References: |
Blackett, Norman & Tall, David O. (1991). Gender and the Versatile Learning of Trigonometry Using Computer Software, In Fulvia Furinghetti, (Ed.), Proceedings of PME XIII, (pp. 144–151), Assisi, Italy. Brown, Anne, DeVries, David J., Dubinsky, Ed & Thomas, Karen (1997). Learning Binary Operations, Groups and Subgroups, Journal of Mathematical Behavior, 16, 187–240. Asiala, Mark, Dubinsky, Ed, Mathews, David M, Morics, Steven & Okta, Asuman (1997). Development of Students' Understanding of Cosets, Normality, and Quotient Groups, Journal of Mathematical Behavior, 16, 241–309. Cottrill, Jim, Dubinsky, Ed, Nichols, Devilyna, Schwingendorf, Keith, Thomas, Karen & Vidakovic, Draga (1996). Understanding the limit concept: Beginning with a co-ordinated process schema. Journal of Mathematical Behavior, 15, 167–192. Davis, Robert B. (1983). Complex Mathematical Cognition. In Herbert P. Ginsburg (Ed.) The Development of Mathematical Thinking, (pp. 254–290). Academic Press, New York. Davis, Robert B. (1984). Learning mathematics: the cognitive science approach to mathematics education. Norwood, NJ: Ablex. Denis, Michel (1996) Imagery and the description of spatial configurations. In Manuel de Vega, Margaret Jean Intons-Peterson, Phillip Johnson-Laird, Michel Denis & Marc Marschark, (Eds), Visuospatial Cognition, (pp. 128–197). Oxford: Oxford University Press. Dienes, Zoltan P. (1960). Building up Mathematics, Hutchinson Educational: London. Dörfler, Willibald. (1993). Fluency in a discourse or manipulation of mental objects, In Ichiei Hirabayashi, Nobuhiko Nohda, Keiichi Shigematsu and Fou-Lai Lin, (Eds.), Proceedings of PME 17, (vol. 2, pp.145–152), Tsukuba, Japan. Dubinsky, Ed (1986), Reflective Abstraction and Computer Experiences: A new approach to teaching theoretical mathematics, In Lappan, Glenda, Even, Ruhama, (Eds), Proceedings of the Eighth Annual Meeting of PME-NA, E. Lansing, Michigan: Michigan State University. Dubinsky, Ed (1991). Reflective Abstraction in Advanced Mathematical Thinking. In David O. Tall (Ed.) Advanced Mathematical Thinking (pp. 95–123). Kluwer: Dordrecht. Dubinsky, Ed, Elterman, Flor & Gong, Cathy (1988). The Student’s Construction of Quantification. For the Learning of Mathematics 8, 44–51. Gray, Eddie, M, Pitta, Demetra (1997). In the Mind … What can imagery tell us about success and failure in arithmetic? In G. A. Makrides (Ed.), Proceedings of the First Mediterranean Conference on Mathematics, (pp. 29–41). Nicosia: Cyprus. Gray, Eddie, M, Pitta, Demetra, Pinto, Marcia M. F., Tall, David O. (in press) Knowledge Construction and diverging thinking in elementary and advanced mathematics, Educational Studies in Mathematics. (to appear). Gray, Eddie M. & Tall, David O. (1991). Duality, Ambiguity and Flexibility in Successful Mathematical Thinking, In Fulvia Furinghetti, (Ed.), Proceedings of PME XIII, (vol. 2, pp. 72–79). Assisi, Italy. Gray, Eddie M. & Tall, David O. (1993). Can You Count On It? Video available from Mathematics Education Research Centre, Warwick University, UK. Gray, Eddie M. & Tall, David O. (1994). Duality, Ambiguity and Flexibility: A Proceptual View of Simple Arithmetic, The Journal for Research in Mathematics Education, 26, 115–141. Greeno, James (1983). Conceptual Entities. In Dedre Gentner, Albert L. Stevens (Eds.), Mental Models, (pp. 227–252). Hillsdale, NJ: Lawrence Erlbaum Associates. Hardy, G. H. (1940). A Mathematician’s Apology (2nd edition, 1967). Cambridge: CUP. Hong, Ye Yoon & Thomas, Michael O. J. (1997). Using the Computer to Improve Conceptual Thinking in Integration, Proceedings of the 21st Conference of the International Group for the Psychology of Mathematics Education, (vol. 3, pp. 81–88). Lahti, Finland. Kieran, Carolyn (1992). The Learning and Teaching of School Algebra. In Douglas A. Grouws (Ed.) The Handbook of Research on Mathematics Teaching and Learning, (pp. 390–419), New York: Macmillan. Lakoff, George & Johnson, Mark (1980). Metaphors We Live By. Chicago: University of Chicago Press. Piaget, Jean (1972). The Principles of Genetic Epistemology. London: Routledge & Kegan Paul. Piaget, Jean (1985). The Equilibrium of Cognitive Structures. Cambridge MA: Harvard University Press. Rosch, Eleanor (1978). Principles of Categorization. In Rosch, Eleanor, Lloyd, Barbara B. (Eds) (pp. 27–48), Cognition and Categorization. Hillsdale, NJ: Lawrence Erlbaum Associates Sfard, Anna (1988). Two conceptions of mathematical notions: operational and structural. In Proceedings of PME XII, (pp.162–169), Montréal, Canada. Sfard, Anna (1989). Transition from Operational to Structural Conception: The notion of function revisited. In Proceedings of PME XIII, (pp.151–158), Paris, France. Sfard, Anna (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. Sfard, Anna (1992). Operational origins of mathematical objects and the quandary of reification—the case of function. In Guershon Harel & Ed Dubinsky (Eds.), The Concept of Function: Aspects of Epistemology and Pedagogy, MAA Notes 25, (pp. 59-84). Washington DC: MAA. Sfard, Anna (1994). Reification as the Birth of Metaphor. For the Learning of Mathematics, 14, 44–55. Sfard, Anna (1995). The Development of Algebra: Confronting Historical and psychological Perspectives, Journal of Mathematical Behavior, 14, 15–39. Skemp, Richard R. (1979). Intelligence, Learning and Action, London: Wiley. Tall, David O. (1985). Understanding the calculus, Mathematics Teaching 110, 49–53. Tall, David O. (1991). Intuition and rigour: the role of visualization in the calculus. In Stephen Cunningham & Walter S. Zimmermann (Eds), Visualization in Teaching and Learning Mathematics, MAA Notes No. 19, (pp.105-119). Washington DC: MAA. Tall, David O. (1995). Mathematical Growth in Elementary and Advanced Mathematical Thinking, (plenary address). In Luciano Meira & David Carraher, (Eds.), Proceedings of PME 19, (vol.1, pp. 61–75). Recife, Brazil. Tall, David. O. & Thomas, Michael O. J. (1989). Versatile Learning and the Computer, Focus, 11, 117–125. Tall, David O. & Thomas, Michael O. J. (1991). Encouraging Versatile Thinking in Algebra using the Computer, Educational Studies in Mathematics, 22, 125–147. Tall, David O. & Vinner, Shlomo (1981). Concept image and concept definition in mathematics, with special reference to limits and continuity, Educational Studies in Mathematics, 12, 151–169. Thomas, Michael O. J. (1988). A Conceptual Approach to the Early Learning of Algebra Using a Computer, Ph.D. Thesis, University of Warwick, UK. Van Hiele, Pierre (1986). Structure and Insight. Orlando: Academic Press. Von Glasersfeld, Ernst (1987). Preliminaries in any Theory of Representation. In Janvier, Claude (Ed.) Problems of Representation in the Teaching and Learning of Mathematics, (pp. 214–225). Hillsdale, NJ: Lawrence Erlbaum Associates |