Skip to main content

Advertisement

Log in

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

  • ORIGINAL PAPER
  • Published:
Mathematics Education Research Journal Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  • 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 

  • 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.

    Article  Google Scholar 

  • 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.

  • Australian Academy of Sciences. (2016). The mathematical sciences in Australia: a vision for 2015. Canberra: Australian Academy of Science.

    Google Scholar 

  • Ball, D. L., Thames, M., & Phelps, G. (2008). Content knowledge for teaching: what makes it special? Journal of Teacher Education, 59(5), 389–407.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Bronfenbrenner, U. (1989). Ecological systems theory. In R. Vasta (Ed.), Annals of child development, Vol. 6 (pp. 187–249). Greenwich, CT: JAI Press.

  • 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 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • Clarke, M., & Pittaway, S. (2014). Marsh's becoming a teacher (6th ed.). Frenchs Forest: Pearson Australia.

    Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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.

  • Danielson, C. (2013). The framework for teacher evaluation instrument. Princeton: The Danielson Group.

    Google Scholar 

  • Elmore, R. F. (2002). Testing trap. Harvard Magazine, 105(1), 35.

    Google Scholar 

  • 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.

  • 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.

    Article  Google Scholar 

  • Gibson, J. J. (1966). The senses considered as perceptual systems. Boston: Houghton Mifflin.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • Goos, M. (2013). Sociocultural perspectives in research on and with mathematics teachers: a zone theory approach. ZDM Mathematics Education, 45(4), 521–533.

    Article  Google Scholar 

  • Goos, M. (2014). Creating opportunities to learn in mathematics education: a sociocultural perspective. Mathematics Educational Research Journal, 26(3), 439–457.

    Article  Google Scholar 

  • Hattie, J. (2015). The applicability of visible learning to higher education. Scholarship of Teaching and Learning in Psychology, 1(1), 79–91.

    Article  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Lawson, M., & Lawson, H. (2013). New conceptual frameworks for student engagement research, policy, and practice. Review of Educational Research, 83, 432–479.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Lerman, S. (2013). Theories in practice: mathematics teaching and mathematics teacher education. ZDM - The International Journal on Mathematics Education, 45(4), 623–631.

    Article  Google Scholar 

  • Miles, M. B., Huberman, A. M., & Saldana, J. (2014). Qualitative data analysis (2nd ed.). Thousand Oaks: SAGE.

    Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • National Council of Teachers of Mathematics [NCTM]. (2014). Principles to actions: ensuring mathematical success for all. Reston: NCTM.

    Google Scholar 

  • NSW Department of Education and Training. (2003). Quality teaching in NSW public schools: discussion paper. Sydney: NSW DET.

    Google Scholar 

  • 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.

  • Office of the Chief Scientist. (2012). Mathematics, engineering and science in the national interest. Canberra: Commonwealth of Australia.

    Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • Richards, L. (2015). Handling qualitative data: a practical guide. Los Angeles: SAGE.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Simon, M. A. (2009). Amidst multiple theories of learning in mathematics education. Journal for Research in Mathematics Education, 40(5), 477–490.

    Google Scholar 

  • Sherin, M. G., & Han, S. Y. (2004). Teacher learning in the context of video club. Teaching and Teacher Education, 20, 163–183.

    Article  Google Scholar 

  • Shulman, L. S. (1986). Those who understand, knowledge growth in teaching. Educational Researcher, 15(2), 4–14.

    Article  Google Scholar 

  • 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 

  • 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.

  • 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.

    Article  Google Scholar 

  • 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 

  • 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 

  • Timperley, H. (2008). Teacher professional learning and development, Educational Practices Series-18, International Bureau of Education, UNESCO.

  • 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 

  • Vygotsky, L. S. (1978). Mind in society. Cambridge: Harvard University Press.

    Google Scholar 

  • 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.

  • 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.

  • Watson, J., Beswick, K., & Brown, N. (2012). Educational research and professional learning in changing times: the MARBLE experience. Rotterdam: Sense Publishers.

    Book  Google Scholar 

  • 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 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Vince Geiger.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Geiger, V., Anderson, J. & Hurrell, D. A case study of effective practice in mathematics teaching and learning informed by Valsiner’s zone theory. Math Ed Res J 29, 143–161 (2017). https://doi.org/10.1007/s13394-017-0191-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13394-017-0191-9

Keywords

Navigation