# Re-mythologizing mathematics through attention to classroom positioning

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## Abstract

With our conceptualization of Harré and van Langenhove’s (1999) positioning theory, we draw attention to immanent experience and read transcendent discursive practices through the moment of interaction. We use a series of spatial images as metaphors to analyze the way positioning is conceptualized in current mathematics education literature and the way it may be alternatively conceptualized. This leads us to claim that changing the way mathematics is talked about and changing the stories (or myths) told about mathematics is necessary for efforts to change the way mathematics is done and the way it is taught.

## Keywords

Agency Disposition Ethnomathematics Identity Immanence Mathematics education Positioning theory Socio-cultural Transcendence## Notes

### Acknowledgments

We thank Richard Barwell for his feedback on an earlier draft of this article. The work was part of an NSF grant (#0347906) entitled “CAREER: Discourse analysis: A catalyst for reflective inquiry in mathematics classrooms” (Herbel-Eisenmann, PI), and an SSHRC grant entitled “Positioning and Authority in Mathematics Classrooms” (Wagner, PI). Any opinions, findings, and conclusions or recommendations expressed in this article are those of the authors and do not necessarily reflect the views of NSF or SSHRC.

## References

- Abbott, E. (1884).
*Flatland: A romance of many dimensions*. London: Seeley.Google Scholar - Adler, J. (2001).
*Teaching mathematics in multilingual classrooms*. Dordrecht: Kluwer.Google Scholar - Ainley, J. (1988). Perceptions of teachers’ questioning styles. In A. Borbás (Ed.),
*Proceedings of the 12th Conference of the International Group for the Psychology of Mathematics Education, vol. I*(pp. 92–99). Hungary: Vezsprém.Google Scholar - Banks, C. A. M., & Banks, J. (1995). Equity pedagogy: an essential component of multicultural education.
*Theory into Practice*,*34*(3), 152–158.CrossRefGoogle Scholar - Cabral, T., & Baldino, R. (2002). Lacanian psychoanalysis and pedagogical transfer: Affect and cognition. In A. Cockburn, & E. Nardi (Eds.),
*Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education, vol. 2*(pp. 169–176). UK: Norwich.Google Scholar - Cobb, P., Yackel, E., & Wood, T. (1993). Theoretical orientation. In T. Wood, P. Cobb, E. Yackel, & D. Dillon (Eds.),
*Rethinking elementary school mathematics: Insights and issues*,*monograph #6*. Reston: NCTM.Google Scholar - Cohen, D. K., & Ball, D. L. (1999). Instruction, capacity, and improvement.
*CPRE Research Report*. Available at: http://www.cpre.org/images/stories/cpre_pdfs/rr43.pdf. - D’Ambrosio, U. (2006).
*Ethnomathematics: Link between traditions and modernity*. Sense: Rotterdam.Google Scholar - Davies, B., & Harré, R. (1999). Positioning and personhood. In R. Harré, & L. van Langenhove (Eds.),
*Positioning theory: Moral contexts of intentional action*(pp. 32–51). Blackwell: Oxford.Google Scholar - Edwards, D. (1997).
*Discourse and cognition*. London: Sage.Google Scholar - Evans, J. (2000).
*Adults mathematical thinking and emotions: A study of numerate practice*. London: Routledge/Falmer.Google Scholar - Gates, P. (2006). Going beyond belief systems: exploring a model for the social influence on mathematics teacher beliefs.
*Educational Studies in Mathematics*,*63*, 347–369. doi: 10.1007/s10649-005-9007-z.CrossRefGoogle Scholar - Goodwin, C. (2007). Participation, stance and affect in the organization of activities.
*Discourse & Society*,*18*(1), 53–73. doi: 10.1177/0957926507069457.CrossRefGoogle Scholar - Goffman, E. (1981).
*Forms of talk*. Philadelphia: University of Philadelphia Press.Google Scholar - Gresalfi, M., & Cobb, P. (2006). Cultivating students’ discipline-specific dispositions as a critical goal for pedagogy and equity.
*Pedagogies: An International Journal*,*1*(1), 49–57. doi: 10.1207/s15544818ped0101_8.CrossRefGoogle Scholar - Harré, R., & van Langenhove, L. (1999).
*Positioning theory: Moral contexts of intentional action*. Oxford: Blackwell.Google Scholar - Herbel-Eisenmann, B. (2007). From intended curriculum to written curriculum: Examining the “voice” of a mathematics textbook.
*Journal for Research in Mathematics Education*,*38*(4), 344–369.CrossRefGoogle Scholar - Herbel-Eisenmann, B. (2009). Negotiation of the “presence
*of*the text”: How might teachers’ language choices influence the positioning of the textbook? In J. Remillard, B. Herbel-Eisenmann, & G. Lloyd. (Eds.),*Mathematics teachers at work: Connecting curriculum materials and classroom instruction*(pp. 134–151). Studies in Mathematical Thinking and Learning (A. Schoenfeld, Series Editor). New York: Routledge.Google Scholar - Herbel-Eisenmann, B., & Wagner, D. (2007). A framework for uncovering the way a textbook may position the mathematics learner.
*For the Learning of Mathematics*,*27*(2), 8–14.Google Scholar - Herbel-Eisenmann, B., Wagner, D., & Cortes, V. (2008). Encoding authority: Pervasive lexical bundles in mathematics classrooms.
*Proceedings of the 32nd Conference of the International Group for the Psychology of Mathematics Education held jointly with the 30th Conference of PME-NA*, Morelia, Mexico, vol. 3, pp. 153–160.Google Scholar - Holland, D., Lachicotte, W., Skinner, D., & Cain, C. (1998).
*Identity and agency in cultural worlds*. Cambridge: Harvard University Press.Google Scholar - Juzwik, M. (2006). Situating narrative-minded research: a response to Anna Sfard’s and Anna Prusak’s ‘Telling identities’.
*Educational Researcher*,*25*(9), 13–21.CrossRefGoogle Scholar - Lerman, S. (2001). Cultural, discursive psychology: a sociocultural approach to studying the teaching and learning of mathematics.
*Educational Studies in Mathematics*,*46*, 87–113.CrossRefGoogle Scholar - Mendick, H. (2005). A beautiful myth? The gendering of being/doing ‘good at maths’.
*Gender and Education*,*17*(2), 203–219.CrossRefGoogle Scholar - Moll, L., Amanti, C., Neff, D., & Gonzalez, N. (1992). Funds of knowledge for teaching: using a qualitative approach to connect homes and classrooms.
*Theory and Practice*,*31*, 132–141.Google Scholar - Morgan, C. (2006). What does social semiotics have to offer mathematics education research?
*Educational Studies in Mathematics*,*61*, 219–245.CrossRefGoogle Scholar - Nasir, N., & Saxe, G. (2003). Ethnic and academic identities: a cultural practice perspective on emerging tensions and their management in the lives of minority students.
*Educational Researcher*,*32*(5), 14–18.CrossRefGoogle Scholar - O’Connor, M., & Michaels, S. (1993). Aligning academic task and participation status through revoicing: analysis of a classroom discourse strategy.
*Anthropology and Education Quarterly*,*24*(4), 318–335.CrossRefGoogle Scholar - O'Halloran, K. (2004). Discourses in secondary school mathematics classrooms according to social class and gender. In J. A. Foley (Ed.),
*Language*,*education and discourse: functional approaches*(pp. 191–225). New York: Continuum.Google Scholar - Rittenhouse, P. (1998). The teacher's role in mathematical conversation: Stepping in and stepping out. In M. Lampert, & M. L. Blunk (Eds.),
*Talking mathematics in school: Studies of teaching and learning*. New York: Cambridge University Press.Google Scholar - Sfard, A. (2001). There is more to discourse than meets the ears: looking at thinking as communicating to learn more about mathematics learning.
*Educational Studies in Mathematics*,*46*, 13–57.CrossRefGoogle Scholar - Sensevy, G., Schubauer-Leoni, M., Mercier, A., Ligozat, F., & Perrot, G. (2005). An attempt to model the teacher’s action in the mathematics class.
*Educational Studies in Mathematics*,*59*, 153–181.CrossRefGoogle Scholar - Tholander, M., & Aronsson, K. (2003). Doing subteaching in school group work: positionings, resistance and participation frameworks.
*Language and Education*,*17*(3), 208–234.CrossRefGoogle Scholar - van Langenhove, L., & Harré, R. (1999). Introducing positioning theory. In R. Harré, & L. van Lagenhove (Eds.),
*Positioning theory: Moral contexts of intentional action*(pp. 14–31). Blackwell: Oxford.Google Scholar - Wagner, D. (2007). Students’ critical awareness of voice and agency in mathematics classroom discourse.
*Mathematical Thinking and Learning*,*9*(1), 31–50.CrossRefGoogle Scholar - Wagner, D. (2008). ‘Just go’: mathematics students' critical awareness of routine procedure.
*Canadian Journal of Science, Mathematics and Technology Education*, 8(1), 35–48.CrossRefGoogle Scholar - Wagner, D., & Herbel-Eisenmann, B. (2008). ‘Just don’t:’ the suppression and invitation of dialogue in the mathematics classroom.
*Educational Studies in Mathematics*,*67*(2), 143–157.CrossRefGoogle Scholar - Walkerdine, V. (1988).
*The mastery of reason: cognitive development and the production of rationality*. London: Routledge.Google Scholar - Zevenbergen, R. (2001). Mathematics, social class, and linguistic capital: An analysis of mathematics classroom interactions. In B. Atweh, H. J. Forgasz, & B. Nebres (Eds.),
*Sociocultural research on mathematics education*(pp. 201–215). Mahwah: Lawrence Erlbaum Associates.Google Scholar