Middle School Mathematics Teacher Preparation in a Chinese and an Australian University: Different Starting Mathematics Knowledge.
Keywords:
Initial teacher education, mathematics knowledg, middle schoolAbstract
There is increasing concern with respect to the quality of teacher education preparation processes in the West. This study used mixed methods to examine learning opportunities and knowledge of mathematics in a sample of 192 Australian trainee middle school teachers and 94 Chinese Bachelor of Science trainee teachers. It was found that the Chinese teacher preparation program ensured the that prospective teachers had mastery of basic facts and processes and extended opportunities to connect this mathematics knowledge to pedagogy. Many of the Australian trainee teachers had struggled with the same material and had limited opportunity to remediate this situation prior to commencing classroom engagement. The implications are discussed with regard to program structure and academic governance within the study institution and more broadly across the nation.
References
Author & Author (2016).
International Colleges & Universities. (2015). Universities in China by 2015 University Web Ranking. Retrieved from https://www.4icu.org
Australian Academy of Science. (2015). Desktop review of mathematics education pedagogical approaches and learning resources. Retrieved from www.science.org.au
Australian Curriculum, Assessment and Reporting Authority, (ACARA), (2012). The Australian Curriculum: Mathematics. Retrieved from: https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/
Australian Institute for Teaching and School Leadership (AITSL). (2012). Australian Professional Standards for Teachers (Extract) Graduate Career Stage. Retrieved from http://www.qct.edu.au/PDF/PSU/APST_GraduateStage.pdf
Ball, D. (1988). Unlearning to teach mathematics. For the Learning of Mathematics, 8, 40-48.
Ball, D. (1990). The mathematical understandings that prospective teachers bring to teacher education. Elementary School Journal, 90, 449-466.
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
Ball, S. (2010). The teacher’s soul and terrors of performativity. Journal of Educational Policy. 8 (2), 215-228.
Bernstein, B. (1999). Vertical and horizontal discourse: An essay. British Journal of Sociology of Education, 20(2), 157-173.
Bernstein, B. (2000). Pedagogy, Symbolic control and identity (Rev. ed.). Lanham, Boulder, New York, Oxford: Rowan & Littlefield Publishers, Inc.
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.
Burghes, D. (2007). International comparative study in Mathematics training. CfBT Education Trust. Retrieved from http://www.cimt.plymouth.ac.uk/papers/icsmtt.pdf
Burghes, D.& Geach, R. (2011). International comparative study in Mathematics training: Recommendations for initial teacher training in England. CfBT Education Trust. Retrieved from
Chang, H-J. (2002). Breaking the mould: An institutionalist political economy alternative to the neo-liberal theory of the market and the state. Cambridge Journal of Economics, 26, 539-559.
Cai, J. Mok, I., Reddy, V., & Stacey, K. (2016). International comparative studies in mathematics: Lessons for improving students’ learning. Springer International Publishing. Springeropen.
Chen, O., Kalyuga, S., & Sweller, J. (2016). Relations between the worked example and generation effects on immediate and delayed tests. Learning and Instruction, 45, 20-30.
Curtin University. (2016). Master of science and mathematics education: (Post graduate). Retrieved from: http://courses.curtin.edu.au/course_overview/postgraduate/Master-Science-Mathematics-Education
Dai, Q., & Cheung, K. (2004). The wisdom of traditional Mathematics teaching in China. In L. Fan, N-Y Wong, J. Cai, & S. Li (Eds.), How Chinese learn Mathematics: Perspectives from insiders (pp. 3-42). New Jersey: World Scientific.
Dinham, S. (2015). The worst of both worlds: How U.S. and U.K. models are influencing Australian education. Education Policy Analysis, Archives, 23(49). Retrieved from http://epaa.asu.edu/ojs/
Elton, L. (2000). The UK research assessment exercise: Unintended consequences. Higher Education Quarterly, 54(3), 274-283.
Englemann, S. (2007). Teaching Needy Kids in Our Backward System. Eugene, ADI Press.
Ericsson, K., Krampe, R., & Tesch-Romer, C. (1993). The role of deliberate practice in the acquisition of expert performance. Psychological Review, 100, (3), 363-406.
Fan, L., Miao, Z., & Mok, A. (2004). How Chinese teachers teach Mathematics and pursue professional development: Perspectives from contemporary international research. In L. Fan, N-Y Wong, J. Cai, & S. Li (Eds.), How Chinese learn Mathematics: Perspectives from insiders (pp. 43-70). New Jersey: World Scientific.
Gay, L., Mills, G., & Airasian, P. (2006). Educational research: Competencies for analysis and application. Upper Saddle River: Pearson, Merrill Prentice Hall.
Gess-Newsome, J. (2013). Pedagogical content knowledge. In J. Hattie & E. Anderman (Eds.), International guide to student achievement (pp. 257-259). Routledge: NY
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.
Gregg, J. (1995). The tensions and contradictions of the school mathematics tradition. Journal for Research in Mathematics Education, 26(5), 442-466.
Griffith University. (2016). Course list. Retrieved from https://degrees.griffith.edu.au/Program/1051/Courses/Domestic#0000008794
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.
Hattie, J. (2009). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. London: Routledge.
Hattie, J., & Donoghue, G. (2016). Learning strategies: A synthesis and conceptual model. npj Science of Learning, 1. http://www.nature.com/npjcilearn Accessed 25 May 2017.
Henderson, S., & Rodrigues, S. (2008). Scottish student primary teachers’ levels of mathematical competence and confidence for teaching mathematics: Some implications for national qualifications and initial teacher education. Journal of Education for Teaching, 34(2), 93-107.
Henson, R. K. (2001). Teacher self-efficacy: Substantive implications and measurement dilemmas. Paper presented at the Annual Meeting of the Educational Research Exchange, College Station, TX.
Hill, H., Rowan, B., & Ball, D. (2005). Effects of teacher’s mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371-406.
Hine, G. (2015). Strengthening pre-service teachers’ mathematical content knowledge. Journal of University Teaching and Learning Practice, 12(4). Retrieved from http://researchonline.nd.edu.au/cgi/viewcontent.cgi?article=1159&context=edu_article
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.
Keeling, R., & Hersh, R. (2012). We’re losing our minds. Rethinking American higher education. New York: Palgrave Macmillan.
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.
Kirschner, P., Verscgaffek, L., Star, J., & Van Dooren, W. (2017). There is more variation within than across domains: an interview with Paul A. Kirschner about applying cognitive psychology-based instructional design principles in mathematics teaching and learning. Mathematics Education, 49: 637-643.
Klein, D. (2005). The state of state Math standards. Thomas B. Fordham Foundation.
Kotzee, B. (2012). Expertise, fluency and social realism about professional knowledge, Journal of Education and Work. Retrieved from: http://www.tandfonline.com/doi/abs/10.1080/13639080.2012.738291
Krainer, K., Hsieh, F., Peck, R., & Tatto, M. (2015). The TEDS-M: Important issues, results and questions. In S. J. Cho (Ed.), The Proceedings of the 12th International Congress on Mathematical Education (pp. 99-121). Retrieved from http://link.springer.com/chapter/10.1007%2F978-3-319-12688-3_10#page-1,
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/
Lannin, J., Webb, M., Chval, K., Arbaugh, F., Hicks, S., Taylor, C., & Burton, R. (2013). The development of beginning mathematics teacher pedagogical content knowledge. Journal of Mathematics Teacher Education, 16: 403-426.
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.
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.
Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, N.J.: Lawrence Erlbaum Associates, Inc.
Marginson, S. (2002). Nation-building universities in a global environment: The case of Australia. Higher Education, 43, 409-428.
Marginson, S. (2006). Dynamics of national and global competition in higher education. Higher Education, 52, 1-39.
Marsh, H., & Hattie, J. (2002). The relationship between research productivity and teaching effectiveness: Complementary, antagonistic, or independent constructs? The Journal of Higher Education, 73(5), 603-641.
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/
Masters, G. (2016). Policy insights: Five challenges in Australian school education. Retrieved from: https://research.acer.edu.au/cgi/viewcontent.cgi?article=1004&context=policyinsights
McEwan, H., Bull, B. (1991). The pedagogic nature of subject matter knowledge. American Educational Research Journal, 28, 316-334.
Meyers, D. (2012). Australian universities: A portrait of decline. Retrieved from http://www.australian universities.id.au/
Monash University. (2016). EDF 1206-Mathematics education 1. Retrieved from http://www.monash.edu.au/pubs/2017handbooks/units/EDF5017
Muller, J. (2000). Reclaiming knowledge: Social theory, curriculum and education policy. London and New York: Routledge Falmer.
Muller, J. (2009). Forms of knowledge and curriculum coherence. Journal of Education and Work. Retrieved from http://www.tandfonline.com/loi/cjew20
Muller, J., & Taylor, N. (1995). Schooling and everyday life: Knowledges sacred and profane. Social Epistemology: A Journal of Knowledge, Culture and Policy, 9(3), 257-275. Retrieved from http://dx.doi.org/10.1080/02691729508578791
National Council for Teachers of Mathematics. (2003). Programs for initial preparation of mathematics teachers. Retrieved from http://www.ncate.org/ProgramStandards/NCTM/NCTMSECONStandards.pdf
Organization for Economic Co-operation and Development (OECD). (2014). Education at a glance, 2014. Retrieved from http://www.oecd.org/edu/Education-at-a-Glance-2014.pdf/
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.
Poulson, L. (2001). Paradigm lost? Subject knowledge, primary teachers and education policy. British Journal of Educational Studies, 49(1), 40-55.
Queensland Audit Office. (2013). Supply of specialist subject teachers in secondary schools. Report to Parliament 2: 2013-2014. Retrieved from www.qao.qld.gov.au
Queensland University of Technology. (2016a). Bachelor of Education Secondary- Mathematics. Retrieved from https://www.qut.edu.au/study/courses/bachelor-of-education-secondary/bachelor-of-education-secondary-mathematics
Queensland University of Technology (2016b). Mathematics Curriculum Studies 1. Retrieved from https://www.qut.edu.au/study/courses/bachelor-of-education-secondary/bachelor-of-education-secondary-mathematics
Sahlberg, P. (2006). Education reform for raising economic competitiveness. Journal of Educational Change. Retrieved from http://link.springer.com/article/10.1007/s10833-005-4884-6
Sahlberg, P. (2007). Education policies for raising student learning: The Finnish approach. Journal of Education Policy, 22(2), 147-171.
Sahlberg, P. (2011a). Lessons from Finland. The Professional Educator, 34-38. Retrieved from http://pasisahlberg.com/wp-content/uploads/2013/01/Lessons-from-Finland-AE-2011.pdf
Sahlberg, P. (2011b). PISA in Finland: An education miracle or an obstacle to change? Centre for Education Policy Studies Journal, 1(3), 119-140.
Sahlberg, P., & Oldroyd, D. (2010). Pedagogy for economic competitiveness and sustainable development. European Journal of Education, 45(2)280-299.
Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
Speer, N., King, K., & Howell, H. (2015). Definitions of mathematical knowledge for teaching: Using these constructs in research on secondary and college mathematics teachers. Journal of Mathematics Teacher Education. 18: 105-122.
Stones, E. (1992). Quality Teaching: A sample of cases. London and New York: Routledge.
Sweller, J. (2016). Working memory, long-term memory, and instructional design. Journal of Applied Research in Memory and Cognition, 5, 360-367.
Tatto, M., Rodriguez, M., & Lu, Y. (2015). The influence of teacher education on mathematics teaching knowledge: Local implementation of global ideas. International Perspectives on Education and Society, 27, 279-331. Retrieved from http://www.emeraldinsight.com/doi/pdfplus/10.1108/S1479-367920140000027004/
Tatto, M., Schwille, J., Senk, S., Ingvarason, L., Peck, R., & Rowley, G. (2008). Teacher education and development study in Mathematics (TEDS-M): Policy, practice, and readiness to teach primary and secondary mathematics. Conceptual framework. East Lansing, MI: Teacher Education and Development International Study Center, College of Education, Michigan University.
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
Tricot, A., & Sweller, J. (2014). Domain-specific knowlede and why teaching generic skills does not work. Educational Psychology Review, 26, 265-283.
University of Adelaide (2017). Senior Mathematics Curriculum and Methodology A; Retrieved from: http://www.adelaide.edu.au/course-outlines/105784/1/quad-1/2017
University of Melbourne. (2016). Learning area mathematics 1. Retrieved from https://handbook.unimelb.edu.au/view/2017/EDUC90457
University of Newcastle. (2016). Specialist Studies in Mathematics 1. Retrieved from https://www.newcastle.edu.au/course/EDUC1090
University of Queensland. (2006). Mathematics curriculum foundations. Retrieved from https://www.uq.edu.au/study/course.html?course_code=EDUC6725
University of Sydney. (2016). Teaching Mathematics 1B. Retrieved from http://sydney.edu.au/courses/uos/EDSE3046
US Department of Education. (2008). Success: The final report of the National Mathematics Advisory Panel. Retrieved from http://www2.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf/
Wang, T., Cai, J., & Hwang, S. (2004). Achieving coherence in the mathematics classroom: Towards a framework for examining instructional coherence. In L. Fan, N-Y Wong, J. Cai, & S. Li (Eds.), How Chinese learn Mathematics: Perspectives from insiders (pp. 111- 148). New Jersey: World Scientific.
Watt, H., & Richardson, P. (2013). Teacher motivation and student achievement outcomes. In J. Hattie & E. Anderman (Eds.), International guide to student achievement (pp. 271-273). New York: Routledge.
Wragg, E. C., Bennett, S. N., & Carre, C. (1989). Primary teachers and the national curriculum. Research Papers in Education, 4(1), 17-45.
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.
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.
