### Developing Subject Matter Knowledge through Argumentation

#### Abstract

Argumentation, as a kind of classroom discourse, is beneficial for establishing mathematical knowledge taking place in classroom conversations. It can enhance learners’ development of subject matter knowledge. Hence, this case study was designed to examine the effect of argumentations on developing subject matter knowledge in detail in mathematics. For this purpose, discussions happened in a collective learning environment, designed based on problem-based learning and taking place in a six-week instructional sequence, was investigated focusing on argumentations. 23 preservice middle school mathematics teachers (PMSMT) engaged in tasks designed by the researchers through classroom interaction between them and the instructor in this environment. The PMSMT’s mathematical ideas identified through Toulmin argumentation model were documented in this study. With the help of this model, the mathematical ideas were extracted and the development of PMSMT’s subject matter knowledge was analyzed and documented in detail. It was observed that the PMSMT improved their subject matter knowledge by forming mathematical ideas. They constructed new knowledge and revised their previous knowledge through argumentations.

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Abi-El-Mona, I. & Abd-El-Khalick, F. (2011). Perceptions of the nature and goodness of argument among college students, science teachers and scientists. International Journal of Science Education, 33(4), 573-605.

Andrews, P. (1997). A hungarian perspective on mathematics education. Mathematics Teaching, 161, 14-17.

Author. (2016).

Chapman, O. (2007). Facilitating preservice teachers' development of mathematics knowledge for teaching arithmetic operations. Journal of Mathematics Teacher Education, 10(4), 341-349.

Clements, D. H. & Sarama, J. (2004). Learning trajectories in mathematics education. Mathematical Thinking and Learning, 6(2), 81-89.

Cobb, P. (2000). Conducting classroom teaching experiments in collaboration with teachers. In A. Kelly & R. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 307–334). Mahwah, NJ: Lawrence Erlbaum Associates, Inc.

Cobb, P., & Bauersfeld, H. (1995). Introduction: The coordination of psychological and sociological perspectives in mathematics education. In P. Cobb & H. Bauersfeld (Eds.), The emergence of mathematical meaning: Interaction in classroom cultures (pp. 1–16). Hillsdale, NJ: Erlbaum.

Corcoran, T., Mosher, F. A., & Rogat, A. (2009). Learning progressions in science: An evidence-based approach to reform. New York: Center on Continuous Instructional Improvement Teachers College–Columbia University.

Driver, R., Newton, P., & Osborne, J. (2000). Establishing the norms of scientific argumentation in classrooms. Science Education, 84, 287-312.

Duncan, R. G. (2009). Learning progressions: Aligning curriculum, instruction, and assessment. Journal of Research in Science Teaching, 46(6), 606-609.

Duschl, R. & Osborne, J. (2002). Supporting argumentation discourse in science education. Studies in Science Education, 38, 39-72.

Forman E. A., Larreamendy-Joerns J., Stein M. K., & Brown C. A. (1998). You’re going to want to find out which and prove it. Collective argumentation in a mathematics classroom. Learning and Instruction, 8(6), 527–548.

Goodnough, K. (2006). Enhancing pedagogical content knowledge through self-study: An exploration of problem-based learning. Teaching in Higher Education, 11(3), 301-318.

Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28(5), 534-549.

Hill, H. C. & Ball, D. L. (2004). Learning mathematics for teaching: Results from California's mathematics professional development institutes. Journal for Research in Mathematics Education, 35(5), 330-351.

Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers' topic-specific knowledge of students. Journal for Research in Mathematics Education, 372-400.

Hmelo-Silver, C. E. (2004). Problem-based learning: what and how do students learn? Educational Psychology Review, 16(3), 235-266.

Hufferd-Ackles, K., Fuson, K.C., & Sherin, M.G. (2004). Describing levels and components of a math-talk learning community. Journal for Research in Mathematics Education, 35(2), 81-116.

Jim´enez-Aleixandre, M. P., Bugallo, A., & Duschl, R. A. (2000). Doing the lesson or doing the science: Argument in high school genetics. Science Education, 84(6), 757-792.

Jonassen, D., & Kim, B. (2010). Arguing to learn and learning to argue: Design justifications and guidelines. Educational Technology Research and Development, 58, 439-457.

Lampert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal, 27(1), 29-63.

Lampert, M., & Cobb, P. (2003). White paper on communication and language. In J. Kilpatrick, D. Shifter, & G. Martin (Eds.), Principles and practices of school mathematics: Research companion volume. Reston, VA: National Council of Teachers of Mathematics.

Lester, F. K. (1994). Musings about Mathematical Problem Solving Research: 1970-1994. Journal for Research in Mathematics Education, 25(6), 660-675.

Manuel, S. T. (1998). Instructional qualities of a successful mathematical problem solving class. International Journal of Mathematics Education in Science & Technology, 29(5), 631-645.

National Council of Teachers of Mathematics [NCTM] (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.

National Council of Teachers of Mathematics [NCTM] (2006). Curricular focal points. Reston, VA: National Council of Teachers of Mathematics.

Ng, D. (2011). Indonesian primary teachers' mathematical knowledge for teaching geometry: implications for educational policy and teacher preparation programs. Asia-Pacific Journal of Teacher Education, 39(2), 151-164.

Osborne, J., Erduran, S., & Simon, S. (2004). Enhancing the quality of argumentation in school science. Journal of Research in Science Teaching, 41(10), 994-1020.

Owen, J. E. (1995). Cooperative learning in secondary schools. London: Routledge.

Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26(2), 114-145.

Skemp, R. R. (1978). Relational understanding and instrumental understanding. Arithmetic Teacher, 26(3), 9-15.

Sowder, J., Philipp, R., Armstrong, B., & Schappelle, B. (1998). Middle-grade teachers’ mathematical knowledge and its relationship to instruction: a research monograph. New York: State University of New York Press.

Stake, R.E. (1995). Art of case study research: perspectives on practice. Thousand Oaks, CA: Sage Publications.

Steele, D. F. & Widman, T. F. (1997). Practitioner’s research: a study in changing preservice teachers’ conceptions about mathematics. School Science and Mathematics, 97(4), 184-192.

Steffe, L. P. & Tzur, R. (1994). Interaction and epistemology and mathematical education Children’s mathematics. In P. Ernest (Ed.), Constructing mathematical knowledge. (pp. 8-32). London: Routledge Falmer.

Toulmin, S. E. (1969). The uses of argument. Cambridge: Cambridge University Press.

Van der Sandt, S., & Nieuwoudt, H. D. (2003). Grade 7 teachers’ and prospective teachers’ content knowledge of geometry. South African Journal of Education, 22(1), 199–205.

Voss, J. F., & Van Dyke, J. A. (2001). Argumentation in psychology: Background comments. Discourse Processes, 32, 89-111.

Yin, R. K. (2003). Case study research: Design and methods (3rd ed.). Thousand Oaks, CA: Sage.

Zembaul-Saul, C. (2005, April). Pre-service teachers’ understanding of teaching elementary school science argument. Paper presented at the Annual Meeting of the National Association for Research in Science Teaching, Dallas.

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