Abstract
What is effective teaching in mathematics? How do teachers in Australia, Mainland China, Hong Kong SAR and the US view effective teaching in mathematics? What are the similarities and differences in the views of teachers from the East and West on effective teaching? This paper provides theoretical and methodological bases for addressing these questions, which are dealt with in empirical studies described in the papers of this issue.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
Hong Kong SAR is not a country, so we use the term “region” in papers of this special issue.
References
Bransford, J. D., Brown. A. L., & Cocking, R. R. (2000) How people learn: brain, mind, experience, and school (expanded edition). National Research Council, Washington DC.
Brophy, J. E., & Good, T. L. (1996) Teacher behavior and student achievement. In M. C. Wittrock (Ed.), Handbook of research on teaching (3rd edn., pp. 328–375). New York: Macmillan.
Bruner, J. (1996) The culture of education. Cambridge: Harvard University Press
Cai, J. (2000). Mathematical thinking involved in US and Chinese students' solving process-constrained and process-open problems. Mathematical Thinking and Learning, 2, 309–340.
Cai, J. (2003) Investigating parental roles in students’ learning of mathematics from a cross-national perspective. Mathematics Education Research Journal, 15, 87–106.
Cai, J. (2004) Why do US and Chinese students think differently in mathematical problem solving? Exploring the impact of early algebra learning and teachers’ beliefs. Journal of Mathematical Behavior, 23, 135–167.
Cai, J. (2005) US and Chinese teachers’ knowing, evaluating, and constructing representations in mathematics instruction. Mathematical thinking and Learning: An International Journal, 7(2), 135–169.
Cai, J., & Wang, T. (2006) US and Chinese teachers’ conceptions and constructions of representations: a case of proportional reasoning. International Journal of Science and Mathematics Education, 4,145–186.
Carpenter, T. P., Franke, M. L., Jacobs, V. R., Fennema, E., & Empson, S. B. (1998) A longitudinal study of invention and understanding in children's multidigit addition and subtraction. Journal for Research in Mathematics Education, 29, 3–20.
Cobb P (1994) Where is the mind? Constructivist and sociocultural perspectives on mathematical development. Educational Researcher, 23, 13–20.
Cooney, T. J., Shealy, B. E., & Arvold, B. (1998) Conceptualizing belief structures of preservice secondary mathematics teachers. Journal for Research in Mathematics Education, 29(3), 306–333.
Ernest, P. (1989) The impact of beliefs on the teaching of mathematics. In P. Ernest (Ed.), Mathematics teaching: the state of the art (pp. 249–254). New York: Flamer.
Floden, R. E. (2001) Research on effects of teaching: a continuing model for research on reaching. In: V. Richardson (Ed.), Handbook of research on teaching (4th edn., pp. 3–16). Washington DC: American Educational Research Association.
Good, T., Grouws, D., & Ebmeier, M. (1983) Active mathematics teaching. New York: Longman.
Greeno, J. G. (1987) Instructional representations based on research about understanding. In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 61–88). Academic, New York.
Hatano, G. (1993) Time to merge Vygotskian and constructivist conceptions of knowledge acquisition. In E. A. Forman, N. Minick, & C. A. Stone (Eds.), Contexts for learning: sociocultural dynamics in children's development (pp. 153–166). Oxford University Press, New York.
Hiebert, J., & Wearne, D. (1993) Instructional tasks, classroom discourse, and students' learning in second-grade arithmetic. American Educational Research Journal, 30(2), 393–425.
Kuhs, T. M., & Ball, D. L. (1986) Approaches to teaching mathematics: mapping the domains of knowledge, skills, and dispositions. Research Memo, Michigan State University, Center on Teacher Education, East Lansing.
Lave, J., (1988) Cognition in practice: mind, mathematics, and culture in everyday life. Cambridge: Cambridge University Press.
Leinhardt, G. (1993) On teaching. In R. Glaser (Ed.), Advances in instructional psychology (Vol 4, pp 1–54). Hillsdale: Erlbaum.
Marton, F., Dall’Alba, G., & Tse, L. K. (1996) Memorizing and understanding: the keys to the paradox? In D. A. Watkins, & J. B. Biggs (Eds.), Cultural, psychological and contextual influences. Comparative Education Research Centre, Hong Kong; The Australian Council for Educational Research, Victoria, pp 69–83.
Miles, M. B., & Huberman, A. M. (1994) Qualitative data analysis: an expanded sourcebook (2nd edn.) Thousand Oaks: Sage.
Perry, M., VanderStoep, S. W., & Yu, S. L. (1993) Asking questions in first-grade mathematics classes: potential influences on mathematical thought. Journal of Educational Psychology, 85(1), 31–40.
Perry, B., Wong, N. Y., & Howard, P. (2006) Comparing primary and secondary mathematics teachers’ beliefs about mathematics, mathematics learning and mathematics teaching in Hong Kong and Australia. In: K. D. Graf, F. K. S. Leung, & F. Lopez-Real (Eds.), Mathematics education in different cultural traditions: a comparative study of East Asia and the West. Dordrecht: Kluwer.
Schoenfeld, A. H. (2000) Models of the teaching process. Journal of Mathematical Behaviors, 18, 243–261.
Stigler, J. W., & Hiebert, J. (1999) The teaching gap: best ideas from the world's teachers for improving education in the classroom. New York: Free Press
Stigler, J. W., & Perry, M. (1988) Cross cultural studies of mathematics teaching and learning: recent findings and new directions. In D. A. Grouws, T. J. Cooney, & D. Jones (Eds.), Effective mathematics teaching (pp. 104–223). Reston, VA: NCTM.
Strauss, A., & Corbin, J. (1990) Basics of qualitative research: grounded theory procedures and techniques. Newbury Park: Sage.
Thompson, A. G. (1992) Teachers' beliefs and conceptions: a synthesis of the research. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 127–146). New York: Macmillan.
Tirosh, D., & Graeber, A. O. (2003) Challenging and changing mathematics teaching classroom practices. In A. J. Bishop, M. A. Clements , C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.), Second international handbook of mathematics education (pp. 643–687). Dordrecht: Kluwer.
Acknowledgments
The development of the initial ideas of studying the beliefs on effective teaching of Chinese and US teachers was supported, in part, by grants from the Spencer Foundation. Any opinions expressed herein are those of the author and do not necessarily represent the views of the Spencer Foundation. I gratefully acknowledge the valuable collaboration of Bob Perry and Ngai-Ying Wong in extending the original study to include teachers from Australia and Hong Kong. I also would like to acknowledge the active participation of Tao Wang, who not only brought some significant articles to my attention, but also worked with me in analyzing the Chinese and US data. Of course, I am solely responsible for any errors. Special thanks go to Gabriele Kaiser, who generously accepted our study for publication as a special issue of ZDM and who also offered a commentary of the findings from a European perspective. In addition to the editors, Vic Cifarelli, Liping Ding, Liang-huo Fan, Keith Jones and Gabriele Kaiser have reviewed earlier versions of the manuscripts in this special issue. Their insightful reviews are greatly appreciated.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Cai, J. What is effective mathematics teaching? A study of teachers from Australia, Mainland China, Hong Kong SAR, and the United States. ZDM Mathematics Education 39, 265–270 (2007). https://doi.org/10.1007/s11858-007-0029-0
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11858-007-0029-0