375
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Using Open-response Tasks to Reveal the Conceptual Understanding of Learners—Learners Teaching the Teacher what they Know about Trigonometry

& ORCID Icon

References

  • Becker, J. P., & Shimada, S. (Eds.) (2007). The open-ended approach: A new proposal for teaching mathematics. Reston, VA: National Council of Teachers of Mathematics.
  • Cohen, L., Manion, L. & Morrison, K. (2011). Research methods in education (7th ed.). London: Routledge.
  • Department of Basic Education (2011). Report on the National Senior Certificate Examination 2011—National Diagnostic Report on Learner performance. Retrieved from http://www.education.gov.za/Portals/0/Documents/Reports/201120NSC20DiagnosticReport.pdf?ver=2015-06-25-104952-187
  • Didis, M. G., Erbas, A. K., Cetinkaya, B., Cakiroglu, E. & Alacaci, C. (2016). Exploring prospective secondary mathematics teachers’ interpretation of student thinking through analysing students’ work in modelling. Mathematics Education Research Journal, 28(3), 349–378. doi: 10.1007/s13394-016-0170-6
  • Hiebert, J. & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics. (pp. 1–17) Hillsdale, NJ: Lawrence Erlbaum.
  • Kilpatrick, J., Swafford, J. & Findell, B. (Eds.) (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
  • Naidoo, K. & Naidoo, R. (2011). Exploring a blended learning model to teach first year mathematics education students trigonometry at a UoT. Journal of College Teaching and Learning, 4(8), 719–726.
  • Premprayoon, K., Loipha, S., & Inprasitha, M. (2014). Language and symbol students use in Thai mathematical classroom of lesson study and open approach. Creative Education, 5(16), 1523–1527. doi: 10.4236/ce.2014.516169
  • Schneider, M. & Stern, E. (2010). The developmental relations between conceptual and procedural knowledge: A multimethod approach. Developmental Psychology, 46(1), 178–192. doi: 10.1037/a0016701
  • Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22, 1–36. doi: 10.1007/BF00302715
  • Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20–26.
  • Star, J. R. & Stylianides, G. J. (2013). Procedural and conceptual knowledge: Exploring the gap between knowledge type and knowledge quality. Canadian Journal of Science, Mathematics and Technology Education, 13(2), 169–181. doi: 10.1080/14926156.2013.784828
  • Suh, J. (2007). Tying it all together: Classroom practices that promote mathematical proficiency for all students. Teaching Children Mathematics, 14(3), 163–169.
  • Tall, D. & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12, 151–169. doi: 10.1007/BF00305619
  • van Jaarsveld, P. P. (2007). Hermeneutic and empirical analyses of graphically inspired mathematics that reflect critical consciousness within perspectives of personal and social justice. Unpublished PhD thesis. Rhodes University, Grahamstown, South Africa.
  • Vinner, S. (2002). The role of definitions in the teaching and learning of mathematics. In D. Tall (Ed.), Advanced mathematical thinking (pp. 65–81). New York: Kluwer.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.