Exercising Mathematical Authority: Three Cases of Preservice Teachers’ Algebraic Justifications

Priya Vinata Prasad, Victoria Jasmine Barron

Abstract


Students’ ability to reason for themselves is a crucial step in developing conceptual understandings of mathematics, especially if those students are preservice teachers. Even if classroom environments are structured to promote students’ reasoning and sense-making, students may rely on prior procedural knowledge to justify their mathematical arguments. In this study, we employed a multiple-case-study research design to investigate how groups of elementary preservice teachers exercised their mathematical authority on a growing visual patterns task.  The results of this study emphasize that even when mathematics teacher educators create classroom environments that delegate mathematical authority to learners, they still need to attend to the strength of preservice teachers’ reliance on their prior knowledge.


Keywords


Pre-service Teachers; Algebraic Reasoning; Justification; Mathematical Authority

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References


Aguirre, J. M., Turner, E. E., Bartell, T. G., Kalinec-Craig, C., Foote, M. Q., Roth McDuffie, A., & Drake, C. (2013). Making connections in practice: How prospective elementary teachers connect to children’s mathematical thinking and community funds of knowledge in mathematics instruction. Journal of Teacher Education, 64(2), 178–192.

Ball, D. L. (1990). The mathematical understandings that prospective teachers bring to teacher education. The Elementary School Journal, 90(4), 449–466.

Berk, D., & Hiebert, J. (2009). Improving the mathematics preparation of elementary teachers, one lesson at a time. Teachers and Teaching, 15(3), 337–356.

Blanton, M. L., & Kaput, J. J. (2005). Characterizing a classroom practice that promotes algebraic reasoning. Journal for Research in Mathematics Education, 36(5), 412–446.

Boaler, J. (2015). Mathematical mindsets: Unleashing students' potential through creative math, inspiring messages and innovative teaching. San Francisco, CA: John Wiley & Sons.

Cai, J., Morris, A., Hwang, S., Hohensee, C., Robison, V., & Hiebert, J. (2017). Improving the impact of educational research. Journal for Research in Mathematics Education, 48(1), 2–6.

Cohen, E. G., & Lotan, R. A. (2014). Designing groupwork: Strategies for the heterogeneous classroom (3rd ed.). New York, NY: Teachers College Press.

Cuff, C. K. (1993). Beyond the formulas—Mathematics education for prospective elementary school teachers. Education, 114(2), 221–224.

Dunleavy, T. (2015). Delegating mathematical authority as a means to strive toward equity. Journal of Urban Mathematics Education, 8(1), 62–82.

Gresalfi, M. S., & Cobb, P. (2006). Cultivating students’ discipline-specific dispositions as a critical goal for pedagogy and equity. Pedagogies, 1(1), 49–57.

Keazer, L. M., & Menon, R. S. (2016). Reasoning and sense-making begins with the teacher. The Mathematics Teacher, 109(5), 343–349.

Krippendorff, K. (2012). Content analysis: An introduction to its methodology. Los Angeles, CA: Sage.

Langer-Osuna, J. (2016). The social construction of authority among peers and its implications for collaborative mathematics problem solving. Mathematical Thinking and Learning, 18(2), 107–124.

Langer-Osuna, J. M. (2017). Authority, identity, and collaborative mathematics. Journal for Research in Mathematics Education, 48(3), 237–247.

Liljedahl, P., & Zazkis, R. (2002). Generalization of patterns: The tension between algebraic thinking and algebraic notation. Educational Studies in Mathematics, 49(3), 379–402.

Lloyd, G., & Wilson, M. (2000). Sharing mathematical authority with students: The challenge for high school teachers. Journal of Curriculum & Supervision, 15(2), 146–169.

Lotan, R. A. (2003). Group-worthy tasks. Educational Leadership, 60(6), 72–75.

Povey, H., & Burton, L. (1999). Learners as authors in the mathematics classroom. In L. Burton (ed.), Learning mathematics, from hierarchies to networks. London, England: Falmer.

Reinholz, D. (2012). Becoming a mathematical authority: The solution lies in the solution. In L. R. van Zoest, J.-J. Lo, & J. L. Kratky (eds.), Proceedings of the 34th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Kalamazoo, MI: Western Michigan University.

Schoenfeld, A. H., & Sloane, A. H. (2016). Mathematical thinking and problem solving. New York, NY: Routledge.

Stein, M. K., Engle, R. A., Smith, M. S., & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical thinking and learning, 10(4), 313–340.

Warren, E. & Cooper, T. (2008). Generalising the pattern rule for visual growth patterns: Actions that support 8 year olds’ thinking. Educational Studies in Mathematics, 67, 171–185.

Webel, C. (2010). High school students’ perspectives on collaboration in their mathematics class. In P. Brosnan, D. B. Erchick, & L. Flevares. (Eds.). Proceedings of the 32nd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Columbus, OH: The Ohio State University.

Zazkis, R. (2011). Relearning mathematics: A challenge for prospective elementary school teachers. Charlotte, NC: Information Age Publishing.


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