematics education, there is a continuing debate about the nature of mathematics, which some claim to be an objective science, whereas others note its socially and individually constructed nature. From a strict cultural–historical perspective, the objective and subjective sides of mathematics are but manifestations of a higher-order phenomenon that may be summarized by the aphorism that mind is in society to the extent that society is in the mind. In this study, we show, drawing on exemplifying materials from a second-grade unit on three-dimensional geometry, how mathematics manifests itself both as objective science all the while being subjectively produced. A particular three-turn interactional sequence comes to play a central role. We conclude by re-assigning a positive role to a much-maligned sequentially ordered conversational routine.

Keywords

Vygotsky Husserl Cultural re/production IRE Conversation analysis Ethnomethodology Higher psychological functions Material relations 
This is a preview of subscription content, log in to check access.

Notes

Acknowledgments

The data collection was supported by a grant from the Social Sciences and Humanities Research Council of Canada. The authors thank the children and teachers for their participation. We also thank the members of the Transcription Analysis Group (TAG)—which brings together scholars from the University of Queensland, Queensland University of Technology, and Griffith University for the purpose of interactively analyzing data—for their comments on the data and to our developing ideas.

References

  1. Bourdieu, P. (1992). The practice of reflexive sociology (The Paris workshop). In P. Bourdieu & L. J. D. Wacquant (Eds.), An invitation to reflexive sociology (pp. 216–260). Chicago: University of Chicago Press.Google Scholar
  2. Cazden, C. B. (2001). Classroom discourse. Portsmouth: Heineman.Google Scholar
  3. Collins, R. (2004). Interaction ritual chains. Princeton: Princeton University Press.Google Scholar
  4. Durkheim, E. (1893). De la division du travail. Livres II et III [On the division of labor. Books 2 and 3]. Paris: Felix Alcan.Google Scholar
  5. Durkheim, E. (1919). Les règles de la méthode sociologique septième édition [Rules of sociological method 7th ed.]. Paris: Felix Alcan.Google Scholar
  6. Gardner, R. (2001). When listeners talk. Amsterdam: John Benjamins.Google Scholar
  7. Gardner, R. (2012). Conversation analysis in the classroom. In T. Stivers & J. Sidnell (Eds.), The handbook of conversation analysis. Oxford: Wiley.Google Scholar
  8. Garfinkel, H. (1967). Studies in ethnomethodology. Englewood Cliffs: Prentice-Hall.Google Scholar
  9. Garfinkel, H. (1996). Ethnomethodology’s program. Social Psychology Quarterly, 59, 5–21.CrossRefGoogle Scholar
  10. Garfinkel, H. (2002). Ethnomethodology’s program: Working out Durkheim’s aphorism. Lanham: Rowman & Littlefield.Google Scholar
  11. Garfinkel, H., & Sacks, H. (1986). On formal structures of practical action. In H. Garfinkel (Ed.), Ethnomethodological studies of work (pp. 160–193). London: Routledge.Google Scholar
  12. Greiffenhagen, C. (2008). Video analysis of mathematical practice? Different attempts to open up mathematics for sociological investigation. FQS: Forum Qualitative Sozialforschung / Forum Qualitative Social Research, 9(3). http://nbn-resolving.de/urn:nbn:de:0114-fqs0803323. Accessed 1 April 2012.
  13. Greiffenhagen, C., & Sharrock, W. (2006). Mathematical relativism: logic, grammar, and arithmetic in cultural comparison. Journal for the Theory of Social Behaviour, 36, 97–117.CrossRefGoogle Scholar
  14. Greiffenhagen, C., & Sharrock, W. (2008). School mathematics and its everyday other? Revisiting Lave’s “cognition in practice”. Educational Studies in Mathematics, 69, 1–21.CrossRefGoogle Scholar
  15. Husserl, E. (1939). Die Frage nach dem Ursprung der Geometrie als intentional–historisches problem [The question of the origin of geometry as intentional–historical problem]. Revue Internationale de Philosophie, 1, 203–225.Google Scholar
  16. Husserl, E. (1976). Husserliana Band III/1. Ideen zu einer reinen Phänomenologie und phänomenologischen Philosophie: Erstes Buch: Allgemeine Einführung in die reine Phänomenologie. The Hague: Martinus Nijhoff [Husserliana vol. III/1. Ideas to a pure phenomenology and phenomenological philosophy vol 1. General introduction to a pure phenomenology].Google Scholar
  17. Koshik, I. (2002). Designedly incomplete utterances: a pedagogical practice for eliciting knowledge displays in error correction sequences. Research on Language and Social Interaction, 35, 277–309.CrossRefGoogle Scholar
  18. Lee, Y.-A. (2007). Third turn position in teacher talk: contingency and the work of teaching. Journal of Pragmatics, 39, 180–206.CrossRefGoogle Scholar
  19. Leont’ev, A. N. (1983). Dejatel’nost’. Soznanie. Ličnost’. [Activity, consciousness, personality]. In Izbrannye psixhologičeskie proizvedenija vol. 2 (pp. 94–231). Moscow: Pedagogika.Google Scholar
  20. Lerman, S. (1998). Research on socio-cultural perspectives of mathematics teaching and learning. In A. Sierpinska & J. Kilpatrick (Eds.), Mathematics education as a research domain: a search for identity. An ICMI study book 2 (pp. 333–350). Dordrecht: Kluwer Academic Publishers.CrossRefGoogle Scholar
  21. Lerman, S. (2000). The social turn in mathematics education research. In J. Boaler (Ed.), Multiple perspectives on mathematics teaching and learning (pp. 19–44). Westport: Ablex.Google Scholar
  22. Livingston, E. (1986). The ethnomethodological foundation of mathematics. London: Routledge.Google Scholar
  23. Mannheim, K. (2004). Beiträge zur Theorie der Weltanschauungs-Interpretation [Contributions to the theory of worldview interpretation]. In J. Strübing & B. Schnettler (Eds.), Methodologie interpretativer Sozialforschung: Klassische Grundlagentexte (pp. 103–153). Konstanz: UVK.Google Scholar
  24. Poole, D. (1994). Routine testing practices and the linguistic construction of knowledge. Cognition and Instruction, 12, 125–150.CrossRefGoogle Scholar
  25. Roth, W.-M. (2011). Geometry as objective science in elementary classrooms: mathematics in the flesh. New York: Routledge.Google Scholar
  26. Roth, W.-M., & Radford, L. (2010). Re/thinking the zone of proximal development (symmetrically). Mind, Culture, and Activity, 17, 299–307.CrossRefGoogle Scholar
  27. Roth, W.-M., & Thom, J. (2009a). Bodily experience and mathematical conceptions: from classical views to a phenomenological reconceptualization. Educational Studies in Mathematics, 70, 175–189.CrossRefGoogle Scholar
  28. Roth, W.-M., & Thom, J. (2009b). The emergence of 3d geometry from children's (teacher-guided) classification tasks. The Journal of the Learning Sciences, 18, 45–99.CrossRefGoogle Scholar
  29. Selting, M., Auer, P., Barden, B., Bergmann, J., Couper-Kuhlen, E., Günthner, S., Meier, C., Quasthoff, U., Schlobinski, P., & Uhmann, S. (1998). Gesprächsanalytisches Transkriptionssystem [Conversation analytic transcription system]. Linguistische Berichte, 173, 91–122.Google Scholar
  30. Vološinov, V. N. (1930). Marksizm i folosofija jazyka: osnovye problemy sociologičeskogo metoda b nauke o jazyke [Marxism and the philosophy of language: main problems of the sociological method in linguistics]. Leningrad: Priboj.Google Scholar
  31. Vygotskij, L. S. (2005). Psyxhologija razvitija čeloveka [Psychology of human development]. Moscow: Eksmo.Google Scholar
  32. Vygotsky, L. S. (1978). Mind in society: the development of higher psychological processes. Cambridge: Harvard University Press.Google Scholar
  33. Yackel, E., Gravemeijer, K., & Sfard, A. (2011). A journey in mathematics education research. Dordrecht: Springer.Google Scholar

Copyright information

© Mathematics Education Research Group of Australasia, Inc. 2012

Authors and Affiliations

  1. 1.Griffith Institute of Educational ResearchGriffith UniversityMt. GravattAustralia
  2. 2.School of Education and Professional StudiesGriffith UniversityMt. GravattAustralia

Personalised recommendations

Cite article

Buy options