Abstract
Studies such as the Effective Teachers of Numeracy Study (Askew, Brown, Rhodes, Johnson, & Wiliam (1997) have contributed much to our understanding of what constitutes effective teaching of numeracy. This paper aims to build on these findings and to contribute a model that could be used to understand teachers’ numeracy practices and the factors that influence these practices. Through a synthesis of the literature, the author has devised a set of principles of practice which encapsulates effective teaching of numeracy and has identified six teacher actions which can be used to enact these principles. Findings from case studies conducted with three teachers indicated that the model provided a useful framework for observing and understanding classroom numeracy practices.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Ahmed, A., Clark-Jeavons, A. & Oldknow, A. (2004). How can teaching aids improve the quality of mathematics education?Educational Studies in Mathematics, 56, 313–328.
Anthony, G., & Walshaw, M. (2007).Effective pedagogy in mathematics/Pangarau. Wellington, NZ: Ministry of Education.
Arbaugh, F., & Brown, C. A. (2005). Analyzing mathematical tasks: A catalyst for change?Journal of Mathematics Teacher Education, 8, 499–536.
Askew, M. (2004).Mediation and interpretation: Exploring the interpersonal and the intrapersonal in primary mathematics lessons. Paper presented at the 28th Conference of the International Group for the Psychology of Mathematics Education.
Askew, M., Brown, M., Rhodes, V., Johnson, D., & Wiliam, D. (1997).Effective teachers of numeracy. London: School of Education, King’s College.
Ball, D. L. (1990). The mathematical understandings that prospective teachers bring to teacher education.The Elementary School Journal, 90 (1), 449–466.
Bills, L., Dreyfus, T., Mason, J., Tsamir, P., Watson, A., & Zaslavsky, O. (2006).Exemplification in mathematics education. Paper presented at the 30th Conference of the International Group for the Psychology of Mathematics Education, Prague, Czech Republic.
Blair, D. (Ed.). (1982).The pocket Macquarie dictionary. Netley, SA: Jacaranda Press.
Borasi, R., & Fonzi, J. (1998).Teaching practices that support an inquiry approach to mathematics instruction. Retrieved 31 October, 2004 from http://www.rochester.edu/radiate/C/c1c_sttx.htm
Borko, H., Mayfield, V., Marion, S., Flexer, R. J., & Cumbo, K. (1997).Teachers’ developing ideas and practices about mathematics performance assessment: Successes, stumbling blocks and implications for professional development. Los Angeles: National Center for Research on Evaluation, Standards, and Student Testing (CRESST).
Burns, R. (2000).Introduction to research methods (3rd ed.). Melbourne: Longman.
Carroll, J. (2005). Developing effective teachers of mathematics: Factors contributing to development in mathematics education for primary school teachers. In P. Clarkson, A. Downton, D. Gronn, M. Horne, A. McDonough, R. Pierce & A. Roche (Eds.),MERGA 28 Building connections: Research, theory and practice (Proceedings of the 28th Annual Conference of the Mathematics Education Research Group of Australasia, Melbourne, pp. 201–208). Sydney: MERGA.
Charles, R. I. (1999).What to look for in a powerful mathematics classroom. Paper presented at the Conference of the National Council of Supervisors of Mathematics, San Francisco, April, 1999.
Clarke, D., Cheeseman, J., Gervasoni, A., Gronn, D., Horne, D., McDonough, A. et al. (2002).Early numeracy research project final report. Melbourne, Australia: Australian Catholic University.
Clarke, D., & Clarke, B. (2002).Challenging and effective teaching in junior primary mathematics: What does it look like? Paper presented at Mathematics: Making Waves (Proceedings of the 19th Biennial Conference of the Australian Association of Mathematics Teachers).
Coben, D., Colwell, D., Macrae, S., Boaler, J., Brown, M. & Rhodes, V. (2003).Adult numeracy: Review of research and related literature. London: NRDC.
Department of Education and Children’s Services. (2003).Understanding the relationship between mathematics and numeracy. Retrieved 30 April 2008, from http://www.decs.sa.gov.au/thenetwork/files/pages/phna/reculturing/page2.htm
Department of Employment, Education, Training and Youth Affairs. (1997).Numeracy=Everyone’s Business. Adelaide, SA.: AAMT.
Doig, B. (2007). Chameleons in the classroom: Middle years teachers of mathematics. In K. Milton, H. Reeves, & T. Spencer (Eds.),Mathematics: Essential for learning, essential for life (Proceedings of the 21st Biennial Conference of the Australian Association of Mathematics Teachers Inc., Hobart, 149–154). Adelaide, SA: AAMT.
Doig, B., McCrae, B., & Rowe, K. (2003).A good start to numeracy. Canberra, ACT: Commonwealth of Australia.
Galton, M., Hargreaves, L., Comber, C., Wall, D., & Pell, A. (1999).Inside the primary classroom 20 years on. London, NY: Routledge.
Galton, M., Simon, B. & Croll, P. (1980).Inside the primary classroom. London: Routledge & Kegan Paul Ltd.
Grouws, D. A., & Lembke, L. O. (1996). Influential factors in student motivation to learn mathematics: The teacher and classroom culture. In M. Carr (Ed.),Motivation in mathematics (pp. 39–62). Cresskill, NJ: Hampton Press.
Groves, S., Mousley, J., & Forgasz, H. (2006).Primary Numeracy: A mapping, review and analysis of Australian research in numeracy learning at the primary school level. Canberra, ACT: Commonwealth of Australia.
Guskey, T. R. (1995).Results-oriented professional development: In search of an optimal mix of effective practices. Retrieved 27 June, 2006, from http:www.ncrel.org/sdrs/areas/rpl_esys/pdlitrev.htm
Hargreaves, A. (1996). Development and desire: A postmodern perspective. In T. R. Guskey & M. Huberman (Eds.),Professional development in education (pp. 9–34). New York: Teachers College Press.
Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning.Journal for Research in Mathematics Education, 28, 524–549.
Huckstep, P., Rowland, T., & Thwaites, A. (2003).Primary teachers’ mathematics content knowledge: What does it look like in the classroom? Retrieved 12 October, 2005, from http://www.leeds.ac.uk/educol/documents/00002534.htm
Hurst, C. (2007). Reflective teaching + connective teaching = effective teaching. In K. Milton, H. Reeves, & T. Spencer (Eds.).Mathematics: Essential for learning, essential for life (Proceedings of the 21st Biennial Conference of the Australian Association of Mathematics Teachers Inc., Hobart, pp. 307–313). Adelaide, SA: AAMT.
Jones, S., Tanner, H., & Treadaway, M. (2000).Raising standards in mathematics through effective classroom practice. Paper presented at the Annual Meeting of the Australian Association for Research in Education, Sydney, Australia.
Kanes, C., & Nisbet, S. (1994).An investigation into the knowledge bases of primary and secondary mathematics teachers: Report on a pilot study. Paper presented in the Proceedings of the 17th Annual Conference of the Mathematics Education Research Group of Australasia, Lismore.
Kilpatrick, J., Swafford, J., & Findell, B. E. (2001).Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
Leinhardt, G. (1990). Capturing craft knowledge in teaching.Educational Researcher, 19 (2), 18–25.
McIntosh, A. (2002).Principles for improving numeracy in schools. Retrieved 23 April 2004, from http://www.ltag.education.tas.gov.au
Mewborn, D. (2001). Teachers’ content knowledge, teacher education, and their effects on the preparation of elementary teachers in the United States.Mathematics Teacher Education and Development, 3, 28–36.
Moyer, P. S. (2001). Are we having fun yet? How teachers use manipulatives to teach mathematics.Educational Studies in Mathematics, 47, 175–197.
Muir, T. (2007). Setting a good example: Teachers choice of examples and their contribution to effective teaching of numeracy. In J. Watson & K. Beswick (Eds.),Mathematics: Essential research, essential practice (Proceedings of the 30th Annual Conference of the Mathematics Education Research Group of Australasia, Hobart, pp. 513–522). Adelaide, SA: MERGA.
National Council for the Teachers of Mathematics (NCTM). (2000).Principles and standards for school mathematics. Reston, VA: NCTM.
Reynolds, D., & Muijs, D. (1999). The effective teaching of mathematics: A review of research.School Leadership & Management, 19 (3), 273–289.
Shuell, T. J. (1996). Teaching and learning in a classroom context. In D. C. Berliner & R. C. Calfee (Eds.),Handbook of educational psychology (pp. 726–764). NY: Simon & Schuster Macmillan.
Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform.Harvard Educational Review, 57 (1), 1–22.
Stake, R. E. (1995).The art of case study research. Thousand Oaks, California: Sage Publications.
Stephens, M. (2000).Identification and evaluation of teaching practices that enhance numeracy achievement. Canberra, ACT: Commonwealth of Australia.
Stodolsky, S. (1988).The subject matters. Chicago: University of Chicago.
Thomas, G., & Ward, J. (2002).An evaluation of the early numeracy project 2001: Exploring issues in mathematics education. Wellington: Ministry of Education.
Thompson, A. G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D. Grouws (Ed.),Handbook of research on mathematics teaching and learning (pp. 127–146). New York: MacMillan Publishing Company.
Van de Walle, J. A. (2004).Elementary and middle school mathematics (5th ed.). Boston, MA: Pearson Education Inc.
Watson, A., & De Geest, E. (2005). Principled teaching for deep progress: Improving mathematical learning beyond methods and materials.Educational Studies in Mathematics, 58, 209–234.
Watson, A., & Mason, J. (2002). Student-generated examples in the learning of mathematics.Canadian Journal of Science, Mathematics and Technology Education, 2 (2), 237–249.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Muir, T. Principles of practice and teacher actions: Influences on effective teaching of numeracy. Math Ed Res J 20, 78–101 (2008). https://doi.org/10.1007/BF03217531
Issue Date:
DOI: https://doi.org/10.1007/BF03217531