Supporting argumentation in mathematics classrooms

The role of teachers’ mathematical knowledge

Authors

  • John Francisco Department of Teacher Education and Curriculum Studies (TECS), University of Massachusetts Amherst, USA

DOI:

https://doi.org/10.31129/LUMAT.10.2.1701

Keywords:

mathematical knowledge for teaching, argumentation, mathematical arguments, collective argumentation, teacher support of argumentation

Abstract

Reform movements in mathematics education advocate that mathematical argumentation play a central role in all classrooms. However, research shows that mathematics teachers at all grade level find it challenging to support argumentation in mathematics classrooms. This study examines the role of teachers’ mathematical knowledge in teachers’ support of argumentation in mathematics classroom. The study addresses a documented need for a better understanding of the relationship between mathematical knowledge for teaching and instruction by focusing on how the knowledge influences teachers’ support of argumentation. The results provide insights into particular aspects of teachers’ mathematical knowledge that influence teachers’ support of students’ development of valid mathematical arguments in mathematics classrooms and suggest implications for research and practice.

References

Adler, J., & Davis, Z. (2006). Opening another black box: Researching mathematics for teaching in mathematics teacher education. Journal for Research in Mathematics Education, 37, 270-296.

Ayalon, M., & Even, R. (2016). Factors shaping students’ opportunities to engage in argumentative activity. International Journal of Science and Mathematics Education, 14, 575–601.

Ayalon, M., & Hershkowitz, R. (2017). Mathematics teachers’ attention to potential classroom situations of argumentation. The Journal of Mathematical Behavior, 49, 163–173.

Baker, M. (2003) ‘Computer-mediated interactions for the co-elaboration of scientific notions’, in: J. Andriessen, M. Baker and D. Suthers (eds) Arguing to Learn: confronting cognitions in computer supported collaborative learning environments, Dordrecht, The Netherlands: Kluwer.

Ball, D.L. (1988). Unlearning to teach mathematics. For the Learning of Mathematics, 8(1), 40–48.

Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407.

Ball, D. L., Bass, H., & Hill, H. C. (2004). Knowing and using mathematical knowledge in teaching: Learning what matters. Paper presented at the 12th annual conference of the Southern African association for research in mathematics, science, and technology education, Cape Town, South Africa.

Ball, D. L., Lubienski, S. T., & Mewborn, D. S. (2001). Research on teaching mathematics: The unsolved problem of teachers’ mathematical knowledge. In V. Richardson (Ed.), Handbook of research on teaching. New York: Macmillan.

Bieda, K. N. (2010). Enacting proof-related tasks in middle school mathematics: Challenges and opportunities. Journal for Research in Mathematics Education, 41(4), 351–382.

Bleiler, S. K., Thompson, D. R., & Krajčevski, M. (2014). Providing written feedback on students’ mathematical arguments: Proof validations of prospective secondary mathematics teachers. Journal of Mathematics Teacher Education, 17, 105–127.

Cengiz, N., Kline, K., & Grant, T. J. (2011). Extending students’ mathematical thinking during whole-group discussions. Journal of Mathematics Teacher Education, 14, 355-374.

Conner, A., Singletary, L. M., Smith, R. C., Wagner, P. A., & Francisco, R. T. (2014). Teacher support for collective argumentation: A framework for examining how teachers support students’ engagement in mathematical activities. Educational Studies in Mathematics, 86, 401–429.

Douek, N. (1999). Argumentation and conceptualization in context: A case study on sun shadows in primary school. Educational Studies in Mathematics, 39, 89–110.

Erickson, F. (2006). Definition and analysis of data from videotape: Some research procedures and their rationales. In J. Green, J. Camilli, & P. Elmore (Eds.), Handbook of complementary methods in educational research (3rd ed., pp. 177–191). Mahwah, NJ: Lawrence Erlbaum.

Fennema, E., & Franke, L. M. (1992). Teachers’ knowledge and its impact. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 147–164). New York, NY: Macmillan.

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, 6, 527–548.

Harel, G., & Sowder, L. (2007). Toward comprehensive perspectives on the learning and teaching of proof. In F. K. Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 805–842). Charlotte, NC: Information Age Publishing.

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.

Hill, H. C., Schilling, S. G., & Ball, D. L. (2004). Developing measures of teachers’ mathematics knowledge for teaching. The Elementary School Journal, 105(1), 11–30.

Inglis, M., Mejia-Ramos, J. P., & Simpson, A. (2007). Modelling mathematical argumentation: The importance of qualification. Educational Studies in Mathematics, 66, 3–21.

Knipping, C., & Reid, D. (2015). Reconstructing argumentation structures: A perspective on proving processes in secondary mathematics classroom interaction. In A. Bikner-Ahsbahs, C. Knipping, & N. Presmeg (Eds.), Approaches to qualitative research in mathematics education: Examples of methodology and methods (pp. 75-101). New York: Springer.

Krummheuer, G. (1995). The ethnography of argumentation. In P. Cobb & H. Bauersfeld (Eds.), The emergence of mathematical meaning: Interaction in classroom cultures (pp. 229–269). Hillsdale, NJ: Lawrence Erlbaum.

Kosko, K. W., Rougee, A., & Herbst, P. (2014). What actions do teachers envision when asked to facilitate mathematical argumentation in the classroom? Mathematics Education Research Journal, 26, 459–476.

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

Maher, C. A. (1998). Can teachers help children make convincing arguments? A glimpse into the process. Rio de Janeiro, Brazil: Universidade Santa Ursula (in Portuguese and English).

Maher, C., Landis, J., & Palius, M. (2010). Teachers Attending to Students’ Reasoning: Using Videos as Tools. Journal of Mathematics Education, 3(2), 1–24.

Mueller, M., Yankelewitz, D., & Maher, C. (2014). Teachers promoting student mathematical reasoning. Investigations in Mathematics Learning, 7(2), 1–20.

National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common core state standards: Mathematics standards. Washington, DC: National Governors Association Center for Best Practices, Council of Chief State School Officers. http://www.corestandards. org/the-standards/mathematics.

Petrou, M., & Goulding, M. (2011). Conceptualising teachers’ mathematical knowledge in teaching. In T. Rowland, & K. Ruthven (Eds.), Mathematical knowledge in teaching (pp. 9-25). Dordrecht: Springer.

Powell, A. B., Francisco, J. M., and Maher, C. A. (2003). An analytical model for studying the development of learners' mathematical ideas and reasoning using videotape data. Journal of Mathematical Behavior, 22, 405–435.

Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.

Rowland, T. (2005). The Knowledge Quartet: A tool for developing mathematics teaching. In: A. Gagatsis (Ed.), Proceedings of the 4th Mediterranean conference on mathematics education (pp. 69–81). Nicosia: Cyprus Mathematical Society.

Rowland, T. (2007). Developing knowledge for teaching: A theoretical loop. In: S. Close, D. Corcoran, & T. Dooley (Eds.), Proceedings of the 2nd national conference on research in mathematics education (pp. 14–27). Dublin: St Patrick’s College.

Rowland, T., Huckstep, P., & Thwaites, A. (2003). The knowledge quartet. In: J. Williams (Ed.), Proceedings of the British Society for Research into Learning Mathematics, 23(3), 97–102. Schoen, H. L., Fey, J. T., Hirsch, C. R., & Coxford, A. F. (1999). Issues and options in the math wars. Phi Delta Kappan, 80, 444–453.

Schwarz, B. B., Hershkowitz, R., & Prusak, N. (2010). Argumentation and Mathematics. In C. Howe & K. Littleton (Eds.), Educational dialogues: Understanding and promoting productive interaction (pp. 115–141). New York, NY: Routledge.

Stake, R. E. (1994). Case studies. In N. K. Denzin & Y. S. Lincoln (Eds.), Handbook of qualitative research (p. 236–247). Sage Publications, Inc.

Staples, M. E., Bartlo, J., & Thanheiser, E. (2012). Justification as a Teaching and Learning Practice: Its (Potential) Multifacted Role in Middle Grades Mathematics Classrooms. Journal of Mathematical Behavior, 31(4), 447–462. https://doi.org/10.1016/j.jmathb.2012.07.001

Tirosh, D., & Even, R. (2007). Teachers’ knowledge of students’ mathematical learning: An examination of commonly held assumptions. Mathematics knowledge in teaching seminar series: Conceptualising and theorizing mathematical knowledge for teaching (Seminar1) Cambridge, MA: University of Cambridge.

Toulmin, S. E. (2003). The uses of argument (updated ed.). New York: Cambridge University Press. Original work published 1958.

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

Ubuz, B., Dincer, S., & Bulbul, A. (2012). Argumentation in undergraduate math courses : A study on proof generation. In T.-Y. Tso (Ed.), Proceedings of the 36th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 163– 170). Taipeh, Taiwan: PME

van Eemeren, F. H., Grootendorst, R., Henkenmans, F. S., Blair, J. A., Johnson, R. H, Krabb, E. C., Plantin, C., Walton, D. N., Willard, C. A., Woods, J. and Zarefsky, D. (1996) Fundamentals of Argumentation Theory: a handbook of historical background and contemporary developments, Hillsdale, NJ: Lawrence Erlbaum.

Van Ness, C. & Maher, C. A. (2019). Analysis of the argumentation of nine-year olds engaged in discourse about comparing fraction models. Journal of Mathematical Behavior, (53), 13-41. Elsevier, London.

Whitenack, J., & Knipping, N. (2002). Argumentation, instructional design theory and students’ mathematical learning: A case for coordinating interpretive lenses. Journal of Mathematical Behavior, 21, S0732-3123(02)00144-X.

Yackel, E. (2002). What we can learn from analyzing the teacher’s role in collective argumentation. Journal of Mathematical Behavior, 21, 423–440.

Downloads

Published

2022-06-30

How to Cite

Francisco, J. (2022). Supporting argumentation in mathematics classrooms: The role of teachers’ mathematical knowledge. LUMAT: International Journal on Math, Science and Technology Education, 10(2), 147–170. https://doi.org/10.31129/LUMAT.10.2.1701

Similar Articles

<< < 9 10 11 12 13 14 15 16 17 18 > >> 

You may also start an advanced similarity search for this article.