‘The Area of a Triangle is 180⁰C’—An Analysis of Learners' Idiosyncratic Geometry Responses through the Lenses of Vygotsky's Theory of Concept Formation

References

• Berger, M. (2004a). Heaps, complexes and concepts (part 1). For the Learning of Mathematics, 24(2), 2–6.
   Google Scholar
• Berger, M. (2004b). Heaps, complexes and concepts (part 2). For the Learning of Mathematics, 24(3), 11–17.
   Google Scholar
• Berger, M. (2005). Vygotsky's theory of concept formation and mathematics education. 29th Conference of the International Group for the Psychology of Mathematics Education, Melbourne: PME, 153–160.
   Google Scholar
• Berger, M. (2006). Making mathematical meaning: From pre-concepts to pseudo concepts to concepts. Pythagoras, 63, 14–21.
   Google Scholar
• Burger, W. F., & Shaughnessy, J. M. (1986). Characterising the van Hiele levels of development in geometry. Journal for Research in Mathematics Education, 17(1), 31–48. doi: 10.2307/749317
   Web of Science ®Google Scholar
• Clarke, D. J. (1992). Activating assessment alternatives in mathematics. Arithmetic Teacher, 39(6), 24–29.
   Google Scholar
• Clements, D. (2003). Teaching and learning geometry. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), Research companion to principles and standards of school mathematics (pp. 151–178). Reston, VA: NCTM.
   Google Scholar
• Cobb, P., Yackel, E., & Wood, T. (1992). A constructivist alternative to the representational view of mind in mathematics education. Journal for Research in Mathematics Education, 23, 2–33. doi: 10.2307/749161
   Web of Science ®Google Scholar
• Dindyal, J. (2007). The need for an inclusive framework for students' thinking in school Geometry. The Montana Mathematics Enthusiast, 4(1), 73–83.
   Google Scholar
• Gutiérrez, A., Jaime, A., & Fortuny, J. M. (1991). An alternative paradigm to evaluate the acquisition of the van Hiele levels. Journal for Research in Mathematics Education, 22(3), 237–251. doi: 10.2307/749076
   Web of Science ®Google Scholar
• Jones, K. (2000). Critical issues in the design of the Geometry curriculum. In B. Barton (Ed.), Reading in mathematics education (pp. 75–90) Auckland, New Zealand: University of Auckland.
   Google Scholar
• Mahn, H. (2012). Vygotsky's analysis of children's meaning making processes. International Journal of Educational Psychology, 1(2), 100–126.
   Google Scholar
• Mayberry, J. (1983). The van Hiele levels of geometric though in undergraduate preservice teachers. Journal for Research in Mathematics Education, 14(1), 58–69. doi: 10.2307/748797
   Google Scholar
• Murray, M. (2004). Teaching mathematics vocabulary in context. Portsmouth: NH, Heinemann.
   Google Scholar
• Pegg, J. (1997). Broadening the descriptors of van Hieles' levels 2 and 3. In F. Biddulph & K. Carr (Eds.), The proceedings of the 20^th Mathematics Education Research Group of Australasia Conference (pp. 391–396). New Zealand, Rotorua: University of Waikato.
   Google Scholar
• Pimm, D. (1987). Speaking mathematically: Communication in mathematics classrooms. London: Routledge & Kegan.
   Google Scholar
• Presmeg, N. (2006). Research on visualization in learning and teaching mathematics. In A. Gutierrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education (pp. 205–237). Dordrecht: Sense.
   Google Scholar
• Radford, L. (2000). Signs and meanings in students' emergent algebraic thinking: A semiotic analysis. Educational Studies in Mathematics, 42, 237–268. doi: 10.1023/A:1017530828058
   Google Scholar
• Sawyer, W. W. (1977). ‘In praise of geometry’. In W. W. Willson (Ed.), The mathematics curriculum: Geometry. Glasgow: Blackie.
   Google Scholar
• Sierpinska, A. (1993). The development of concepts according to Vygotsky. Focus on Learning Problems in Mathematics, 15(2 & 3), 87–107.
   Google Scholar
• Vygotsky, L. S. (1962). Thought and language. Cambridge, MA: MIT Press.
   Google Scholar
• Vygotsky, L. S. (1978). Mind in society. Cambridge, MA: Harvard.
   Google Scholar
• Vygotsky, L. (1981). The genesis of higher mental functions. In J. Wertsch (Ed.), The concept of activity in soviet psychology (pp. 144–188). Armonk, NY: M. E. Sharpe.
   Google Scholar
• Vygotsky, L. (1986). Thought and language (A. Kozulin Trans. & Ed.). Cambridge, MA: MIT Press.
   Google Scholar