A Case Study of Two Selected Teachers as they Integrated Dynamic Geometry Software as a Visualisation Tool in Teaching Geometry

References

• Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52(3), 215–241. doi: 10.1023/A:1024312321077
   Google Scholar
• 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. doi: 10.1177/0022487108324554
   Web of Science ®Google Scholar
• Cohen, L., Manion, L., & Morrison, K. (2007). Research methods in education (6th ed.). Oxford: Routledge.
   Google Scholar
• Department of Basic Education Ministerial Committee (2013). Investigation into the implementation of maths, science and technology. Pretoria: Department of Basic Education, South Africa.
   Google Scholar
• Duval, R. (2013). The first crucial point in geometry learning: Visualization. Mediterranean Journal for Research in Mathematics Education, 12(1–2), 23–37.
   Google Scholar
• Duval, R. (2014). Commentary: Linking epistemology and semio-cognitive modeling in visualization. ZDM—International Journal on Mathematics Education, 46(1), 159–170. doi: 10.1007/s11858-013-0565-8
   Google Scholar
• Gueudet, G., & Trouche, L. (2011). Mathematics teacher education advanced methods: An example in dynamic geometry. ZDM—International Journal on Mathematics Education, 43, 399–411. doi: 10.1007/s11858-011-0313-x
   Google Scholar
• Guzmán, M. De (2002). The role of visualization in the teaching and learning of mathematical analysis. In Proceedings of the International Conference on the Teaching of Mathematics, Crete. Available from: https://eric.ed.gov/?id = ED472047 (accessed 4 September 2018).
   Google Scholar
• Hölzl, R. (2001). Using dynamic geometry software to add contrast to geometric situations—A case study. International Journal of Computers for Mathematical Learning, 6, 63–86. doi: 10.1023/A:1011464425023
   Google Scholar
• Hölzl, R., & Schäfer, M. (2013). Dynamic geometry software as a dynamic tool for spatial exploration. Learning and Teaching Mathematics, 15, 41–45.
   Google Scholar
• Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it Up: Helping Children Learn Mathematics. Washington, DC: National Academy Press.
   Google Scholar
• Laborde, C. (2001). Integration of technology in the design of geometry tasks with cabri-geometry. International Journal of Computers for Mathematical Learning, 6, 283–317. doi: 10.1023/A:1013309728825
   Google Scholar
• Leung, A. (2011). An epistemic model of task design in dynamic geometry environment. ZDM—International Journal on Mathematics Education, 43, 325–336. doi: 10.1007/s11858-011-0329-2
   Google Scholar
• Mhlolo, M. K., & Schäfer, M. (2013). ‘The area of a triangle is 180°C’—An analysis of learners’ idiosyncratic geometry responses through the lenses of Vygotsky’s theory of concept formation. African Journal of Research in Mathematics, Science and Technology Education, 17(1–2), 83–93.
   Google Scholar
• Moyer, P.S., Bolyard, J., & Spikell, M. (2002). What are virtual manipulatives? Teaching Children Mathematics (NCTM), 8, 372–377.
   Google Scholar
• Naidoo, J., & Govender, R. (2014). Exploring the use of a dynamic online software programme in the teaching and learning of trigonometric graphs. Pythagoras, 35(2), 1–13. doi: 10.4102/pythagoras.v35i2.260
   Google Scholar
• Ndlovu, M., Wessels, D., & de Villiers, M. (2013). Competencies in using Sketchpad in geometry teaching and learning: Experiences of preservice teachers. African Journal of Research in Mathematics, Science and Technology Education, 17(3), 231–243.
   Google Scholar
• Noss, R., & Hoyles, C. (1996). Windows on mathematical meanings: Learning cultures and computers. Dordrecht: Kluwer Academic.
   Google Scholar
• Presmeg, N. (2006). Research on visualization in learning and teaching mathematics: Emergence from psychology. In A. Gutierrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education (pp. 205–235). Rotterdam: Sense.
   Google Scholar
• Presmeg, N. (2014). Contemplating visualization as an epistemological learning tool in mathematics. ZDM—International Journal on Mathematics Education, 46(1), 151–157. doi: 10.1007/s11858-013-0561-z
   Google Scholar
• Ruthven, K., Hennessy, S., & Deaney, R. (2008). Constructions of dynamic geometry: A study of the interpretative flexibility of educational software in classroom practice. Computers and Education, 51(1), 297–317. doi: 10.1016/j.compedu.2007.05.013
   Web of Science ®Google Scholar
• Stols, G., & Kriek, J. (2011). Why don’t all maths teachers use dynamic geometry software in their classrooms? Australasian Journal of Educational Technology, 27(1), 137–151. doi: 10.14742/ajet.988
   Web of Science ®Google Scholar
• Stols, G., Mji, A., & Wessels, D. (2008). The potential of teacher development with Geometer’s Sketchpad. Pythagoras, 68, 15–21.
   Google Scholar