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Mathematics Education Research Journal

, Volume 28, Issue 2, pp 327–348 | Cite as

Examining equity of opportunities for learning mathematics through positioning theory

  • Sandi L. Tait-McCutcheon
  • Judith Loveridge
Original Article

Abstract

This exploratory study examined how two teachers from two New Zealand primary schools introduced and taught the same mathematics lesson to their lowest ability group of year 2 and 3 students. Emphasis was given to analysing the positioning of the teacher and students and the developing storylines and social acts from that positioning. Different positionings by teachers of themselves and their students led to inequitable opportunities for active and collaborative participation in the mathematics. The differences in pedagogy revealed through the use of positioning theory suggest that the way teachers positioned themselves and their students was more influential than the resources they were teaching with.

Keywords

Primary Numeracy Positioning Collaboration Participation Equity 

References

  1. Abrami, P. C., Lou, Y., Chambers, B., Poulsen, C., & Spence, J. (2000). Why should we group students within-class for learning? Educational Research and Evaluation, 6(2), 158–179.CrossRefGoogle Scholar
  2. Angrosino, M. V., & Mays de Perez, K. A. (2003). Rethinking observation from method to context. In N. K. Denzin & Y. S. Lincoln (Eds.), Collecting and interpreting qualitative materials (pp. 107–154). Thousand Oaks: Sage.Google Scholar
  3. Anthony, G., & Hunter, R. (2005). A window into mathematics classrooms: traditional to reform. New Zealand Journal of Educational Studies, 40(1), 25–43.Google Scholar
  4. Askew, M. (2011). Unscripted maths: emergence and improvisation. In J. Clark, B. Kissane, J. Mousley, T. Spencer, & S. Thornton (Eds.). Mathematics: traditions and [new] practices. Proceedings of the 34th annual conference of the Mathematics Education Research Group of Australasia and the 23rd biennial conference of the Australian Association of Mathematics Teachers (pp. 56-67). Alice Springs: Australia, MERGA.Google Scholar
  5. Attard, C. (2011). The influence of teachers on student engagement with mathematics during the middle years. In J. Clark, B. Kissane, J. Mousley, T. Spencer, & S. Thornton (Eds.). Mathematics: Traditions and [new] practices. Proceedings of the 34th annual conference of the Mathematics Education Research Group of Australasia and the 23rd biennial conference of the Australian Association of Mathematics Teachers (pp. 68-74). Alice Springs, Australia: MERGA.Google Scholar
  6. Babbie, E. (2007). The practice of social research (11th ed.). Belmont CA: Thomson.Google Scholar
  7. Barnes, M. (2004). The use of positioning theory in studying student participation in collaborative learning activities. Paper presented at the Annual Meeting of the Australian Association for Research in Education. Melbourne, Australia.Google Scholar
  8. Boaler, J. (2008). Promoting ‘relational equity’ and high mathematics achievement through an innovative mixed-ability approach. British Educational Research Journal, 34(2), 167–194.CrossRefGoogle Scholar
  9. Boaler, J. (2014). Ability grouping in mathematics classrooms. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 1–5). Netherlands: Springer.Google Scholar
  10. Boaler, J., Wiliam, D., & Brown, M. (2000). Students’ experiences of ability grouping: disaffection, polarisation and the construction of failure. British Educational Research Journal, 26, 631–648.CrossRefGoogle Scholar
  11. Bobis, J., Clarke, B., Clarke, D., Thomas, G., Wright, B., & Young-Loveridge, J. (2005). Supporting teachers in the development of young children’s mathematical thinking: three large scale cases. Mathematics Education Research Journal, 16(3), 27–57.CrossRefGoogle Scholar
  12. Brophy, J. (Ed.). (2002). Social constructivist teaching: affordances and constraints. Oxford, UK: Elsevier Science.Google Scholar
  13. Brophy, J. (2006). Graham Nuthall and social constructivist teaching: research-based cautions and qualifications. Teaching and Teacher Education, 22, 529–537.CrossRefGoogle Scholar
  14. Choppin, J. (2011). The impact of professional noticing on teachers’ adaptations of challenging tasks. Mathematical Thinking and Learning, 13(3), 175–197.CrossRefGoogle Scholar
  15. Cobb, P. (1994). Where is the mind? Constructivist and sociocultural perspectives on mathematical development. Educational Researcher, 23(7), 13–20.CrossRefGoogle Scholar
  16. Cobb, S. C. (2012). You use your imagination: an investigation into how students use ‘imaging’ during numeracy activities. University of Canterbury, Christchurch. Retrieved http://ir.canterbury.ac.nz/handle/10092/7168
  17. Cohen, L., Manion, L., & Morrison, K. (2007). Research methods in education (6th ed.). London: Routledge.Google Scholar
  18. Corbin, J., & Strauss, A. C. (2008). Basics of qualitative research: techniques and procedures for developing grounded theory (3rd ed.). Los Angeles, CA: Sage.Google Scholar
  19. Davies, B., & Harré, R. (1990). Positioning: the discursive production of selves. Journal for the Theory of Social Behaviour, 20(1), 43–63. doi: 10.1111/j.1468-5914.1990.tb00174.x.CrossRefGoogle Scholar
  20. 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: Blackwell.Google Scholar
  21. Denscombe, M. (2010). The good research guide for small-scale social research projects (4th ed.). England: Open University Press.Google Scholar
  22. Denzin, N. K., & Lincoln, Y. S. (Eds.). (2011). The sage handbook of qualitative research (4th ed.). Thousand Oaks: Sage.Google Scholar
  23. DfES. (2005). Higher standards, better schools for all: more choice for parents and pupils. London: DFES.Google Scholar
  24. Doyle, W., & Carter, K. (1984). Academic tasks in classrooms. Curriculum Inquiry, 14(2), 129–149.CrossRefGoogle Scholar
  25. Edwards, D. (1997). Discourse and cognition. London: Sage.Google Scholar
  26. Edwards, D., & Potter, J. (1992). Discursive psychology. London: Sage.Google Scholar
  27. Elia, I., Van den Heuvel-Panhuizen, M., & Kolovou, A. (2009). Exploring strategy use and strategy flexibility in non-routine problem solving by primary school high achievers in mathematics. ZDM Mathematics Education, 41, 605–618. doi: 10.1007/s11858-009-0184-6.CrossRefGoogle Scholar
  28. Ernest, P. E. (1996). Varieties of constructivism: a framework for comparison. In L. P. Steffe & P. Nesher (Eds.), Theories of mathematical learning (pp. 335–349). Mahwah, NJ: Lawrence Erlbaum.Google Scholar
  29. Ewing, B. (2011). Direct instruction in mathematics: issues for schools with high indigenous enrolments: a literature review. Australian Journal of Teacher Education, 36(5), 63–91.CrossRefGoogle Scholar
  30. Garden, R. (1996). Mathematics performance of New Zealand form 2 and form 3 students. National results from New Zealand’s participation in the Third International Mathematics and Science Study. Wellington, New Zealand: Ministry of Education.Google Scholar
  31. Garden, R. (1997). Mathematics and science in middle primary school: results from New Zealand’s participation in the Third International Mathematics and Science Study. Wellington: Research and International Section, Ministry of Education.Google Scholar
  32. Gillham, B. (2000). Case study research methods. New York: Continuum.Google Scholar
  33. Habibis, D. (2006). Ethics and social research. In M. Walter (Ed.), Social research methods: an Australian perspective (pp. 53–82). Melbourne, VA: Oxford University Press.Google Scholar
  34. Harré, R. (1997). Forward to Aristotle: a case for a hybrid ontology. Journal for the Theory of Social Behaviour, 27(2/3), 173–191.Google Scholar
  35. 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: Praeger.Google Scholar
  36. Harré, R., & Moghaddam, F.M. (2014). Positioning theory. In N. Bozatzis and T. Dragonas (Eds.) The discursive turn in social psychology (pp 129-138). Retrieved http://www.taosinstitute.net/Websites/taos/images/PublicationsWorldShare/DiscursiveTurn_f_v2.pdf#page=129
  37. Harré, R., & Secord, P. F. (1972). The explanation of social behaviour. Oxford: Blackwell.Google Scholar
  38. Harré, R., & Slocum, N. (2003). Disputes as complex social events: on the uses of positioning theory. In R. Harré & F. Moghaddam (Eds.), The self and others: positioning individuals and groups in personal, political, and cultural contexts (pp. 123–136). Westport: Praeger.Google Scholar
  39. Harré, R., & van Langenhove, L. (1991). Varieties of positioning. Journal for the Theory of Social Behaviour, 21(4), 393–407.CrossRefGoogle Scholar
  40. Harré, R., & van Langenhove, L. (1999). The dynamics of social episodes. In R. Harré & L. van Langenhove (Eds.), Positioning theory: moral contexts of intentional action (pp. 1–14). Oxford: Blackwell.Google Scholar
  41. Haylock, D. W. (1987). A framework for assessing mathematical creativity in school children. Educational Studies in Mathematics, 18(1), 59–74.CrossRefGoogle Scholar
  42. Herbel-Eisenmann, B. A., Wagner, D., Johnson, K. R., Suh, H., & Figueras, H. (2015). Positioning in mathematics education: revelations on an imported theory. Educational Studies in Mathematics, 89(2), 185–204. doi: 10.1007/s10649-014-9588-5.CrossRefGoogle Scholar
  43. Higgins, J., & Parsons, R. (2009). A successful professional development model in mathematics: a system-wide New Zealand case. Journal of Teacher Education, 60(3), 231–242.CrossRefGoogle Scholar
  44. Higgins, J., Irwin, K., Thomas, G., Trinick, T., & Young-Loveridge, J. (2005). Findings from the New Zealand Numeracy Development Project 2004. Wellington, New Zealand: Ministry of Education.Google Scholar
  45. Hollway, W. (1984). Gender difference and the production of subjectivity. In J. Henriques, W. Hollway, C. Urwin, L. Venn, & V. Walkerdine (Eds.), Changing the subject: psychology, social regulation and subjectivity. London: Methuen.Google Scholar
  46. Holt, G. (2001). Mathematics education for Māori students in mainstream classrooms. ACE Papers, 11, 18–29.Google Scholar
  47. Hunter, J. (2006). The Numeracy Project: foundations and development. ACE Papers, 17. Retrieved from http://www.education.auckland.ac.nz
  48. Johnson, M., Griffiths, D., & Wang, M. (2011). Positioning theory, roles and the design and implementation of learning technology. Journal of Universal Computer Science, 17(9), 1329–1346.Google Scholar
  49. Kolovou, A., Van Den Heuvel-Panhuizen, M., & Bakker, A. (2009). Non-routine problem solving tasks in primary school mathematics textbooks—a needle in a haystack. Mediterranean Journal for Research in Mathematics Education, 8(2), 31–68.Google Scholar
  50. Kutnick, P., Sebba, J., Blatchford, P., Galton, M., & Thorp, J. (2005). The effects of pupil grouping: literature review. London, DfES. Research Report 688.Google Scholar
  51. Lampert, M. (1990). When the problem is not the question and the solution is not the answer: mathematical knowing and teaching. American Educational Research Journal, 27, 29–63.CrossRefGoogle Scholar
  52. Lee, C. Y., & Chen, M. P. (2009). A computer game as a context for non-routine mathematical problem solving: the effects of type of question prompt and level of prior knowledge. Computers and Education, 52(3), 530–542.CrossRefGoogle Scholar
  53. Lincoln, Y. S., & Guba, E. G. (1985). Naturalistic inquiry. Beverly Hills, CA: Sage.Google Scholar
  54. MacIntyre, H., & Ireson, J. (2002). Within-class ability grouping: placement of pupils in groups and self concept. British Educational Research Journal, 28(2), 249–263.CrossRefGoogle Scholar
  55. Mamona-Downs, J., & Downs, M. (2005). The identity of problem solving. Journal of Mathematical Behaviour, 24(3-4), 385–401.CrossRefGoogle Scholar
  56. Marchis, J. (2012). Non-routine problems in primary mathematics workbooks from Romania. Acta Didactica Napocensia, 5(3), 49–56.Google Scholar
  57. Merriam, S. B. (1998). Qualitative research and case study applications in education (revised and expanded from case study research in education). San Francisco: Jossey-Bass.Google Scholar
  58. Merriam, S. B. (2009). Qualitative research: a guide to design and implementation (2nd ed.). San Francisco, CA: Jossey-Bass.Google Scholar
  59. Mertens, D. (2005). Research and evaluation in psychology: integrating diversity with quantitative, qualitative, and mixed methods (2nd ed.). Thousand Oaks, CA: Sage.Google Scholar
  60. Ministry of Education. (2007a). Numeracy Professional Development Projects: book 5: teaching addition and subtraction. New Zealand: Wellington.Google Scholar
  61. Ministry of Education. (2007b). Numeracy Professional Development Projects: book 1: the number framework. New Zealand: Wellington.Google Scholar
  62. Ministry of Education. (2007c). Numeracy Professional Development Projects: book 3: getting started. New Zealand: Wellington.Google Scholar
  63. Moghaddam, F., Harré, R., & Lee, N. (2008). Positioning and conflict: an introduction. In F. Moghaddam, R. Harré, & N. Lee (Eds.), Global conflict resolution through positioning analysis (pp. 3–20). New York: Springer.CrossRefGoogle Scholar
  64. Muhlhauser, P., & Harré, R. (1990). Pronouns and people. Oxford: Blackwell.Google Scholar
  65. Mullis, I. V. S., Martin, M. O., Smith, T. A., Garden, R. A., Gregory, K. D., Gonzalez, E. J., et al. (2003). TIMSS assessment frameworks and specifications 2003 (2nd ed.). Chestnut Hill, MA: Boston College.Google Scholar
  66. Murphy, J. (1988). Equity as student opportunity to learn. Theory Into Practice, 27(2), 145–151.CrossRefGoogle Scholar
  67. Murphy, C. (2013). Thinkpiece: making space for mathematics learning to happen in group work: is this really possible? Teachers and Curriculum, 13, 108–111.CrossRefGoogle Scholar
  68. O’Keeffe, L., & O’Donoghue, J. (2011). A review of school textbooks for project maths. Retrieved http://www.nce-stl.ie/_fileupload/Reports/Project%20Maths%20Textbook%20Report%20November%202012.pdf
  69. Partington, G. (2001). Qualitative research interviews: identifying problems in technique. Issues in Educational Research, 11(2), 32–44.Google Scholar
  70. Powell, A. B., Francisco, J. M., & Maher, C. A. (2003). An analytical model for studying the development of learners’ mathematical ideas and reasoning using videotape data. Journal of Mathematical Behaviour, 22(4), 405–435.CrossRefGoogle Scholar
  71. Redman, C., & Fawns, R. (2010). How to use pronoun grammar as a methodological tool for understanding the dynamic lived space of people. In S. Rodrigues (Ed.), Using analytical frameworks for classroom research: collecting data and analysing narrative (pp. 163–182). New York: Routledge.Google Scholar
  72. Rogoff, B. (1990). Apprenticeship in thinking: cognitive development in social context. New York: Oxford University Press.Google Scholar
  73. Scouller, D. (2009). Has strategy become the new algorithm? The New Zealand Mathematics Magazine, 46(3), 1–11.Google Scholar
  74. Sfard, A. (2000). Symbolizing mathematical reality into being—or, how mathematical discourse and mathematical objects can create each other. In P. Cobb, E. Yackel, & K. McClain (Eds.), Symbolizing and communicating in mathematical classrooms: perspectives on discourse, tools and mathematical design (pp. 37–98). Mahwah, NJ: Erlbaum.Google Scholar
  75. Slocum-Bradley, N. (2010). The positioning diamond: a trans-disciplinary framework for discourse analysis. Journal for the Theory of Social Behaviour, 40(1), 79–107.CrossRefGoogle Scholar
  76. Smith, M. S., & Stein, M. K. (2011). Five practices for orchestrating productive mathematics discussions. Reston, VA: NCTM.Google Scholar
  77. Tait-McCutcheon, S. (2014). Teacher practice in primary mathematics classrooms: a story of positioning (unpublished doctoral thesis). Wellington, New Zealand: Victoria University of Wellington.Google Scholar
  78. Teong, S. K., Hedberg, J. G., Ho, K. F., Lioe, L. T., Tiong, Y. S. J., Wong, K. Y. & Fang, Y. P. (2009). Developing the repertoire of heuristics for mathematical problem solving: project 1. Final Technical Report for Project CRP1/04 JH. Singapore: Centre for Research in Pedagogy and Practice, National Institute of Education, Nanyang Technological University. http://hdl.handle.net/10497/4151.
  79. Thomas, G., & Tagg, A. (2004). An evaluation of the Early Numeracy Project 2003. Wellington, New Zealand: Ministry of Education.Google Scholar
  80. 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: Blackwell.Google Scholar
  81. Varela, C. R., & Harré, R. (1996). Conflicting varieties of realism: causal powers and the problems of social structure. Journal for the Theory of Social Behaviour, 26(3), 313–325.CrossRefGoogle Scholar
  82. von Glasersfeld, E. (1992). Aspects of radical constructivism and its educational recommendations. Paper presented at the ICME-7, Draft to working group #4, Montreal. Retrieved from www.umass.edu/srri/vonGalsersfeld/onlinePapers/html/195.html
  83. Wagner, D., & Herbel-Eisenmann, B. (2009). Re-mythologizing mathematics through attention to classroom positioning. Educational Studies in Mathematics, 72(1), 1–15.CrossRefGoogle Scholar
  84. Waite, L. (2014). Mathematics or numeracy: education indications from Steiner and the New Zealand curriculum (Doctoral dissertation, Auckland University of Technology).Google Scholar
  85. Walshaw, M., & Anthony, G. (2006). Classroom arrangements that benefit students. In 29th annual conference of the Mathematics Education Research Group of Australasia. Identities cultures and learning spaces. Canberra, Australia: MERGA.Google Scholar
  86. Wittgenstein, L. (1953). Philosophical investigations. Oxford, England: Blackwell.Google Scholar
  87. Wittgenstein, L. (1969). On certainty. (Trans. D. Paul & G. E. M. Anscombe). Oxford: Blackwell.Google Scholar
  88. Yin, R. K. (2003). Case study research, design and methods. Thousand Oaks: Sage.Google Scholar
  89. Young-Loveridge, J. (2010). A decade of reform in mathematics education: results for 2009 and earlier years. In Findings from the New Zealand Numeracy Development Projects: 2009 (pp. 15–35). Wellington, New Zealand: Learning Media.Google Scholar

Copyright information

© Mathematics Education Research Group of Australasia, Inc. 2016

Authors and Affiliations

  1. 1.Victoria University of WellingtonWellingtonNew Zealand

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