Advertisement

Journal of Mathematics Teacher Education

, Volume 21, Issue 3, pp 263–285 | Cite as

Primary mathematics teacher education in Australia and China: What might we learn from each other?

  • Stephen Norton
  • Qinqiong Zhang
Article

Abstract

The preparation of teachers to teach mathematics to primary school children differs across nations and cultures. This study used mixed methods to examine the basic content knowledge of trainee teachers in Australia and China. A simple test (30 questions) of content based on an international comparative study in mathematics teacher training found that many of the Australian trainee teachers struggled with material that they might be expected to teach, while the Chinese teachers largely demonstrated mastery. The significance of this finding is examined in the context of the teacher preparation programs in two teacher training institutions. Cultural commentary is added by leading academics in each institution. It was found that in the Australian teacher training institution there was a focus on generic skills and relatively limited opportunity to develop trainee teachers’ content knowledge or specific pedagogy. The relevance of the findings is discussed through the framework of different beliefs in the nature of mathematics and mathematics teaching that have been reported to dominate the different educational systems in China and Australia.

Keywords

Primary mathematics Teacher training China Australia Content knowledge 

References

  1. An, S. (2004). Capturing the way of teaching: The learning-questioning and learning-reviewing instructional model. In L. Fan, N.-Y. Wong, J. Cai, & S. Li (Eds.), How Chinese learn mathematics: Perspectives from insiders (pp. 462–502). New Jersey: World Scientific.CrossRefGoogle Scholar
  2. Australian Academy of Science. (2015). Desktop review of mathematics education pedagogical approaches and learning resources. Retrieved from www.science.org.au.
  3. Australian Association of Mathematics Teachers. (1996). Statement on the use of calculators and computers for mathematics in Australian schools. Retrieved from www.aamt.edu.au/content/download/725/19521/file/tech_st.pdf.
  4. Australian Association of Mathematics Teachers. (2015). Desktop Review of Mathematics School Education Pedagogical Approaches and Learning Resources. Retrieved from https://docs.education.gov.au/documents/desktop-review-mathematics-school-education-pedagogical-approaches-and-learning-resources.
  5. Australian Curriculum Assessment and Reporting Authority (ACARA). (2012). The Australian curriculum: Mathematics. Retrieved from http://www.australiancurriculum.edu.au/Mathematics/Rationale.
  6. Australian Institute for Teaching and School Leadership. (2011). Australian professional standards for teachers. Retrieved from http://www.aitsl.edu.au/australian-professional-standards-for-teachers/standards/list.
  7. Ball, D. (1988). Unlearning to teach mathematics. For the Learning of Mathematics, 8, 40–48.Google Scholar
  8. Ball, D. (1990). The mathematical understandings that prospective teachers bring to teacher education. Elementary School Journal, 90, 449–466.CrossRefGoogle Scholar
  9. Ball, D., Hill, H., & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, Fall. Retrieved from www.aft.org/pubs-reports/americian_educator/fall05.
  10. Bernstein, B. (1990). The structure of pedagogic discourse, vol IV: Class, codes and control. London: Routledge.CrossRefGoogle Scholar
  11. Boesen, J. (2006). Assessing mathematical creativity: Comparing national and teacher made tests, explaining the differences and impact. www.gu.se/forskning/publikation/?publicationId=128530.
  12. Brown, T., McNamara, D., Hanley, V., & Jones, L. (1999). Primary student teachers’ understanding of mathematics and its teaching. British Educational Research Journal, 25(3), 299–322.CrossRefGoogle Scholar
  13. Burghes, D. (2007). International comparative study in mathematics training. CfBT Education Trust. Retrieved from http://www.cimt.plymouth.ac.uk/papers/icsmtt.pdf.
  14. Burghes, D. (2011). International comparative study in mathematics training: Recommendations for initial teacher training in England. CfBT Education Trust. Retrieved from https://www.nationalstemcentre.org.uk/res/documents/page/International%20comparative%20study%20in%20mathematics%20teacher%20training.pdf.
  15. Department of Education and Science. (1982). Inquiry into the teaching of mathematics in schools, mathematics Counts (Cockcroft Report). London: HMSO.Google Scholar
  16. Dinham, S. (2013). The quality teaching movement in Australia encounters difficult terrain: A personal perspective. Australian Journal of Education, 57(2), 91–106.CrossRefGoogle Scholar
  17. Gay, L., Mills, G., & Airasian, P. (2006). Educational research: Competencies for analysis and application. Upper Saddle River: Pearson, Merrill Prentice Hall.Google Scholar
  18. Goulding, M., Rowland, T., & Barber, P. (2002). Does it matter? Primary teacher trainees’ subject knowledge in mathematics. British Educational Research Journal, 28(5), 689–704.CrossRefGoogle Scholar
  19. Gu, L., Huang, R., & Marton, F. (2004). Teaching with variation: A Chinese way of promoting effective mathematics learning. In L. Fan, N.-Y. Wong, J. Cai, & S. Li (Eds.), How Chinese learn mathematics: Perspectives from insiders (pp. 309–347). New Jersey: World Scientific.CrossRefGoogle Scholar
  20. Hattie, J. (2009). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. London: Routledge.Google Scholar
  21. Hiebert, J. (2003). What research says about the NCTM standards. In J. Kilpatrick, W. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 5–23). Reston, VA: NCTM.Google Scholar
  22. Huang, R., & Leung, K. (2004). Cracking the paradox of Chinese learners: Looking into mathematics classrooms in Hong Kong and Shanghai. In L. Fan, N.-Y. Wong, J. Cai, & S. Li (Eds.), How Chinese learn mathematics: Perspectives from insiders (pp. 348–381). New Jersey: World Scientific.CrossRefGoogle Scholar
  23. International Colleges and Universities. (2015). Universities in China by 2015 University Web Ranking. Retrieved from http://www.4icu.org/cn/.
  24. Kirschner, P., Sweller, J., & Clark, R. (2006). Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching. Educational Psychologist, 41(2), 75–86.CrossRefGoogle Scholar
  25. Lai, M., & Murray, S. (2012). Teaching with procedural variation: A Chinese way of promoting deep understanding of mathematics. International Journal of Mathematics Teaching and Learning. Retrieved from http://www.cimt.plymouth.ac.uk/journal/.
  26. Li, J. (2004). Chinese cultural model of learning. In L. Fan, N.-Y. Wong, J. Cai, & S. Li (Eds.), How Chinese learn mathematics: Perspectives from insiders (pp. 124–156). New Jersey: World Scientific.CrossRefGoogle Scholar
  27. Li, Y., Zhao, D., Huong, R., & Ma, Y. (2008). Mathematics preparation of elementary teachers in China: Changes and issues. Journal of Mathematics Teacher Education, 11, 417–430.CrossRefGoogle Scholar
  28. Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates Inc.Google Scholar
  29. Marshall, J. (2003). Math wars: Taking sides. Phi Delta Kappan, 85(3), 193–200. Retrieved from http://www2.ed.gov/about/bdscomm/list/mathpanel/documents/math-wars-taking-sides.pdf.
  30. Masters, G. (2009). A shared challenge: Improving literacy, numeracy and science learning in Queensland primary schools. Australian Council for Educational Research. Retrieved from http://education.qld.gov.au/mastersreview/.
  31. Ministerial Council on Education, Employment, Training and Youth Affairs (MCEETYA). (2008–2014). National assessment program, literacy and numeracy: Numeracy. Carlton, Victoria: Curriculum Corporation.Google Scholar
  32. Muller, J. (2000). Reclaiming knowledge: Social theory, curriculum and education policy. London, New York: Routledge Falmer.Google Scholar
  33. Muller, J., & Taylor, N. (1995). Schooling and everyday life: Knowledges sacred and profane. Social Epistemology, 9(3), 257–275.CrossRefGoogle Scholar
  34. Mullis, I., Martin, M., Foy, P., & Arora, A. (2012). TIMMS International Results in Mathematics. Retrieved from: http://timssandpirls.bc.edu/timss2011/international-results-mathematics.html.
  35. Nardi, E., & Steward, S. (2003). Is mathematics T.I.R.E.D? A profile of quiet disaffection in the secondary mathematics classroom. British Journal of Educational Research, 29(3), 345–367.CrossRefGoogle Scholar
  36. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston: NCTM.Google Scholar
  37. National Council of Teachers of Mathematics. (2014). Executive summary: Focus in high school mathematics: Reasoning and sense making. Retrieved from http://www.nctm.org/standards/content.aspx?id=23749.
  38. National Council of Teachers of Mathematics. (2015). Principles and standards of school Mathematics. Retrieved from http://www.nctm.org/Standards-and-Positions/Principles-.and-Standards/Principles,-Standards,-and-Expectations/.
  39. Norton, S. (2011). How deeply and how well? How ready to teach mathematics after a one year program? Mathematics Teacher Education and Development, 12(1), 65–82.Google Scholar
  40. Norton, S. (2012). Prior study of mathematics as a predictor of pre-service teachers’ success on mathematics content and pedagogical content knowledge tests. Mathematics Teacher Education and Development, 14(1), 2–26.Google Scholar
  41. Norton, S., & Zhang, Q. (2013). A post card from a primary mathematics classroom in Chongqing China. Australian Primary Mathematics Classroom, 18(2), 9–14.Google Scholar
  42. Owen, E., & Sweller, J. (1989). Should problem solving be used as a learning device in mathematics? Journal for Research in Mathematics Education, 20(3), 322–328.CrossRefGoogle Scholar
  43. Poulson, L. (2001). Paradigm Lost? Subject knowledge, primary teachers and education policy. British Journal of Educational Studies, 49(1), 40–55.CrossRefGoogle Scholar
  44. Rotherham, A., & Willingham, D. (2009). 21st Century skills: The challenges ahead. Educational Leadership, 67(1), 16–21.Google Scholar
  45. Ruthven, K. (2001). The English experience of a calculator-aware number curriculum. In J. Anghileri (Ed.), Principles and practices in arithmetic teaching: Innovative approaches for the primary classroom (pp. 165–188). Buckingham: Open University Press.Google Scholar
  46. Ruthven, K. (2009). Towards a calculator-aware number curriculum. Mediterranean Journal for Research in Mathematics Education, 8(1), x-x. Retrieved from https://www.educ.cam.ac.uk/people/staff/ruthven/RuthvenMJRMEpreprint.pdf.
  47. Sealey, P., & Noyes, A. (2010). On the relevance of mathematics curriculum to young people. The Curriculum Journal, 21(3), 239–253.CrossRefGoogle Scholar
  48. Sfard, A. (2003). Balancing the unbalanceable: The NCTM standards in the light of theories of learning mathematics. In J. Kilpatrick, W. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 353–392). Reston: National Council of Teachers of Mathematics.Google Scholar
  49. Shuard, H., Walsh, A., Goodwin, J., & Worchester, V. (1991). Calculators, children and mathematics. London, UK: Simons & Schuster.Google Scholar
  50. Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.CrossRefGoogle Scholar
  51. Sriraman, B. (2004). The characteristics of mathematical creativity. The Mathematics Educator, 14(1), 19–34.Google Scholar
  52. Teacher Education Ministerial Advisory Group. (2014). Action now! Classroom ready teachers. Retrieved from http://docs.education.gov.au/system/files/doc/other/action_now_classroom_ready_teachers_print.pdf.
  53. Thomson, S., Hillman, K., Wernert, N., Schmid, M., & Munene, A. (2012). Highlights from the TIMMS AND PIRLS 2011 from Australia’s perspective. Melbourne: Australian Council for Educational Research.Google Scholar
  54. Thomson, S., Wernert, N., Underwood, C., & Nicholas, M. (2007). TIMSS 07: Taking a closer look at mathematics and science in Australia. Retrieved from http://www.acer.edu.au/documents/TIMSS_2007-AustraliaFullReport.pdf.
  55. Torbeyns, J., Verschaffel, L., & Ghesquiere, P. (2005). Simple addition strategies in a first-grade class with multiple strategy instruction. Cognition and Instruction, 23(1), 121.CrossRefGoogle Scholar
  56. U.S. Department of Education. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Retrieved from http://www2.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf.
  57. Wang, T., & Murphy, J. (2004). An examination of coherence in a Chinese mathematics classroom. In L. Fan, N.-Y. Wong, J. Cai, & S. Li (Eds.), How Chinese learn mathematics: Perspectives from insiders (pp. 107–124). New Jersey: World Scientific.CrossRefGoogle Scholar
  58. Wragg, E. C., Bennett, S. N., & Carre, C. (1989). Primary teachers and the national curriculum. Research Papers in Education, 4(1), 17–45.CrossRefGoogle Scholar
  59. Zhang, D., Li, S., & Tang, R. (2004). The “two basics”: Mathematics teaching and learning in mainland China. In L. Fan, N.-Y. Wong, J. Cai, & S. Li (Eds.), How Chinese learn mathematics: Perspectives from insiders (pp. 189–207). New Jersey: World Scientific.CrossRefGoogle Scholar
  60. Zhang, Q., & Stephens, M. (2013). Utilising a construct of teacher capacity to examine national curriculum reform in mathematics. Mathematics Education Research Journal, 25, 481–502.CrossRefGoogle Scholar

Copyright information

© Her Majesty the Queen in Right of Australia 2016

Authors and Affiliations

  1. 1.Griffith UniversityMount GravattAustralia
  2. 2.Wenzhou UniversityWenzhouChina

Personalised recommendations