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Mathematics Education Research Journal

, Volume 29, Issue 2, pp 143–161 | Cite as

A case study of effective practice in mathematics teaching and learning informed by Valsiner’s zone theory

  • Vince Geiger
  • Judy Anderson
  • Derek Hurrell
ORIGINAL PAPER
First Online:

Abstract

The characteristics that typify an effective teacher of mathematics and the environments that support effective teaching practices have been a long-term focus of educational research. In this article we report on an aspect of a larger study that investigated ‘best practice’ in mathematics teaching and learning across all Australian states and territories. A case study from one Australian state was developed from data collected via classroom observations and semi-structured interviews with school leaders and teachers and analysed using Valsiner’s zone theory. A finding of the study is that ‘successful’ practice is strongly tied to school context and the cultural practices that have been developed by school leaders and teachers to optimise student learning opportunities. We illustrate such an alignment of school culture and practice through a vignette based on a case of one ‘successful’ school.

Keywords

Mathematics teaching Mathematics instruction Mathematics pedagogy Mathematics achievement School environment Valsiner 
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References

  1. Anthony, G., & Walshaw, M. (2009). Characteristics of effective teaching of mathematics: a view from the west. Journal of Mathematics Teacher Education, 2(2), 147–164.Google Scholar
  2. Appleton, J. J., Christenson, S. L., & Furlong, M. J. (2008). Student engagement with school: critical conceptual and methodological issues of the construct. Psychology in the Schools, 45, 369–386.CrossRefGoogle Scholar
  3. Australian Curriculum, Assessment and Reporting Authority (ACARA). (2013). Guide to understanding 2013 Index of Community Socio-educational Advantage values. Downloaded from http://www.acara.edu.au/_resources/Guide_to_understanding_2013_ICSEA_values.pdf.
  4. Australian Academy of Sciences. (2016). The mathematical sciences in Australia: a vision for 2015. Canberra: Australian Academy of Science.Google Scholar
  5. Ball, D. L., Thames, M., & Phelps, G. (2008). Content knowledge for teaching: what makes it special? Journal of Teacher Education, 59(5), 389–407.CrossRefGoogle Scholar
  6. Bennison, A. (2015). Supporting teachers to embed numeracy across the curriculum: a sociocultural approach. ZDM - The International Journal on Mathematics Education, 47(4), 561–573.CrossRefGoogle Scholar
  7. Blanton, M., Westbrook, S., & Carter, G. (2005). Using Valsiner’s zone theory to interpret teaching practices in mathematics and science classrooms. Journal of Mathematics Teacher Education, 8, 5–33.CrossRefGoogle Scholar
  8. Borko, H., Jacobs, J., Eiteljorg, E., & Pittman, M. E. (2009). Video as a tool for fostering productive discussions in mathematics professional development. Teaching and Teacher Education, 24, 417–436.CrossRefGoogle Scholar
  9. Bronfenbrenner, U. (1989). Ecological systems theory. In R. Vasta (Ed.), Annals of child development, Vol. 6 (pp. 187–249). Greenwich, CT: JAI Press.Google Scholar
  10. Chapman, E. (2003). Alternative approaches to assessing student engagement rates. Practical Assessment, Research and Evaluation, 8, 13 .http://www.PAREonline.net/getvn.asp?v=8&n=13 (accessed December 12, 2012)Google Scholar
  11. Charalambous, C. Y., Hill, H. C., & Mitchell, R. (2012). Two negatives don’t always make a positive: exploring how limitations in teacher knowledge and the curriculum contribute to instructional quality. Journal of Curriculum Studies, 44(4), 489–513.CrossRefGoogle Scholar
  12. Chetty, R., Friedman, J. N., & Rockoff, J. E. (2014). Measuring the impacts of teachers II: evaluating bias in teacher value-added estimates. American Economic Review, 104(9), 2593–2632.CrossRefGoogle Scholar
  13. Clarke, D. (2007). Ten key principles from research for the professional development of mathematics teachers. In G. C. Leder & H. J. Forgasz (Eds.), Stepping stones for the 21st century. Australasian mathematics education research (pp. 27–37). Rotterdam: Sense Publishers.Google Scholar
  14. Clarke, M., & Pittaway, S. (2014). Marsh's becoming a teacher (6th ed.). Frenchs Forest: Pearson Australia.Google Scholar
  15. Cobb, P., & Jackson, K. (2011). Towards an empirically grounded theory of action for improving the quality of mathematics teaching at scale. Mathematics Teacher Education and Development, 13(1), 6–33.Google Scholar
  16. Cobb, P., Zhao, Q., & Dean, C. (2009). Conducting design experiments to support teachers’ learning: a reflection from the field. Journal of the Learning Sciences, 18, 165–199.CrossRefGoogle Scholar
  17. Confrey, J. (2011). What now? Priorities in implementing the common core state standards for mathematics. In W. H. Schmidt (Ed.), Research in mathematics education: where do we go from here? (pp. 37–48). East Lansing: Michigan State University Institute for Research on Mathematics and Science Education.Google Scholar
  18. Confrey, J., Maloney, A., Nguyen, K., Mojica, G., & Myers, M. (2009). Equipartitioning/splitting as a foundation of rational number reasoning using learning trajectories. Paper presented at the 33rd Conference of the International Group for the Psychology of Mathematics Education, Thessaloniki, Greece.Google Scholar
  19. Danielson, C. (2013). The framework for teacher evaluation instrument. Princeton: The Danielson Group.Google Scholar
  20. Elmore, R. F. (2002). Testing trap. Harvard Magazine, 105(1), 35.Google Scholar
  21. Elmore, R. F. (2006). Leadership as the practice of improvement. Paper presented at the OECD International Conference on Perspectives on Leadership for Systemic Improvement, London.Google Scholar
  22. Fredricks, J. A., Blumenfeld, P. C., & Paris, A. H. (2004). School engagement: potential of the concept, state of the evidence. Review of Educational Research, 74(1), 59–109.CrossRefGoogle Scholar
  23. Gibson, J. J. (1966). The senses considered as perceptual systems. Boston: Houghton Mifflin.Google Scholar
  24. Goos, M. (2005). A sociocultural analysis of the development of pre-service and beginning teachers’ pedagogical identities as users of technology. Journal of Mathematics Teacher Education, 8(1), 35–59.CrossRefGoogle Scholar
  25. Goos, M. (2007). Developing numeracy in the learning areas (middle years). Adelaide: Keynote address delivered at the South Australian Literacy and Numeracy Expo.Google Scholar
  26. Goos, M. (2013). Sociocultural perspectives in research on and with mathematics teachers: a zone theory approach. ZDM Mathematics Education, 45(4), 521–533.CrossRefGoogle Scholar
  27. Goos, M. (2014). Creating opportunities to learn in mathematics education: a sociocultural perspective. Mathematics Educational Research Journal, 26(3), 439–457.CrossRefGoogle Scholar
  28. Hattie, J. (2015). The applicability of visible learning to higher education. Scholarship of Teaching and Learning in Psychology, 1(1), 79–91.CrossRefGoogle Scholar
  29. Hiebert, J., & Grouws, D. (2007). The effects of classroom mathematics teaching on students’ learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 371–404). Greenwich: Information Age.Google Scholar
  30. Horn, I. S., & Little, J. W. (2010). Attending to problems of practice: routines and resources for professional learning in teachers’ workplace interactions. American Educational Research Journal, 47(1), 181–217.CrossRefGoogle Scholar
  31. Jansen, A., Bartell, T., & Berk, D. (2009). The role of learning goals in building a knowledge base for elementary mathematics teacher education. Elementary School Journal, 109(5), 525–536.CrossRefGoogle Scholar
  32. Kazemi, E., & Hubbard, A. (2008). New directions for the design and study of professional development: attending to the coevolution of teachers’ participation across contexts. Journal of Teacher Education, 59, 428–441.CrossRefGoogle Scholar
  33. Lawson, M., & Lawson, H. (2013). New conceptual frameworks for student engagement research, policy, and practice. Review of Educational Research, 83, 432–479.CrossRefGoogle Scholar
  34. Lerman, S. (1996). Editorial for special issue on. Socio-cultural approaches to mathematics teaching and learning. Educational Studies in Mathematics, 31(1–2), 1–9.CrossRefGoogle Scholar
  35. Lerman, S. (2013). Theories in practice: mathematics teaching and mathematics teacher education. ZDM - The International Journal on Mathematics Education, 45(4), 623–631.CrossRefGoogle Scholar
  36. Miles, M. B., Huberman, A. M., & Saldana, J. (2014). Qualitative data analysis (2nd ed.). Thousand Oaks: SAGE.Google Scholar
  37. Millett, A., & Bibby, T. (2004). The context for change. In A. Millett, M. Brown, & M. Askew (Eds.), Primary mathematics and the developing professional (pp. 1–17). Dordrecht: Kluwer Academic Publishers.CrossRefGoogle Scholar
  38. National Council of Teachers of Mathematics [NCTM]. (2014). Principles to actions: ensuring mathematical success for all. Reston: NCTM.Google Scholar
  39. NSW Department of Education and Training. (2003). Quality teaching in NSW public schools: discussion paper. Sydney: NSW DET.Google Scholar
  40. Oerter, R (1992). The zone for proximal development for learning and teaching. In Oser, F., Dick, A. & Patry, J. (Eds.), Effective and responsible teaching: The new synthesis, (pp. 187–202). San Francisco, Jossey-Bass Publishers.Oesterle, & C. Allan (Eds.), Proceedings of the Joint Meeting of PME 38 and PME-NA 36 (Vol 2, pp. 137–144). Vancouver, Canada: PME.Google Scholar
  41. Office of the Chief Scientist. (2012). Mathematics, engineering and science in the national interest. Canberra: Commonwealth of Australia.Google Scholar
  42. Reschly, A. L., & Christenson, S. L. (2012). Jingle, jangle, and conceptual haziness: evolution and future directions of the engagement construct. In C. Wylie, S. L. Christenson, & A. L. Reschly (Eds.), Handbook of research on student engagement (pp. 3–19). New York: Springer.CrossRefGoogle Scholar
  43. Richards, L. (2015). Handling qualitative data: a practical guide. Los Angeles: SAGE.Google Scholar
  44. Schoenfeld, A. H. (2014). What makes for powerful classrooms, and how can we support teachers in creating them? A story of research and practice, productively intertwined. Educational Researcher, 43(8), 404–412.CrossRefGoogle Scholar
  45. Simon, M. A. (2009). Amidst multiple theories of learning in mathematics education. Journal for Research in Mathematics Education, 40(5), 477–490.Google Scholar
  46. Sherin, M. G., & Han, S. Y. (2004). Teacher learning in the context of video club. Teaching and Teacher Education, 20, 163–183.CrossRefGoogle Scholar
  47. Shulman, L. S. (1986). Those who understand, knowledge growth in teaching. Educational Researcher, 15(2), 4–14.CrossRefGoogle Scholar
  48. Stein, M. K., & Kim, G. (2009). The role of mathematics curriculum materials in large-scale urban reform: an analysis of demands and opportunities for teacher learning. In J. T. Remillard, B. Herbel-Eisenmann, & G. Lloyd (Eds.), Mathematics teachers at work: connecting curriculum materials and classroom instruction (pp. 37–55). New York: Routledge.Google Scholar
  49. Stein, M. K., Remillard, J. T., & Smith, M. S. (2007). How curriculum influences student learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 1, pp. 319–371). Greenwich, CT: Information Age.Google Scholar
  50. Swars, S., Hart, L. C., Smith, S. Z., Smith, M. E., & Tolar, T. (2007). A longitudinal study of elementary pre-service teachers’ mathematics beliefs and content knowledge. School Science and Mathematics, 107(9), 325–335.CrossRefGoogle Scholar
  51. Thomson, S., De Bortoli, L., & Underwood, C. (2016a). PISA 2015: a first look at Australia’s results. Melbourne: Australian Council of Educational Research.Google Scholar
  52. Thomson, S., Wernert, N., O’Grady, E., & Rodrigues, S. (2016b). TIMSS 2015: a first look at Australia’s results. Melbourne: Australian Council of Educational Research.Google Scholar
  53. Timperley, H. (2008). Teacher professional learning and development, Educational Practices Series-18, International Bureau of Education, UNESCO.Google Scholar
  54. Valsiner, J. (1997). Culture and the development of children’s action: a theory of human development (2nd ed.). New York: John Wiley & Sons.Google Scholar
  55. Vygotsky, L. S. (1978). Mind in society. Cambridge: Harvard University Press.Google Scholar
  56. Yoon, K. S., Duncan, T., Lee, C., Scarloss, B., & Shapley, K.L. (2007). Reviewing the evidence on how teacher professional development affects student achievement. Issues & Answers Report, REL 2007–No. 033. Washington, DC, U.S. Department of Education, Institute of Education Sciences, National Center for Education Evaluation and Regional Assistance, Regional Educational Laboratory Southwest.Google Scholar
  57. Young-Loveridge, J., & Mills, J. (2009). Teaching multi-digit multiplication using array-based materials. In R. Hunter, B. Bicknell, & T. Burgess (Eds.), Crossing divides. Proceedings of the 32nd annual conference of the Mathematics Education Research Group of Australasia (pp. 635–643). Palmerston North, NZ: MERGA.Google Scholar
  58. Watson, J., Beswick, K., & Brown, N. (2012). Educational research and professional learning in changing times: the MARBLE experience. Rotterdam: Sense Publishers.CrossRefGoogle Scholar
  59. Zambo, R., & Zambo, D. (2008). The impact of professional development in mathematics on teachers’ individual and collective efficacy: the stigma of underperforming. Teacher Education Quarterly, 35(1), 159–168.Google Scholar

Copyright information

© Mathematics Education Research Group of Australasia, Inc. 2017

Authors and Affiliations

  1. 1.Learning Sciences Institute AustraliaAustralian Catholic UniversityBrisbane CBDAustralia
  2. 2.Faculty of Education and Social WorkUniversity of SydneySydneyAustralia
  3. 3.School of EducationUniversity of Notre DameNotre DameAustralia

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