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Mathematics Education Research Journal

, Volume 25, Issue 4, pp 481–502 | Cite as

Utilising a construct of teacher capacity to examine national curriculum reform in mathematics

  • Qinqiong Zhang
  • Max Stephens
Original Article
First Online:

Abstract

This study involving 120 Australian and Chinese teachers introduces a construct of teacher capacity to analyse how teachers help students connect arithmetic learning and emerging algebraic thinking. Four criteria formed the basis of our construct of teacher capacity: knowledge of mathematics, interpretation of the intentions of official curriculum documents, understanding of students’ thinking, and design of teaching. While these key elements connect to what other researchers refer to as mathematical knowledge for teaching, several differences are made clear. Qualitative and quantitative analyses show that our construct was robust and effective in distinguishing between different levels of teacher capacity.

Keywords

Algebra Cross-cultural studies Curriculum development Number concepts Teacher capacity Mathematical knowledge for teaching 
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References

  1. Australian Curriculum, Assessment and Reporting Authority (2010). The Australian curriculum: Mathematics. Sydney: Author.Google Scholar
  2. Ball, D., & Cohen, D. (1996). Reform by the book: what is–or might be–the role of curriculum materials in teacher learning and instructional reform? Educational Researcher, 25(14), 6–8.Google Scholar
  3. Ball, D., Thames, M., & Phelps, G. (2008). Content knowledge for teaching: what makes it special? Journal of Teacher Education, 59, 389–407.CrossRefGoogle Scholar
  4. Christie, K. (2001). Learning from the experience of others. Phi Delta Kappan, 83, 105–106.Google Scholar
  5. Cohen, D., & Ball, D. (1990). Policy and practice: an overview. Educational Evaluation and Policy Analysis, 12(3), 233–239.Google Scholar
  6. Datnow, A., & Castellano, M. (2001). Teachers’ responses to success for all: how beliefs, experiences and adaptations shape curriculum. American Educational Research Journal, 37, 775–800.CrossRefGoogle Scholar
  7. Department of Education and Early Childhood Development (2006). Mathematics developmental continuum. Melbourne: author.Google Scholar
  8. Department of Education and Early Childhood Development (2009a). National partnerships. http://www.education.vic.gov.au/about/directions/nationalpartnerships/matterschools/leadteach.htm, last accessed 12 December, 2011.
  9. Department of Education and Early Childhood Development (2009b). Key characteristics of effective numeracy teaching P-6. Melbourne: author.Google Scholar
  10. Fennema, E., & Franke, M. (1992). Teachers’ knowledge and its impact. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 147–164). New York: Macmillan.Google Scholar
  11. Fennema, E., Carpenter, T., & Franke, M. (1992). Cognitively guided instruction. The Teaching and Learning of Mathematics, 1(2), 5–9.Google Scholar
  12. Floden, R., Goertz, M., & O’Day, J. (1996). Capacity building in systemic reform. Phi Delta Kappan, 77(1), 19–21.Google Scholar
  13. Fullan, M. (2010). All systems go: The change imperative for whole system reform. Thousand Oaks: Corwin Press.Google Scholar
  14. Fullan, M. (2011). Change leader. New York: Wiley.Google Scholar
  15. Grossman, P., Wilson, S., & Shulman, L. (1989). Teachers of substance: Subject matter knowledge for teaching. In M. Reynolds (Ed.), The knowledge base for beginning teachers (pp. 23–36). New York: Pergamon.Google Scholar
  16. Hill, H., Ball, D., & Schilling, S. (2008). Unpacking pedagogical content knowledge: conceptualizing and measuring teachers’ topic-special knowledge of students. Journal for Research in Mathematics Education, 39(4), 372–400.Google Scholar
  17. Hodgen, J. (2011). Knowing and identity: A situated theory of mathematics teacher knowledge. In T. Rowland & K. Ruthven (Eds.), Mathematical knowledge in teaching (pp. 27–42). Dordrecht: Springer.CrossRefGoogle Scholar
  18. Irwin, K., & Britt, M. (2005). The algebraic nature of students’ numerical manipulation in the New Zealand Numeracy Project. Educational Studies in Mathematics, 58, 169–188.CrossRefGoogle Scholar
  19. Jacobs, V., Franke, M., Carpenter, T., Levi, L., & Battey, D. (2007). Developing children’s algebraic reasoning. Journal for Research in Mathematics Education, 38(3), 258–288.Google Scholar
  20. Katz, J., & Raths, D. (1985). Dispositions as goals for teacher education. Teaching and Teacher Education, 1(4), 301–307.CrossRefGoogle Scholar
  21. McDiarmid, B. (2006). Rethinking teacher capacity. http://scimath.unl.edu/MIM/rew2006/Powerpoints/REW06McDiarmid.ppt, last accessed 1 December 2011.
  22. Ministry of Education of PRC. (2001). Mathematics curriculum standards for compulsory education. Beijing: Beijing Normal University Press.Google Scholar
  23. Ministry of Education of PRC. (2011). Mathematics curriculum standards for compulsory education. Beijing: Beijing Normal University Press.Google Scholar
  24. NSW Smarter Schools National Partnerships (2010). Smarter schools national partnerships on improving teacher quality. http://www.nationalpartnerships.nsw.edu.au/resources/documents/ITQ-HAT-DETGuidelines.pdf, last accessed 5 August 2011.
  25. O’Day, J., Goertz, M., Floden, R. (1995). Building capacity for education reform. Consortium for Policy Research in Education. http://www.cpre.org/sites/default/files/policybrief/859_rb18.pdf, last accessed 2 April, 2012.
  26. Pallant, J. (2001). SPSS survival manual. Crows Nest NSW: Allen & Unwin.Google Scholar
  27. Petrou, M. (2009). Cypriot pre-service teachers’ content knowledge and its relationship to their teaching. Unpublished doctoral dissertation, University of Cambridge, Cambridge, UK.Google Scholar
  28. Petrou, M., & Goulding, M. (2011). Conceptualising teachers’ mathematical knowledge in teaching. In T. Rowland & K. Ruthven (Eds.), Mathematical knowledge in teaching (pp. 9–25). Dordrecht: Springer.CrossRefGoogle Scholar
  29. Rowland, T. (2005). The knowledge quartet: A tool for developing mathematics teaching. In A. Gagatsis (Ed.), Proceedings of the 4th Mediterranean conference on mathematics education (pp. 69–81). Nicosia: Cyprus Mathematical Society.Google Scholar
  30. Rowland, T. (2007). Developing knowledge for teaching: A theoretical loop. In S. Close, D. Corcoran, & T. Dooley (Eds.), Proceedings of the 2nd national conference on research in mathematics education (pp. 14–27). Dublin: St Patrick’s College.Google Scholar
  31. Rowland, T., Huckstep, P., Thwaites, A. (2003). The knowledge quartet. In J. Williams (Ed.), Proceedings of the British Society for Research into Learning Mathematics, 23(3), 97–102.Google Scholar
  32. Rowland, T., Huckstep, P., & Thwaites, A. (2005). Elementary teachers’ mathematics subject knowledge: the knowledge quartet and the case of Naomi. Journal of Mathematics Teacher Education, 8(3), 255–281.CrossRefGoogle Scholar
  33. Ruthven, K. (2011). Conceptualising mathematical knowledge in teaching. In T. Rowland & K. Ruthven (Eds.), Mathematical knowledge in teaching (pp. 83–98). Dordrecht: Springer.CrossRefGoogle Scholar
  34. Shulman, L. (1986). Those who understand: knowledge growth in teaching. Educational Researcher, 15(2), 4–14.CrossRefGoogle Scholar
  35. Shulman, L. (1987). Knowledge and teaching: foundations of the new reform. Harvard Educational Review, 57, 1–22.Google Scholar
  36. Smyth, J. (1995). Teachers’ work and the labor process of teaching: Central problematics in professional development. In T. Guskey & M. Huberman (Eds.), Professional development education: New paradigms and practices (pp. 69–91). New York: Teachers’ College Press.Google Scholar
  37. Snow-Renner, R. (1998). Mathematics assessment practices in CO classrooms: Implications about variations in capacity and students’ opportunity to learn. Paper presented at the Annual Meeting of the American Educational Research Association, San Diego, CA: April 13–17.Google Scholar
  38. Spillane, J. (1999). External reform initiatives and teachers’ efforts to reconstruct their practice: the mediating role of teachers’ zones of enactment. Journal of Curriculum Studies, 31, 143–175.CrossRefGoogle Scholar
  39. Spillane, J., & Jennings, N. (1997). Aligned instructional policy and ambitious pedagogy: exploring instructional reform from the classroom perspective. Teachers College Record, 98, 449–481.Google Scholar
  40. Steinbring, H. (2011). Changed views on mathematical knowledge in the course of didactical theory development–independent corpus of scientific knowledge or result of social constructions? In T. Rowland & K. Ruthven (Eds.), Mathematical knowledge in teaching (pp. 43–64). Dordrecht: Springer.CrossRefGoogle Scholar
  41. Stephens, M. (2008). Some key junctures in relational thinking. In M. Goss, R. Brown, & K. Makar (Eds.), Navigating currents and charting directions: 31st annual conference of the Mathematics Education Group of Australasia (pp. 491–498). Brisbane: MERGA.Google Scholar
  42. Tirosh, D., & Even, R. (2007). Teachers’ knowledge of students’ mathematical learning: An examination of commonly held assumptions. Mathematics knowledge in teaching seminar series: Conceptualising and theorizing Mathematical knowledge for teaching (Seminar 1). Cambridge: Harvard University.Google Scholar
  43. Victorian Curriculum and Assessment Authority (2008). Victorian essential learning standards (mathematics). Melbourne: author.Google Scholar
  44. Watson, J. (2001). Profiling teachers’ competence and confidence to teach particular mathematics topics: the case of chance and data. Journal of Mathematics Teacher Education, 4, 305–337.CrossRefGoogle Scholar
  45. Watson, A., & Barton, B. (2011). Teaching mathematics as the contextual application of mathematical modes of enquiry. In T. Rowland & K. Ruthven (Eds.), Mathematical knowledge in teaching (pp. 65–82). Dordrecht: Springer.CrossRefGoogle Scholar
  46. Xu, W. (2003). Algebraic thinking in arithmetic: quasi-variable expressions. Journal of Subject Education (in Chinese), 11(6–10), 24.Google Scholar

Copyright information

© Mathematics Education Research Group of Australasia, Inc. 2013

Authors and Affiliations

  1. 1.College of Mathematics and Information ScienceWenzhou UniversityWenzhouChina
  2. 2.Graduate School of EducationThe University of MelbourneVictoriaAustralia

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