References: |
Ahsen, Akhter (1996). Guided Imagery, The quest for a science. Journal of Mental Imagery, 20, 165–204. Beth, Evert W. & Piaget, Jean (1966). Mathematical Epistemology and Psychology, (W. Mays, trans.). Dordrecht: Reidel. Bruner, Jerome S. (1968). Toward a theory of instruction. New York: W. W. Norton & Co. Bruner, Jerome S., Oliver, R. O., & Greenfield, P. M., (1966). Studies in cognitive growth. New York: Wiley. 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 Behaviour, 15, 167–192. Davis, Gary, E. (1996). What is the difference between remembering someone posting a letter and remembering the square root of 2? In Luis Puig and Angel Guitiérrez (Eds.), Proceedings of XX International Conference for the Psychology of Mathematics Education, Vol. 2, 265–272. Valencia: Spain. Davis, Robert B. (1984). Learning mathematics: the cognitive science approach to mathematics education. Norwood, NJ: Ablex. Dehaene, Stanislas & Cohen, Laurent (1994). Towards an Anatomical and Functional Model of Number Processing. Mathematical Cognition, 1, 1, 83–120. Dienes, Zoltan P (1960). Building up mathematics. Hutchinson Educational: London. Drake, Susan, M. (1996). Guided imagery and education: Theory, practice and experience. Journal of Mental Imagery, 20, 1–58. Dubinsky, Ed (1991). Reflective Abstraction. In David O. Tall (Ed), Advanced Mathematical Thinking. Dordrecht: Kluwer Academic Publishers. Geary, D.C. (1994). Children’s mathematical development. Washington: American Psychological Association Gonzalez, Esther G. & Kolers, Paul A. (1982). Mental manipulation of arithmetic symbols. Journal of Experimental Psychology. Learning, memory and cognition, 8, 308-319. Gray, Eddie M. (1991). An analysis of diverging approaches to simple arithmetic: Preference and its consequences. Educational Studies in Mathematics, 22, 551–574. Gray, Eddie M. & Tall, David O. (1994). Duality, ambiguity and flexibility: A proceptual view of simple arithmetic. Journal for Research in Mathematics Education, 25, 2, 115–141. Gray, Eddie M. & Pitta, Demetra (1996). Number Processing: Qualitative differences in thinking and the role of imagery. In Luis Puig and Angel Guitiérrez (Eds.), Proceedings of XX International Conference for the Psychology of Mathematics Education, Vol. 4, 155–162. Valencia: Spain. Gregg, Vernon, (1990). Eidectic Imagery. In Michael W. Eysenck, (Ed.), The Blackwell Dictionary of Cognitive Psychology. Blackwell: Oxford. Kamii, Constance (1985). Young children reinvent arithmetic. New York: Teachers College Press. Kosslyn, Stephen M. (1980). Image and mind. Cambridge, Mass: Harvard University Press. Leask, J., Haber, R. N., & Haber, R. B. (1969). Eidetic imagery in children: II Longitudinal and experimental results. Psychonomic Monograph Supplements, 3, 25–48. Mason, John (1992). Doing and construing mathematics in screen space. In Beth Southwell, Bob Perry and Kay Owens (Eds.), Proceedings of the 15th Annual Conference of the Mathematics Education Research Group of Australasia, 1–17. University of Western Sydney: Nepean, Australia Paivio, Alan (1991). Dual coding theory: retrospect and current status. Canadian Journal of Psychology, 45, 255–287. Piaget, Jean, & Inhelder, Barbel, (1971). Mental imagery in the child. New York: Basic. Piaget, Jean (1965). The child’s conception of number, (C. Gattengo & F. M. Hodgson, trans.), London: Routledge & Kegan Paul. Piaget, Jean (1971). Genetic Epistemology, (Eleanor Duckworth, trans). New York: Columbia University Press. Piaget, Jean (1973). Comments on mathematical education, In A. Geoffrey Howson (Ed.), Developments in Mathematical Education: Proceedings on the Second International Conference on Mathematics Education. Cambridge, Cambridge University Press. Piaget, Jean (1985). The Equilibrium of Cognitive Structures. Cambridge MA: Harvard University Press. Pirie, Susan, & Kieran, Tom (1994). Growth in mathematical understanding: How can we characterise it and how can we represent it? Educational Studies in Mathematics, 26, 165–190. Pitta, Demetra & Gray, Eddie M. (1997). In the Mind … What can imagery tell us about success and failure in arithmetic? In Gregory. A. Makrides (Ed.), Proceedings of the First Mediterranean Conference on Mathematics, 29–41. Nicosia: Cyprus. Pitta, Demetra & Gray Eddie M. (1996). Nouns, Adjectives and Images in Elementary Mathematics. In Luis Puig and Angel Guitiérrez (Eds.), Proceedings of XX International Conference for the Psychology of Mathematics Education, Vol. 3, 35–42. Valencia: Spain. Pylyshyn, Zenon W., (1973). What the mind’s eye tells the mind’s brain. Psychological Bulletin, 80, 1–24. Seron, Xavier, Pesenti, Mauro, Noël, Marie-Pascal, Deloche, Gérard, & Cornet, Jacques-André, (1992). Images of numbers, or “When 98 is upper left and 6 sky blue”. Cognition, 44, 159-196. 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. Skemp, Richard S. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20-26. Steffe, Les P., von Glaserfeld, Ernst, Richards, John, & Cobb, Paul (1983). Children’s Counting Types: Philosophy, Theory and Applications. Preagar: New York. Tall, David O. & Vinner, Shlomo (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12, 151-169. Thomas, Noel, Mulligan, Joanne, & Goldin, Gerald, A. (1996). Children’s representation of the counting sequence 1–100: Cognitive structural development. In Luis Puig and Angel Guitiérrez (Eds.), Proceedings of XX International Conference for the Psychology of Mathematics Education, Vol. 4, 307–314. Valencia: Spain. Thornton, Carol A. (1990). Solution strategies: Subtraction number facts. Educational Studies in Mathematics, 21, 241-263. Tulving, Endel, (1985). How many memory systems are there? American Psychologist, 40, 385–398. |