Leveraging Reasoning through Discourse: A Case Study in Secondary Mathematics Classrooms

Authors: Cory A. Bennett

Abstract:

Teaching and learning through the use of discourse support students’ conceptual understanding by attending to key concepts and relationships. One discourse structure used in primary classrooms is number talks wherein students mentally calculate, discuss, and reason about the appropriateness and efficiency of their strategies. In the secondary mathematics classroom, the mathematics understudy does not often lend itself to mental calculations yet learning to reason, and articulate reasoning, is central to learning mathematics. This qualitative case study discusses how one secondary school in the Middle East adapted the number talk protocol for secondary mathematics classrooms. Several challenges in implementing ‘reasoning talks’ became apparent including shifting current discourse protocols and practices to a more student-centric model, accurately recording and probing student thinking, and specifically attending to reasoning rather than computations.

Keywords: Discourse, reasoning, secondary mathematics, teacher development.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1317162

References:

[1] Seeley, C. L. Making sense of math: How to help every student become a mathematical thinker and problem solver. Alexandria, VA: ASCD, 2016.
[2] Bennett, C. A. “It's hard getting kids to talk about math”: Helping new teachers improve mathematical discourse.” Action in Teacher Education, vol. 32, no. 3, pp. 79-89, 2010.
[3] Parrish, S. Number talks: Helping children build mental math and computation strategies. Sausalito, CA: Math Solutions, 2014.
[4] National Council of Teachers of Mathematics. Principles and Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics, 2000.
[5] Piccolo, D. L., Harbaugh, A. P., Carter, T. A., Capraro, M. M., & Capraro, R. M. “Quality of instruction: Examining discourse in middle school mathematics instruction.” Journal of Advanced Academics, vol. 19, no. 3, pp. 376-410, 2008.
[6] Roberts, T., & Billings, L. “Speak up and listen.” Phi Delta Kappan, vol. 91, no. 2, pp. 81-85, 2009.
[7] Kuhn, D. Education for thinking. Cambridge, MA: Harvard University Press, 2005.
[8] National Council of Teachers of Mathematics. Principles to action: Ensuring mathematical success for all. Reston: National Council of Teachers of Mathematics, 2014.
[9] Alvarez, D. “Engaging students in their learning.” Leadership, vol. 32, no. 2, pp. 12–15, 2002.
[10] Bryson, C., & Hand, L. “The role of engagement in inspiring teaching and learning.” Innovations in Education and Teaching International, vol. 44, no. 4, pp. 349-362, 2007.
[11] Falle, J. “Let’s talk maths: A model for teaching to reveal student understandings.” Australian Senior Mathematics Journal, vol. 18, no. 2, pp. 17-27, 2004.
[12] Clarke, D., & Sullivan, P. “Is a question the best answer?” The Australian Mathematics Teacher, vol. 46, no. 3, pp. 30-33, 1990.
[13] Staples, M. “Supporting whole-class collaborative inquiry in a secondary mathematics classroom.” Cognition and Instruction, vol. 25, no. 2, pp. 161-217, 2007.
[14] Mercer, N. “Talk and the development of reasoning and understanding.” Human Development, vol. 51, pp. 90-100, 2008.
[15] Humphreys, C. & Parker, R. Making number talks matter. Portland, ME: Stenhouse Publishers, 2015.
[16] Lannin, J. K., Elliott, R., & Ellis, A. B. Developing essential understanding of mathematical reasoning for teaching mathematics in prekindergarten-grade 8. Reston, VA: National Council of Teachers of Mathematics, 2011.
[17] Bennett, C. A. “Reasoning talks: Bridging number talks by focusing on reasoning.” Retrieved from http://smithcurriculumconsulting.com/ middle-school-number-talks/
[18] Desimone, L. M. “Improving impact studies of teachers’ professional development: Toward better conceptualizations and measures.” Educational Researcher, vol. 38, pp. 181–199, 2009.
[19] Corbin, J., & Strauss, A. Basics of qualitative research: Techniques and procedures for developing grounded theory (3rd ed.). Thousand Oaks, CA: Sage, 2007.
[20] Smith, M. S., & Stein, M. K. 5 practices for orchestrating productive mathematical discussions. Reston, VA: National Council of Teachers of Mathematics, 2011.
[21] Patton, M. Q. Qualitative research and evaluation methods (3nd Ed). Thousand Oaks, CA: Sage, 2002.
[22] Cazden, C. B. Classroom discourse: The language of teaching and learning. Portsmouth, NH: Heinemann, 1988.
[23] Huang, J., Normandia, B., & Greer, S. “Communicating mathematically: Comparison of knowledge structures in teacher and student discourse in a secondary math classroom.” Communicating Education, vol. 54, no. 1, pp. 34-51, 2005.
[24] Hmelo-Silver, C. E., & Barrows, H. S. “Facilitating collaborative knowledge building.” Cognition and Instruction, vol. 26, pp. 48-94, 2008.
[25] Skemp, R. “Relational understanding and instrumental understanding.” Mathematics Teaching, vol. 77, pp. 20-26, 1976.
[26] Rigelman, N. M. “Eliciting high-level student mathematical discourse: Relationships between the intended and enacted curriculum,” in L. Knott (Ed.), The role of mathematics discourse in producing leaders of discourse (pp. 153-172). Charlotte, NC: Information Age Publishing, 2010.
[27] Bengo, P. “Secondary mathematics coaching: The components of effective mathematics coaching and implications.” Teaching and Teacher Education, vol. 60, pp. 88-96, 2016.
[28] Van Es, E. A. “A framework for learning to notice student mathematical thinking,” in M.G. Sherin, V. R. Jacobs, & R. Al Philipp (Eds.), Mathematics Teacher Noticing (pp. 134-151). New York: Routledge, 2011.