Communicating understanding in Mathematics

Creating visual representations

In mathematics, students can be encouraged to create a range of visual texts to support their mathematical thinking, reasoning and communication (Dostal and Robinson, 2017; Armstrong, Ming & Helf, 2018). This relates to modal affordance. 

Adapted by Kress (2010), modal affordance refers to the opportunities and limitations different modes of communication offer. What is possible to communicate in one mode may not be possible in another mode. The cliché, 'a picture is worth a thousand words', is a helpful way to think about modal affordance: while written words may be able to describe elements of an image, the image itself offers other possibilities (affordances) to convey meaning.

The strategies in this section demonstrate how teachers can support students to benefit from modal affordance by using visual texts.

References

  • Armstrong, A., Ming, K., & Helf, S. (2018). Content area literacy in the mathematics classroom. The Clearing House: A Journal of Educational Strategies, Issues and Ideas, 91(2), 85–95.
  • Bremigan, E. G. (2005). An analysis of diagram modification and construction in students' solutions to applied calculus problems. Journal for Research in Mathematics Education, 36, 248-277.
  • Dole, S. (1999). Successful percent problem solving for Year 8 students using the proportional number line method. In J. M. Truran & K. M. Truran (Eds.), Making the difference (Proceedings of the 22nd annual conference of the Mathematics Education Research Group of Australasia, pp. 503–512). Adelaide, SA: MERGA.
  • Dostal, H. M., & Robinson, R. (2018). Doing mathematics with purpose: Mathematical text types. The Clearing House: A Journal of Educational Strategies, Issues and Ideas, 91(2), 21–28.
  • Fisher, D., Frey, N., & Hattie, J. (2016). Visible learning for literacy, Grades K-12: Implementing the practices that work best to accelerate student learning. Thousand Oaks, CA: SAGE Publications.
  • Kress, G. (2010). Multimodality: A Social Semiotic Approach to Contemporary Communication London: Routledge
  • Monteiro, C. & Ainley, J. (2003). Interpretation of graphs: Reading through the data. In J. Williams (Ed.), Proceedings of the British Society for Research into Learning Mathematics. Birmingham, UK: BSRLM. Retrieved from http://www.bsrlm.org.uk/IPs/ip23-3/BSRLMTP-23-3-6.pdf
  • Nunokawa, K. (2004). Solvers' making of drawings in mathematical problem solving and their understanding of the problem situations. International Journal of Mathematical Education in Science and Technolog, 35, 173-183.
  • Quinnell, L. (2014). Scaffolding understanding of tables and graphs. Literacy Learning: The Middle Years, 22(2), 15–21

Supporting solutions

Mathematics students should be encouraged to explain their reasoning and provide justification for their answers. Thought of in this way, the ability for students to express solutions resonates with 'adaptive reasoning' (Kilpatrick et al., 2001). Adaptive reasoning can be described as the capacity for logical thought, reflection, explanation and justification (Watson & Sullivan, 2008).

Implementing strategies that support students to express (and justify) their solutions enables students to better demonstrate and develop their mathematical reasoning. As Hollingsworth et al. argue, students would benefit from "more discussion of alternative solutions, and more opportunity to explain their thinking" (2003, p. xxi).

The strategies in this section show how teachers can support students to express and explain their solutions to mathematical problems.

References

  • Ball, L., & Stacey, K. (2003). What should students record when solving problems with CAS? Reasons, information, the plan and some answers. In J. T. Fey, A. Cuoco, C. Kieran, L. Mullin, & R. M. Zbiek (Eds.), Computer algebra systems in secondary school mathematics education (pp. 289–303). Reston, VA: NCTM.
  • Flynn. P., & Asp, G. (2002). Assessing the potential suitability of "show that" questions in CAS-permitted examinations. In B. Barton, K. C. Irwin, M. Pfannkuch, and M. O. J. Thomas (Eds.), Mathematics Education in the South Pacific (Proceedings of the 25th Annual Conference of the Mathematics Education Research Group of Australasia, Vol. 1, pp. 252-259). Auckland: MERGA.
  • Hillman, A. M. (20140. A literature review on disciplinary literacy: How do secondary teachers apprentice students into mathematical literacy? Journal of Adolescent & Adult Literacy, 57(5), 397–406.
  • Hollingsworth, H., Lokan, J., & McCrae, B. (2003). Teaching mathematics in Australia: Results from the TIMSS video study (TIMSS Australia Monograph No. 5). Melbourne: Australian Council for Educational Research.
  • Johnson, H., & Watson, P. A. (2011). What is it they do: Differentiating knowledge and literacy practices across content disciplines. Journal of Adolescent and Adult Literacy, 55(2), 100–109.
  • Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
  • Swan, M. (n.d.). Improving reasoning: Analysing different approaches. Retrieved from http://nrich.maths.org/7812
  • Victorian Curriculum and Assessment Authority (VCAA). (n.d.) Learning in Mathematics. Retrieved from https://victoriancurriculum.vcaa.vic.edu.au/mathematics/introduction/learning-in-mathematics
  • Watson, A., & Sullivan, P. (2008). Teachers learning about tasks and lessons. In D. Tirosh & T. Wood (Eds.), Tools and resources in mathematics teacher education (pp. 109–135). Sense Publishers: Rotterdam.