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Professional Knowledge of Practising Teachers of Mathematics

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Book cover Research in Mathematics Education in Australasia 2008–2011

Abstract

Teachers’ knowledge of mathematics has become a central focus of educational researchers and policy makers with conceptions of teacher knowledge continuously being transformed. Intuitively, we have known for some time what research now provides an evidence base for—that “teacher knowledge matters” (Sullivan, 2008b, p. 2). But exactly what knowledge matters more, and why, are more significant and vexing questions for researchers and educators to address. Consequently, attention has moved beyond looking solely at what knowledge teachers possess to why different types of knowledge are important and how that knowledge is acquired, studied and impacts on the quality of instruction.

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References

  • Anderson J. Teachers' motivation to attend voluntary professional development in K-10 mathematics. In: Sparrow L, Kissane B, Hurst C, editors. Shaping the future of mathematics education (Proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia. Fremantle, WA: MERGA; 2008. p. 51–58.

    Google Scholar 

  • Anderson J, Bobis J, Way J. Teachers as learners: Building knowledge in and through the practice of teaching mathematics. In: Forgasz H, Barkatsas A, Bishop A, Clarke B, Keast S, Seah WT, Sullivan P, editors. Research in mathematics education in Australasia 2004—2007. Rotterdam: Sense; 2008. p. 313–335.

    Google Scholar 

  • Anstey L, Clarke B. Perceived professional learning needs of numeracy coaches. In: Sparrow L, Kissane B, Hurst C, editors. Shaping the future of mathematics education (Proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia. Fremantle, WA: MERGA; 2010. p. 45–52.

    Google Scholar 

  • Ball DL, Thames MH, Phelps G. Content knowledge for teaching: What makes it special? Journal of Teacher Education. 2008;59:389–407.

    Article  Google Scholar 

  • Barton B. Being mathematical, holding mathematics: Further steps in mathematical knowledge for teaching. In: Hunter R, Bicknell B, Burgess T, editors. Crossing divides (Proceedings of the 32nd annual conference on Mathematics Education Research Group of Australasia. Palmerston North, NZ: MERGA; 2009. p. 3–9.

    Google Scholar 

  • Beswick K, Callingham R, Watson J. The nature and development of middle school mathematics teachers' knowledge. Journal of Mathematics Teacher Education. 2011;14(1):1–27.

    Article  Google Scholar 

  • Boaler J. Studying and capturing the complexity of practice—The case of the 'dance of agency'. In: Pateman NA, Dougherty BJ, Zilliox JT, editors. Proceedings of the 2003 Joints Meeting of the International Group for the Psychology of Mathematics Education and the Psychology of Mathematics Education Group North America. Honolulu, HI: University of Hawaii; 2003. p. 3–16.

    Google Scholar 

  • Bobis J. Teachers assessing young children's mathematical development: How confident are they? In: Dooley T, editor. Mathematics for all: Extending mathematical capacity (Proceedings of the 3rd Conference of the Mathematics Education Ireland Association. Dublin, Ireland: MEI; 2009. p. 20–33.

    Google Scholar 

  • Bobis J. The impact of a developmental framework in number on primary teachers' classroom practice. In: Sparrow L, Kissane B, Hurst C, editors. Shaping the future of mathematics education (Proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia. Fremantle, WA: MERGA; 2010. p. 85–92.

    Google Scholar 

  • Bobis, J., Papic, M., & Mulligan, J. (2009/10). The mathematical knowledge of preschool practitioners: Evidence from the field. Journal of Australian Research in Early Childhood Education, 16(2), 87-98.

    Google Scholar 

  • Brophy JE. Conclusion: Teachers' knowledge of subject matter as it relates to their teaching practice. In: Brophy JE, editor. Advances in research on teaching. Greenwich CT: JAI Press; 1991. p. 349–364.

    Google Scholar 

  • Brown, G. (2009). Review of education in mathematics, data science and quantitative disciplines. (Commissioned Report for Go8 Universities). Retrieved from http://www.go8.edu.au/government-abusiness/go8-policy-a-analysis/2010/183-the-go8-review-of-education-in-mathematics-data-scienceand-quantitative-disciplines

  • Brown JP. Concept maps: Implications for the teaching of function for secondary school students. In: Hunter R, Bicknell B, Burgess T, editors. Crossing divides (Proceedings of the 32nd annual conference on Mathematics Education Research Group of Australasia. Palmerston North, NZ: MERGA; 2009b. p. 65–72.

    Google Scholar 

  • Burgess T. Statistical knowledge for teaching: Exploring it in the classroom. For the Learning of Mathematics. 2009;29(3):18–21.

    Google Scholar 

  • Chick H. Teaching and learning by example. In: Watson J, Beswick K, editors. Mathematics: Essential research, essential practice (Proceedings of the 30th annual conference of the Mathematics Education Research Group of Australasia, Hobart. Adelaide, SA: MERGA; 2007. p. 3–21.

    Google Scholar 

  • Chick HL. Choice and use of examples as a window on mathematical knowledge for teaching. For the Learning of Mathematics. 2009a;29(3):26–30.

    Google Scholar 

  • Chick, H. (2009b). Teaching the distributive law: Is fruit salad still on the menu? In R. Hunter, B. Bicknell, & T. Burgess (Eds.), Crossing divides (Proceedings of the 32nd annual conference on Mathematics Education Research Group of Australasia). Palmerston North, NZ: MERGA. Retrieved from http://www.merga.net.au/documents/Chick_RP09.pdf

  • Chick H. Aspects of teachers' knowledge for helping students learn about ratio. In: Sparrow L, Kissane B, Hurst C, editors. Shaping the future of mathematics education (Proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia. Fremantle, WA: MERGA; 2010. p. 145–152.

    Google Scholar 

  • Chick H, Baker M, Pham T, Cheng H. Aspects of teachers' pedagogical content knowledge for decimals. In: Novotná J, Moraová H, Krátká M, Stehlíková N, editors. Mathematics in the centre (Proceedings of the 30th conference of the International Group for the Psychology of Mathematics Education. Prague, Czech Republic: PME; 2006. p. 297–304.

    Google Scholar 

  • Chick HL, Pierce R. Issues associated with using examples in teaching statistics. In: Figueras O, Cortina JL, Alatorre S, Rojano T, Sepulveda A, editors. Mathematical ideas: History, education and cognition (Proceedings of the Joint meeting of PME 32 and PME-NA XXX. Morelia, Mexico: Cinvestav-UMSNH; 2008. p. 321–328.

    Google Scholar 

  • Clarke D. The mathematics teacher as curriculum maker: Developing knowledge for enacting curriculum. In: Sullivan P, Wood T, editors. Knowledge and beliefs in mathematics teaching and teaching development. Rotterdam, The Netherlands: Sense; 2008. p. 133–151.

    Google Scholar 

  • Clarke D. Theoretical perspectives in mathematics teacher education. In: Tzekaki M, Kaldrimidou M, Sakonidis H, editors. In search of theories in mathematics education (Proceedings of the 33rd conference of the International Group for the Psychology of Mathematics Education. Thessaloniki, Greece: PME; 2009. p. 85–93.

    Google Scholar 

  • Clarke D, Roche A. Teachers' extent of the use of particular task types in mathematics and choices behind that use. In: Sparrow L, Kissane B, Hurst C, editors. Shaping the future of mathematics education (Proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia. Fremantle, WA: MERGA; 2010. p. 153–160.

    Google Scholar 

  • Clarke, D. M., Roche A., & Downton, A. (2009). Assessing teacher pedagogical content knowledge: Challenges and insights. In M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.), In search of theories in mathematics education (Proceedings of the 33rd conference of the International Group for the Psychology of Mathematics Education, p. 362). Thessaloniki, Greece: PME.

    Google Scholar 

  • Ding L, Anthony G, Walshaw M. A teacher's implementation of examples in solving number problems. In: Tzekaki M, Kaldrimidou M, Sakonidis H, editors. In search of theories in mathematics education (Proceedings of the 33rd conference of the International Group for the Psychology of Mathematics Education. Thessaloniki, Greece: PME; 2009. p. 425–432.

    Google Scholar 

  • Dole S, Clarke DM, Weight T, Hilton G, Roche A. Eliciting growth in teachers' proportional reasoning: Measuring the impact of a professional development program. In: Goos M, Brown R, Makar K, editors. Navigating currents and charting directions (Proceedings of the 31st annual conference of the Mathematics Education Research Group of Australasia. Brisbane, QLD: MERGA; 2008. p. 163–169.

    Google Scholar 

  • Fennema E, Franke ML. Teachers' knowledge and its impact. In: Grouws DA, editor. Handbook of research on mathematics teaching and learning. New York, NY: Macmillan; 1992. p. 147–164.

    Google Scholar 

  • Frid, S., Goos, M., & Sparrow, L. (2008/9). What knowledge is needed for effective teaching of mathematics? Mathematics Teacher Education and Development, 9, 1-3.

    Google Scholar 

  • Gaffney M, Faragher R. Sustaining improvement in numeracy: Developing pedagogical content knowledge and leadership capabilities in tandem. Mathematics Teacher Education and Development.. 2010;12(2):72–83.

    Google Scholar 

  • Goos M. A sociocultural framework for understanding technology integration in secondary school mathematics. In: Tzekaki M, Kaldrimidou M, Sakonidis H, editors. In search of theories in mathematics education (Proceedings of the 33rd conference of the International Group for the Psychology of Mathematics Education. Thessaloniki, Greece: PME; 2009. p. 113–120.

    Google Scholar 

  • Hattie JAC. What are the attributes of excellent teachers? In: Webber B, editor. Teachers make a difference: What is the research evidence? Wellington: New Zealand Council for Educational Research; 2002. p. 3–26.

    Google Scholar 

  • Higgins J, Parsons R. A successful professional development model in mathematics: A system-wide New Zealand case. Journal of Teacher Education. 2009;60(3):231–242.

    Article  Google Scholar 

  • Hill H, Ball D, Schilling S. Unpacking pedagogical content knowledge: Conceptualising and measuring teachers' topic-specific knowledge of students. Journal for Research in Mathematics Education. 2008;39(4):372–400.

    Google Scholar 

  • Hill HC, Rowan B, Ball DL. Effects of teachers' mathematical knowledge for teaching on student achievement. American Educational Research Journal. 2005;42(2):371–406.

    Article  Google Scholar 

  • Horne M. Using educational research to inform mathematics teaching in a school. In: Figueras O, Cortina JL, Alatorre S, Rojano T, Sepulveda A, editors. Mathematical ideas: History, education and cognition (Proceedings of the Joint meeting of PME 32 and PME-NA XXX. Morelia, Mexico: Cinvestav-UMSNH; 2008. p. 81–86.

    Google Scholar 

  • MacGregor M. A fresh look at fruit salad algebra. Australian Mathematics Teacher. 1986;42(3):9–11.

    Google Scholar 

  • Mason J, Spence M. Beyond mere knowledge of mathematics: The importance of knowing-to act in the moment. Educational Studies in Mathematics. 1999;38:135–161.

    Article  Google Scholar 

  • Muir T. Principles of practice and teacher actions: Influences on effective teaching of numeracy. Mathematics Education Research Journal. 2008;20(3):78–101.

    Article  Google Scholar 

  • Muir T, Beswick K, Williamson J. Up, close and personal: Teachers' responses to an individualised professional learning opportunity. Asia-Pacific Journal of Teacher Education. 2010;38(2):129–146.

    Article  Google Scholar 

  • O'Keefe M, Bobis J. Primary teachers' perceptions of their knowledge and understanding of measurement. In: Goos M, Brown R, Makar K, editors. Navigating currents and charting directions (Proceedings of the 31st annual conference of the Mathematics Education Research Group of Australasia. Brisbane, QLD: MERGA; 2008. p. 391–397.

    Google Scholar 

  • Owens K, Kaleva W. Case studies of mathematical thinking about area in Papua New Guinea. In: Figueras O, Cortina JL, Alatorre S, Rojano T, Sepulveda A, editors. Mathematical ideas: History, education and cognition (Proceedings of the Joint meeting of PME 32 and PME-NA XXX. Morelia, Mexico: Cinvestav-UMSNH; 2008. p. 73–80.

    Google Scholar 

  • Roche A, Clarke D. Making sense of partitive and quotitive division: A snapshot of teachers' pedagogical content knowledge. In: Hunter R, Bicknell B, Burgess T, editors. Crossing divides (Proceedings of the 32nd annual conference on Mathematics Education Research Group of Australasia. Palmerston North, NZ: MERGA; 2009. p. 467–474.

    Google Scholar 

  • Roche A, Clarke D. Some lessons learned from the experience of assessing teacher pedagogical content knowledge in mathematics. In: Clark J, Kissane B, Mousley J, Spencer T, Thornton S, editors. Mathematics: Traditions and [new] practices (Proceedings of the 34th annual conference of the Mathematics Education Research Group of Australasia and the 23rd biennial conference of the Australian Association of Mathematics Teachers, Alice Springs. Adelaide, SA: AAMT & MERGA; 2011. p. 658–666.

    Google Scholar 

  • Rowland T, Huckstep P, Thwaites A. Elementary teachers' mathematics subject knowledge quartet and the case of Naomi. Journal of Mathematics Teacher Education. 2005;8:255–281.

    Article  Google Scholar 

  • Rowland T, Turner F, Thwaites A, Huckstep P. Developing primary mathematics teaching. London, United Kingdom: Sage; 2009.

    Google Scholar 

  • Shulman L. Those who understand: Knowledge growth in teaching. Educational Researcher. 1986;15(2):4–14.

    Google Scholar 

  • Shulman L. Knowledge and teaching: Foundations of the new reform. Harvard Educational Review. 1987;57(1):1–22.

    Google Scholar 

  • Stacey K. Mathematics for secondary teaching: Four components of discipline knowledge for a changing teacher workforce. In: Sullivan P, Wood T, editors. Knowledge and beliefs in mathematics teaching and teaching development. Rotterdam, The Netherlands: Sense; 2008. p. 87–113.

    Google Scholar 

  • Stacey K, Vincent J. Modes of reasoning in explanations in Australian eighth-grade mathematics textbooks. Educational Studies in Mathematics. 2009;72:271–288.

    Article  Google Scholar 

  • Sullivan P. Education for the knowledge to teach mathematics: It all has to come together. Journal of Mathematics Teacher Education. 2008a;11:431–433.

    Article  Google Scholar 

  • Sullivan P. Knowledge for teaching mathematics: Introduction. In: Sullivan P, Wood T, editors. Knowledge and beliefs in mathematics teaching and teaching development. Rotterdam, The Netherlands: Sense; 2008b. p. 1–9.

    Google Scholar 

  • Sullivan P, Clarke D, Clarke B. Converting mathematics tasks to learning opportunities: An important aspect of knowledge for mathematics teaching. Mathematics Education Research Journal. 2009a;21(1):85–105.

    Article  Google Scholar 

  • Sullivan P, Clarke D, Clarke B, O'Shea H. Exploring the relationship between tasks, teacher actions, and student learning. In: Tzekaki M, Kaldrimidou M, Sakonidis H, editors. In search of theories in mathematics education (Proceedings of the 33rd conference of the International Group for the Psychology of Mathematics Education. Thessaloniki, Greece: PME; 2009b. p. 185–192.

    Google Scholar 

  • Tall D. The transition to advanced mathematical thinking: Functions, limits, infinity, and proof. In: Grouws D, editor. Handbook of research on mathematics teaching and learning. New York, NY: Macmillan; 1992. p. 495–511.

    Google Scholar 

  • Vale C, McAndrew A. Deepening the mathematical knowledge of secondary mathematics teachers who lack tertiary mathematics qualifications. In: Goos M, Brown R, Makar K, editors. Navigating currents and charting directions (Proceedings of the 31st annual conference of the Mathematics Education Research Group of Australasia. Brisbane, QLD: MERGA; 2008. p. 539–545.

    Google Scholar 

  • Visnovska J, Cobb P, Dean C. Mathematics teachers as instructional designers: What does it take? In: Gueudet G, Pepin B, Trouche L, editors. From text to 'lived' resources: Mathematics curriculum materials and teacher development. Dordrecht, The Netherlands: Springer; 2011.

    Google Scholar 

  • Warren, E. (2008/9). Early childhood teachers' professional learning in early algebraic thinking: A model that supports new knowledge and pedagogy. Journal of Mathematics Teacher Education & Development, 9, 30-45.

    Google Scholar 

  • Watson J, Brown N, Beswick K, Wright S. Teacher change in a changing educational environment. In: Clark J, Kissane B, Mousley J, Spencer T, Thornton S, editors. Mathematics: Traditions and [new] practices (Proceedings of the 34th annual conference of the Mathematics Education Research Group of Australasia and the 23rd biennial conference of the Australian Association of Mathematics Teachers, Alice Springs. Adelaide, SA: AAMT & MERGA; 2011. p. 760–767.

    Google Scholar 

  • Watson, J., Callingham, R., & Donne, J. (2008a). Establishing PCK for teaching statistics. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (Eds.), Teaching statistics in school mathematics: Challenges for teaching and teacher education (Proceedings of the Joint ICMI/IASE study conference 18 and IASE Round Table Conference, CD). Monterrey, Mexico: ICMI, IASE & ISI. Retrieved from http://www.ugr.es/~icmi/iase_study/Files/Topic2/T2P10_Watson.pdf

  • Watson J, Callingham R, Donne J. Proportional reasoning: Student knowledge and teachers' pedagogical content knowledge. In: Goos M, Brown R, Makar K, editors. Navigating currents and charting directions (Proceedings of the 31st annual conference of the Mathematics Education Research Group of Australasia. Brisbane, QLD: MERGA; 2008b. p. 563–571.

    Google Scholar 

  • Watson J, Callingham R, Nathan E. Probing teachers' pedagogical content knowledge in statistics: "How will Tom get to school tomorrow?". In: Hunter R, Bicknell B, Burgess T, editors. Crossing divides (Proceedings of the 32nd annual conference on Mathematics Education Research Group of Australasia. Palmerston North, NZ: MERGA; 2009. p. 563–570.

    Google Scholar 

  • Watson JM, Nathan EL. Biased sampling and PCK: The case of a marijuana problem. In: Sparrow L, Kissane B, Hurst C, editors. Shaping the future of mathematics education (Proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia. Fremantle, WA: MERGA; 2010. p. 610–617.

    Google Scholar 

  • White AL. Counting On in the middle years. In: Sparrow L, Kissane B, Hurst C, editors. Shaping the future of mathematics education (Proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia. Fremantle, WA: MERGA; 2010. p. 618–625.

    Google Scholar 

  • Yeo KKJ. Teaching area and perimeter: Mathematics-pedagogical-content knowledge-in-action. In: Goos M, Brown R, Makar K, editors. Navigating currents and charting directions (Proceedings of the 31st annual conference of the Mathematics Education Research Group of Australasia. Brisbane, QLD: MERGA; 2008. p. 621–627.

    Google Scholar 

  • Zaslavsky O, Sullivan P. Constructing knowledge for teaching secondary mathematics: Tasks to enhance prospective and practicing teacher learning. New York, NY: Springer; 2011.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Faculty of Education and Social Work, University of Sydney, Sydney, Australia

    Janette Bobis

  2. Faculty of Education and Social Work, University of Sydney, Sydney, Australia

    Joanna Higgins

  3. School of Education, Macquarie University, Burnie TAS 7320, Australia

    Michael Cavanagh

  4. Mathematics Teaching and Learning Research Centre Australian, Catholic University, Washington, United States

    Anne Roche

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  1. Janette Bobis
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  2. Joanna Higgins
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  3. Michael Cavanagh
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  4. Anne Roche
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Editor information

Editors and Affiliations

  1. Research Institute for Professional Practice, Learning and Education, Charles Sturt University, Albury Wodonga, Australia

    Bob Perry

  2. Research Institute for Professional Practice, Learning and Education, Charles Sturt University, Wagga Wagga, Australia

    Tom Lowrie

  3. Research Institute for Professional Practice, Learning and Education, Charles Sturt University, Wagga Wagga, Australia

    Tracy Logan

  4. Research Institute for Professional Practice, Learning and Education, Charles Sturt University, Albury Wodonga, Australia

    Amy MacDonald

  5. Research Institute for Professional Practice, Learning and Education, Charles Sturt University, Wagga Wagga, Australia

    Jane Greenlees

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© 2012 Sense Publishers

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Bobis, J., Higgins, J., Cavanagh, M., Roche, A. (2012). Professional Knowledge of Practising Teachers of Mathematics. In: Perry, B., Lowrie, T., Logan, T., MacDonald, A., Greenlees, J. (eds) Research in Mathematics Education in Australasia 2008–2011. SensePublishers, Rotterdam. https://doi.org/10.1007/978-94-6091-970-1_15

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