Positioning in mathematics education: revelations on an imported theory
- 1.1k Downloads
We develop theory within the field of mathematics education based on analysis of an imported theory—positioning theory—and the way it is used in the field. After summarizing positioning theory, we identify some conceptual fuzziness, particularly in core terms “positioning” and “storyline.” We offer Lemke’s idea of timescales as a way to refine the theory. We then use the refined theory to analyze strong examples from mathematics education literature as a source of insight into how this theory is being and could be used in the field. We identify the need to be clear about scale in describing positioning and storyline, to recognize that multiple storylines and positionings are at play in any interaction, to be specific about the role of communication acts in development of positioning and storyline, and to differentiate among different kinds of positioning. We claim that attention to these issues will help researchers recognize narratives and relationships at play that may be outside their expectation and also underpin stronger warranted claims.
KeywordsPositioning Positioning theory Storylines Timescales
This research was supported, in part, by the National Science Foundation (Grant No. #0918117, Herbel-Eisenmann, PI; Cirillo and Steele, co-PIs). Opinions, findings, and conclusions or recommendations expressed here are the authors’ and do not necessarily reflect the views of NSF. We would like to thank David Pimm, Anna Sfard, and two anonymous reviewers for their insights and feedback.
- Anderson, K. T. (2009). Applying positioning theory to the analysis of classroom interactions: Mediating micro-identities, macro-kinds, and ideologies of knowing. Linguistics and Education, 20(4), 291–310. doi: 10.1016/j.linged.2009.08.001.
- Banks, C. A. M., & Banks, J. A. (1995). Equity pedagogy: An essential component of multicultural education. Theory Into Practice, 34(3), 152–158.Google Scholar
- Barton, A. C., Kang, H., Tan, E., O’Neill, T. B., Bautista-Guerra, J., & Brecklin, C. (2012). Crafting a future in science: Tracing middle school girls’ identity work over time and space. American Educational Research Journal, 50(1), 37–75. doi: 10.3102/0002831212458142.
- Davies, B., & Harré, R. (1999). Positioning and personhood. In R. Harré & L. van Langenhove (Eds.), Positioning theory: Moral contexts of intentional action (pp. 32–52). Oxford, UK: Blackwell Publishers.Google Scholar
- de Freitas, E. (2008). Splitting teacher identity: The disjunction between personal narrative and procedural discourse in the mathematics classroom. In T. Brown (Ed.), The psychology of mathematics education: A psychoanalytic displacement (pp. 139–155). Rotterdam, The Netherlands: Sense Publishing.Google Scholar
- de Freitas, E. (2012). The diagram as story: Unfolding the event-structure of the mathematical diagram. For the Learning of Mathematics, 32(2), 27–33.Google Scholar
- Edwards, D. (1997). Discourse and cognition. London: Sage.Google Scholar
- Engle, R. A., & Conant, F. R. (2002). Guiding principles for fostering productive disciplinary engagement: Explaining an emergent argument in a community of learners classroom. Cognition and Instruction, 20(4), 399–483. doi: 10.1207/S1532690XCI2004_1.
- Epstein, D., Mendick, H., & Moreau, M.-P. (2010). Imagining the mathematician: Young people talking about popular representations of maths. Discourse: Studies in the Cultural Politics of Education, 31(1), 45–60. doi: 10.1080/01596300903465419.
- Esmonde, I. (2009). Mathematics learning in groups: Analyzing equity in two cooperative activity structures. Journal of the Learning Sciences, 18(2), 247–284. doi: 10.1080/10508400902797958.
- Esmonde, I., & Langer-Osuna, J. M. (2013). Power in numbers: Student participation in mathematical discussions in heterogeneous spaces. Journal for Research in Mathematics Education, 44(1), 288–315.Google Scholar
- Foote, M. Q., & Bartell, T. G. (2011). Pathways to equity in mathematics education: How life experiences impact researcher positionality. Educational Studies in Mathematics, 78, 45–68.Google Scholar
- Gee, J. P. (2011). An introduction to discourse analysis: Theory and method (3rd ed.). New York, NY: Routledge.Google Scholar
- Harré, R. (2012). Positioning theory: Moral dimensions of social-cultural psychology. In J. Valsiner (Ed.), The Oxford handbook of culture and psychology (pp. 191–206). NY: Oxford University Press.Google Scholar
- Harré, R., & Moghaddam, F. M. (2003). Introduction: The self and others in traditional psychology and in positioning theory. In R. Harré & F. M. Moghaddam (Eds.), The self and others: Positioning individuals and groups in personal, political, and cultural contexts (pp. 1–11). Westport, CT: Praeger.Google Scholar
- Harré, R., & van Langenhove, L. (Eds.). (1999a). Positioning theory: Moral contexts of intentional action. Oxford, UK: Blackwell Publishers.Google Scholar
- Harré, R., & van Langenhove, L. (1999b). The dynamics of social episodes. In R. Harré & L. van Langenhove (Eds.), Positioning theory: Moral contexts of intentional action (pp. 1–13). Malden, MA: Blackwell Publishers, Ltd.Google Scholar
- Herbel-Eisenmann, B., & Wagner, D. (2010). Appraising lexical bundles in mathematics classroom discourse: Obligation and choice. Educational Studies in Mathematics, 75(1), 43–63. doi: 10.1007/s10649-010-9240-y.
- Herbel-Eisenmann, B., Wagner, D., & Cortes, V. (2010). Lexical bundle analysis in mathematics classroom discourse: The significance of stance. Educational Studies in Mathematics, 75(1), 23–42. doi: 10.1007/s10649-010-9253-6.
- Holland, D., Lachiotte, W., Jr., Skinner, D., & Cain, C. (2001). Identity and agency in cultural worlds. Cambridge, MA: Harvard University Press.Google Scholar
- Jackson, A. (1997a). The math wars: California battles it out over mathematics education reform, part I. Notices of the AMS, 44(6), 695–702.Google Scholar
- Jackson, A. (1997b). The math wars: California battles it out over mathematics education reform, part II. Notices of the AMS, 44(7), 817–823.Google Scholar
- Johnson, K. R. (2013). Illuminating the identities of mathematics teachers and mathematics teacher educators. (Doctoral dissertation). Available from ProQuest Dissertations & Theses database. (UMI No. 3592117).Google Scholar
- Ju, M.-K., & Kwon, O. N. (2007). Ways of talking and ways of positioning: Students’ beliefs in an inquiry-oriented differential equations class. Journal of Mathematical Behavior, 26(3), 267–280. doi: 10.1016/j.jmathb.2007.10.002.
- Kress, G. (1993). Against arbitrariness: The social production of the sign as a foundational issue in critical discourse analysis. Discourse and Society, 4(2), 169–191.Google Scholar
- Lemke, J. L. (2000). Across the scales of time: Artifacts, activities, and meanings in ecosocial systems. Mind, Culture, and Activity, 7(4), 273–290.Google Scholar
- Moghaddam, F. M. (1999). Reflexive positioning: Culture and private discourse. In R. Harré & L. van Langenhove (Eds.), Positioning theory: Moral contexts of intentional action (pp. 74–86). Oxford, UK: Blackwell Publishers.Google Scholar
- Moghaddam, F. M., Harré, R., & Lee. (2008). Positioning and conflict: An introduction. In F. M. Moghaddam, R. Harré, & N. Lee (Eds.), Global conflict resolution through positioning analysis (pp. 3–20). New York: Springer.Google Scholar
- Moghaddam, F. M., Taylor, D. M., & Wright, S. C. (1993). Social psychology in cultural perspective. New York: Freeman.Google Scholar
- Morgan, C. (2012). Studying discourse implies studying equity. In B. Herbel-Eisenmann, J. Choppin, D. Wagner, & D. Pimm (Eds.), Equity in discourse for mathematics education: Theories, practices, and policies (pp. 181–192). New York: Springer.Google Scholar
- National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards. Reston, VA: NCTM.Google Scholar
- National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Reston, VA: NCTM.Google Scholar
- National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.Google Scholar
- Parks, A. N. (2010). Metaphors of hierarchy in mathematics education discourse: The narrow path. Journal of Curriculum Studies, 42(1), 79–97.Google Scholar
- Richardson Bruna, K., & Vann, R. (2007). On pigs and packers: Radically contextualizing a practice of science with Mexican immigrant students. Cultural Studies of Science Education, 2(1), 19–59. doi: 10.1007/s11422-006-9041-x.
- Suh, H., Theakston-Musselman, A., Herbel-Eisenmann, B., & Steele, M. D. (2013). Teacher positioning and agency to act: Talking about “low-level” students. In A. Superfine & M. Martinez (Eds.), Proceedings of the 35th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Chicago, IL: University of Illinois at Chicago.Google Scholar
- Turner, E., Domínguez, H., Maldonado, L., & Empson, S. (2013). English learners’ participation in mathematical discussion: Shifting positionings and dynamic identities. Journal for Research in Mathematics Education, 44(1), 199–234.Google Scholar
- van Langenhove, L., & Harré, R. (1999). Introducing positioning theory. In R. Harré & L. van Langenhove (Eds.), Positioning theory: moral contexts of intentional action (pp. 14–31). Oxford, UK: Blackwell Publishers.Google Scholar
- Yamakawa, Y., Forman, E., & Ansell, E. (2009). Role of positioning: the role of positioning in constructing an identity in a third grade mathematics classroom. In K. Kumpulainen, K. Hmelo-Silver, & M. César (Eds.), Investigating classroom interaction: methodologies in action (pp. 179–202). Rotterdam: Sense Publishers.Google Scholar