Abstract
Teacher knowledge that supports effective mathematics teaching has come under scrutiny alongside associated theoretical developments in the education field. Amongst these developments, the Mathematics Knowledge for Teaching (MKT) framework by Ball et al. (J Teacher Educ 59(5):389–407, 2008) has been one of the most influential. While MKT has been useful in helping us identify the knowledge strands teachers need for effective practice, the interplay among MKT’s knowledge strands during the course of teaching has received less attention. In this study, we address this issue by exploring interaction between Subject Matter Knowledge (SMK) and Pedagogical Content Knowledge (PCK) in the domain of secondary geometry . We provide results of a preliminary study of SMK and PCK in the context of a teacher teaching students how to construct and bisect an acute angle with the aid of compass and ruler only. Our analysis suggests future research needs to consider (a) the particular characteristics of the discipline of geometry and (b) the developmental knowledge trajectories of teachers of geometry in order to better understand how teachers’ SMK influences and influenced by PCK.
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References
Ball, D., Thames, M., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407.
Ball, D. L., & Hill, H. C. (2008). Measuring teacher quality in practice. In D. H. Gitomer (Ed.), Measurement issues and assessment for teaching quality (pp. 80–98). Thousand Oaks, CA: SAGE.
Ball, D. L., Hill, H. C, & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, 29(1), 14–17, 20–22, 43–46.
Beswick, K. (2014). What teachers want: Identifying mathematics teachers’ professional learning needs. The Mathematics Enthusiast, 11(1), 83–108.
Bobis, J., Higgins, J., Cavanagh, M., & Roche, A. (2012). Professional knowledge of practicing teachers of mathematics. In B. Perry, T. Lowrie, T. Logan, A. MacDonald, & J. Greenlees (Eds.), Mathematics Education Research Group of Australasia: Research in mathematics education in Australasia 2008–2011 (pp. 313–341). The Netherlands: Sense Publishers.
Borko, H., & Putnam, R. T. (1996). Learning to teach. In D. C. Berliner & R. C. Calfee (Eds.), Handbook of Educational Psychology (pp. 673–708). New York: Macmillan Library. Reference USA: Simon & Schuster Macmillan.
Butterfield, B., & Chinnappan, M. (2010). Walking the talk: Translation of mathematical content knowledge to practice. In L. Sparrow, B. Kissane, & C. Hurst (Eds.), Shaping the future of mathematics education—Proceedings of the 33rd Annual Conference of the Mathematics Education Research Group of Australasia (pp 109–116). Fremantle, WA: MERGA.
Carreño, E., Rojas, N., Montes, M. A., & Flores, P. (2013). Mathematics teacher’s specialized knowledge. Reflections based on specific descriptors of knowledge. In Proceedings of the CERME, 8, 2976–2984. Antalya, Turkey: ERME.
Chinnappan, M. (1998). Schemas and mental models in geometry problem solving. Educational Studies in Mathematics, 36(3), 201–217.
Chinnappan, M., & White, B. (2015). Specialized content knowledge: Evidence of pre-service teachers’ appraisal of student errors in proportional reasoning. In M. Marshman, V. Geiger, & A. Bennison (Eds.), Mathematics Education in the Margins: Proceedings of the 38th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 157–164). Sunshine Coast: MERGA.
Chinnappan, M., & Forrester, T. (2014). Generating procedural and conceptual knowledge of fractions by pre-service teachers. Mathematics Education Research Journal, 26(4), 871–896.
Chinnappan, M., & Lawson, M. (2005). A framework for analysis of teachers’ geometric content knowledge and geometric knowledge for teaching. Journal of Mathematics Teacher Education, 8(3), 197–221.
Herbst, P., & Kosko, K. (2014). Mathematical knowledge for teaching and its specificity to high school geometry instruction. In J.-J. Lo, K. R. Van Zoest, & R. Laura (Eds.), Research trends in mathematics teacher education (pp. 23–45). New York, NY: Springer. https://doi.org/10.1007/978-3-319-02562-9_2.
Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371–406.
Fennema, E., & Franke, M. L. (1992). Teachers’ knowledge and its impact. In D. A. Grouws (Ed.), Handbook of research in mathematics teaching and learning (pp. 147–164). New York: Macmillan.
Lawson, M. J., & Chinnappan, M. (2015). Knowledge connectedness and the quality of student and teacher mathematical knowledge. In E. A. Silver & P. Kenney (Eds.), More lessons learned from research (pp. 272–277). Reston: National Council of Teachers of Mathematics.
Lawson, M., & Chinnappan, M. (2000). Knowledge connectedness in geometry problem solving. Journal for Research in Mathematics Education, 31(1), 26–43.
Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 33–40). Hillsdale, NJ: Erlbaum.
Mayer, R. E. (1975). Information processing variables in learning to solve problems. Review of Research in Education, 45, 525–541.
Mitchell, R., Charalambous, C. Y., & Hill, H. C. (2014). Examining the task and knowledge demands needed to teach with representations. Journal of Mathematics Teacher Education, 17, 37–60. https://doi.org/10.1007/s10857-013-9253-4.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
Shulman, L. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1–22.
Skemp, R. R. (1978). Relational understanding and instrumental understanding. Arithmetic Teacher, 26(3), 9–15.
Sullivan, P. (2011). Identifying and describing the knowledge needed by teachers of mathematics. Journal of Mathematics Teacher Education, 14, 171–173. https://doi.org/10.1007/s10857-011-9188-6.
Thomson, S., Hillman, K., Wernert, N., Schmid, M., Buckley. S., & Munen, A. (2012). Highlights from TIMSS & PIRLS 2011 from Australia’s perspective. https://www.acer.edu.au/files/TIMSS-PIRLS_Australian-Highlights.pdf.
Thwaites, A., Jared, L., & Rowland, T. (2011). Analysing secondary mathematics teaching with the Knowledge Quartet. Research in Mathematics Education, 13(2), 227–228.
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Chinnappan, M., White, B., Trenholm, S. (2018). Symbiosis Between Subject Matter and Pedagogical Knowledge in Geometry. In: Herbst, P., Cheah, U., Richard, P., Jones, K. (eds) International Perspectives on the Teaching and Learning of Geometry in Secondary Schools. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-77476-3_9
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