Abstract
In Australia, there is increasing scrutiny of teacher education processes in learning to teach primary mathematics. In this study, mixed methods, including linear regression, are used to examine the entry mathematical content knowledge of third-year Bachelor of Education Pre-service Students and to relate this to their graduating level of content and a measure of pedagogical content knowledge based upon capacity to describe student errors and provide learning support. The data indicate low levels of mathematical content knowledge at the beginning of the course, prompting questioning of the focus of earlier mathematics curriculum courses. Over the life of the study, there was improvement in some domains, which is to be expected where knowledge of mathematics was an intended outcome. Mathematical content knowledge at the start, but particularly at the end of the study, was highly predictive of expressions of mathematical pedagogical content knowledge. The stronger predictive value of mathematical content knowledge at the end of the study for mathematical pedagogical content knowledge suggests merit in developing the two aspects of teacher knowledge in tandem, rather than in different courses. The relevance of the data to teacher preparation in the institution and more broadly is discussed.
Similar content being viewed by others
References
Adler, J., & Davis, J. (2006). Opening another black box: Researching mathematics for teaching in mathematics teacher education. Journal for Research in Mathematics Education, 37(40), 270296.
Australian Academy of Science. (2015). Desktop review of mathematics education pedagogical approaches and learning resources. http://www.science.org.au/. Accessed May 15, 2015.
Australian Association of Mathematics Teachers (AAMT). (1996). Statement on the use of calculators and computers for mathematics in Australian schools, 1996. Adelaide: AAMT Inc.
Australian Curriculum, Assessment and Reporting Authority (ACARA). (2012).The Australian Curriculum: Mathematics. http://www.australiancurriculum.edu.au/Mathematics/Rationale/. Accessed May 28, 2013.
Australian Curriculum, Assessment and Reporting Authority (ACARA). (2014a). Numeracy non-calculator year 7. National assessment program litercy and numeracy.
Australian Curriculum, Assessment and Reporting Authority (ACARA). (2014b). Numeracy year 5. National assessment program litercy and numeracy.
Australian Curriculum, Assessment and Reporting Authority (ACARA). (2017a). Australian Curriculum: Mathematics. http://www.v7-5.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=2#page=1. Accessed May 30, 2017.
Australian Curriculum, Assessment and Reporting Authority (ACARA). (2017b). Numeracy across the Australian Curriculum. http://www.v7.australiancurriculum.edu.au/generalcapabilities/numeracy/introduction/numeracy-across-the-curriculum. Accessed Sept 25, 2017.
Australian Institute for Teaching and School Leadership. (AITSL). (2014). Australian professional standards for teachers. https://www.aitsl.edu.au/australian-professional-standards-for-teachers/standards/list/. Accessed Feb 02, 2015.
Ball, D., & Bass, H. (2000). Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics. In J. Boaler (Ed.), Multiple perspectives on the teaching and learning of mathematics (pp. 83–104). Westport: Ablex.
Ball, D., Thames, M., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59, 389–407.
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: Rowan & Littlefield Publishers Inc.
Beswisk, K., & Goos, M. (2012). Measuring pre-service teachers’ knowledge for teaching mathematics. Mathematics Teacher Education and Development, 14(2), 70–90.
Bobis, J., Mulligan, J., & Lowrie, T. (2004). Mathematics for children: Challenging children to think mathematically. Frenchs Forest: Pearson.
Booker, G., Bond, D., Sparrow, L., & Swan, P. (2010). Teaching primary mathematics. Frenchs Forest: Pearson Hall.
Brown, G., & Quinn, R. J. (2006). Algebra students’ difficult with fractions: An error analysis. Australian Mathematics Teacher, 62(4), 28–40.
Brown, G., & Quinn, R. J. (2007). Fraction proficiency and success in algebra. Australian Mathematics Teacher, 63(3), 23–29.
Burghes, D. (2008). International comparative study in mathematics training. Trainee Teacher Primary Mathematics Audit (ICSMTT) CfBT Education Trust. http://www.cimt.plymouth.ac.uk/papers/icsmtt.pdf. Accessed Feb 02, 2015.
Callingham, R., Beswick, K., Clark, J., Kissane, B., Serow, P., & Thorton, S. (2012). Mathematical knowledge for teaching of MERGA Members. In J. Dindyal, L. P. Chen, & S. F. Ng (Eds.), Mathematics education: Expanding horizons (Proceedings of the 35th annual conference of the Mathematics Education Research Group of Australasia). MERGA: Singapore.
Chapman, O. (2015). Understanding and supporting teachers’ knowledge for teaching. Journal of Mathematics Teacher Education, 18, 101–103.
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.
Chick, H., Pham, T., & Baker, M. (2006). Probing teachers’ pedagogical content knowledge: Lessons from the case of the subtraction algorithm. In P. Grootenboer, R. Zevenberg, & M. Chinnapan (Eds.), Identities, cultures and learning spaces: Proceedings of the 29th annual conference of the Mathematics Education Research Group of Australasia (pp. 139–146). MERGA: Adelaide.
Burghes, D., & Geach, R. (2011). International comparative study in mathematics training: Recommendations for initial teacher training in England. CfBT Education Trust. https://www.nationalstemcentre.org.uk/res/documents/page/International%20comparative%20study%20in%20mathematics%20teacher%20training.pdf/. Accessed March 07, 2013.
Delaney, S., Ball, D., Hill, H., Schilling, S., & Zopf, D. (2008). Mathematical content knowledge for teaching: Adapting U.S. measures for use in Ireland. Journal of Mathematics Teacher Education, 11(3), 171–197.
Dohrmann, M., Kaiser, G., & Blomeke, S. (2012). The conceptualisation of mathematics competencies in the international teacher education study TEDS-M. Mathematics Education, 44, 325–340.
Gess-Newsome, J. (2013). Pedagogical content knowledge. In J. Hattie & E. Anderman (Eds.), International guide to student achievement (pp. 257–259). New York: Routledge.
Goldsmith, L., Doerr, H., & Lewis, C. (2014). Mathematics teachers’ learning: A conceptual framework and synthesis of research. Journal of Mathematics Teacher Education, 17, 5–36.
Graven, M. (2002). Mathematics teacher learning, communities of practice and the centrality of confidence. Thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg.
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 May 25, 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.
Hill, H., Rowan, B., & Ball, D. (2005). Effects of teachers’ 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 & Learning, 12(4), 1–13.
Ingram, N., & Linsell, C. (2014). Foundation content knowledge: Pre-service teachers’ attainment and affect. In J. Anderson, M. Cavanagh, & A. Prescott (Eds.), Curriculum in focus: Research guided practice: Proceedings of the 37th annual conference of the Mathematics Education Research Group of Australasia (pp. 712–718). Sydney: MERGA.
Jacobson, E., & Kilpatrick, J. (2015). Understanding teacher affect, knowledge, and instruction over time: An agenda for search on productive disposition for teaching mathematics. Journal of Mathematics Teacher Education, 18, 401–406.
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.
Klein, D. (2005). The state of state Math standards. Fordham Foundation: Thomas B.
Kotzee, B. (2012). Expertise, fluency and social realism about professional knowledge. Journal of Education and Work, 27(2), 161–178. http://www.tandfonline.com/doi/abs/10.1080/13639080.2012.738291. Accessed Feb 02, 2015.
Krainer, K., Hsieh, F. J., Peck, R., & Tatto, M. (2015). The TEDS-M: Important issues, results and questions. In S. J. Cho (Ed.), Proceedings of the 12th international congress on mathematical education. Intellectual and attitudinal challenges (pp. 99–122). Springer, Open.
Leung, F., Park, K., Shimizu, Y., & Xu, B. (2015). Mathematics education in East Asia. The TEDS-M: Important issues, results and questions. In S. J. Cho (Ed.), Proceedings of the 12th international congress on mathematical education. Intellectual and attitudinal challenges (pp. 123–143). Springer, Open.
Livy, S., & Herbert, S. (2013). Pre-service teachers’ responses for ratio and proportion items. In V. Steinle, L. Ball, & C. Bardini (Eds.), Mathematics education: Yesterday, today and tomorrow. Proceedings of the 36th annual conference of the Mathematics Education Research Group of Australasia (pp. 450–457). Melbourne: MERGA.
Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah: Lawrence Erlbaum Associates Inc.
Major, K., & Perger, P. (2014). Personal number sense and New Zealand pre-service teachers. In J. Anderson, M. Cavanagh, & A. Prescott (Eds.), Proceedings of the 37th annual conference of the Mathematics Education Research Group of Australasia (pp. 710–713). Sydney: MERGA.
Marshman, M., & Porter, G. (2013). Pre-service teachers’ pedagogical content knowledge: Implications for teaching. In V. Steinle, L. Ball, & C. Bardini (Eds.), Mathematics education: Yesterday, today and tomorrow. Proceedings of the 36th annual conference of the Mathematics Education Research Group of Australasia (pp. 474–481). Melbourne: MERGA.
Mason, J. (2016). Rising above a cause-and-effect stance in mathematics education research. Journal of Mathematics Teacher Education, 19, 297–300.
Masters, G. (2009). A shared challenge: Improving literacy, numeracy and science learning in Queensland primary schools. Australian Council for Educational Research. http://education.qld.gov.au/mastersreview/. Accessed Jan 31, 2011.
Meyers, D. (2012). Australian universities: A portrait of decline. http://www.australianuniversities.id.au/. Accessed May 09, 2014.
Ministerial Council on Education, Employment, Training and Youth Affairs (MCEETYA). (2014–2015). National assessment program, literacy and numeracy: Numeracy. Carlton: Curriculum Corporation.
Muller, J. (2000). Reclaiming knowledge: Social theory, curriculum and education policy. London: Routledge Falmer.
Muller, J. (2009). Forms of knowledge and curriculum coherence. Journal of Education and Work, 22(3), 205–226. http://www.tandfonline.com/loi/cjew20. Accessed Nov 24, 2012.
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. https://doi.org/10.1080/02691729508578791.
Mullis, I., Martin, M., Foy, P., & Arora, A. (2012). TIMMS international results in mathematics. http://timssandpirls.bc.edu/timss2011/international-results-mathematics.html/. Accessed May 09, 2014.
National Council of Teachers of Mathematics. (2014). Executive summary: Focus in high school mathematics: Reasoning and sense making. http://www.nctm.org/standards/content.aspx?id=23749/. Accessed March 25, 2015.
National Council of Teachers of Mathematics. (2015). Principles and standards of school mathematics. http://www.nctm.org/Standards-and-Positions/Principles-and-Standards/Principles,-Standards,-and-Expectations/. Accessed Jan 14, 2016.
Norton, S. (2012). The use of alternative algorithms in whole number computation. International Journal of Mathematics Teaching and Learning, pp 2–16. Available from: http://www.cimt.plymouth.ac.uk/journal/default.htm.
Norton, S. (2014). Teaching and learning fundamental mathematics. Available online :https://mathematicseducation.vhx.tv/products/teaching-and-learning-fundamental-mathematics
Norton. S. (2016). Primary mathematics teacher education encountering difficult terrain: A personal perspective. International Journal of Mathematics Teaching and Learning. Available from: http://www.cimt.org.uk/ijmtl/index.php/IJMTL/article/view/3/8.
Norton, S. & Zhang, Q. (2016). Primary mathematics teacher education in Australia and China: What might we learn from each other? Journal of Mathematics Teacher Education. Available online from: https://doi.org/10.1007/s10857-016-9359-6.
Organization for Economic Co-operation and Development (OECD). (2014). Education at a glance, 2014. http://www.oecd.org/edu/Education-at-a-Glance-2014.pdf/. Accessed Dec 10, 2015.
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.
Qian, H., & Youngs, P. (2016). The effect of teacher education programs on future elementary mathematics teacher’s knowledge: A five country analysis using TEDS-M data. Journal of Mathematics Teacher Education, 19, 371–396.
Reisman, F. (1978). A guide to the diagnostic teaching of arithmetic. Columbus: Charles E. Merrill Publishing Company.
School of Education and Professional Studies. (2017). A rewarding teacher career starts here. https://www.griffith.edu.au/education/school-education-professional-studies. Accessed March 07, 2017.
Shulman, L. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1–22.
Sonnabend, T. (1993). Mathematics for elementary teachers: An interactive approach. New York: Saunders College Publishing.
Stipek, D., Givvin, K., Salmon, J., & MacGyvers, V. (2001). Teachers’ beliefs and practices related to mathematics instruction. Teacher and Teaching Education, 17, 213–226.
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. http://www.emeraldinsight.com/doi/pdfplus/10.1108/S1479-367920140000027004/. Accessed Dec 12, 2015.
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: Teacher Education and Development International Study Center, College of Education, Michigan University.
Teacher Education Ministerial Advisory Group, (2014). Action now! Classroom ready teachers. http://docs.education.gov.au/system/files/doc/other/action_now_classroom_ready_teachers_print.pdf/. Accessed Dec 10, 2014.
The World University Rankings, (2017). Graduate employability: Top universities in Australia ranked by employers. https://www.timeshighereducation.com/student/best-universities/graduate-employability-top-universities-australia-ranked-employers. Accesssed May 09, 2017.
U.S. Department of Education. (2008). Success: The final report of the National Mathematics Advisory Panel. http://www2.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf/. Accessed Feb 04, 2014.
Van de Walle, J. (2007). Elementary and middle school Mathematics: Teaching developmentally. Boston: Pearson.
Wilson, P., Cooney, T., & Stinson, D. (2005). What constitutes good mathematics teaching and how it develops: Nine high school teachers’ perspectives. Journal of Mathematics Teacher Education, 8(2), 83–111.
Young, M. (2011). The return to subjects: A sociological perspective on the U.K. Coalition government’s approach to the 14-19 curriculum. The Curriculum Journal, 22(2), 265–278.
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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Norton, S. The relationship between mathematical content knowledge and mathematical pedagogical content knowledge of prospective primary teachers. J Math Teacher Educ 22, 489–514 (2019). https://doi.org/10.1007/s10857-018-9401-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10857-018-9401-y