Objects, Actions, and Images: A Perspective on Early Number Development

Journal of Mathematical Behavior

Volumn 18, Issue 4, 2000, Pages 401-413

  Gray, Eddie ^a   Pitta, Demetra ^a   Tall, David ^a  

^a UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041686153     PISSN: 07323123     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0732-3123(00)00025-0     Document Type: Article

References (35)

1. Beth Evert W., Piaget Jean Mathematical epistemology and psychology. 1966;Reidel, Dordrecht, The Netherlands. (W. Mays, trans.).
2. Bruner Jerome S. Toward a theory of instruction. 1968;W.W. Norton, New York.
3. Bruner Jerome S., Oliver R.O., Greenfield P.M. Studies in cognitive growth. 1966;Wiley, New York.
4. Cottrill Jim, Dubinsky Ed, Nichols Devilyna, Schwingendorf Keith, Thomas Karen, Vidakovic Draga Understanding the limit concept: Beginning with a co-ordinated process schema. Journal of Mathematical Behaviour. 15:1996;167-192.
5. Davis Gary E. What is the difference between remembering someone posting a letter and remembering the square root of 2? Puig Luis, Guitiérrez Angel Proceedings of XX International Conference for the Psychology of Mathematics Education. Vol. 2:1996;265-272. Valencia, Spain.
6. Davis Robert B. Learning mathematics: The cognitive science approach to mathematics education. 1984;Ablex, Norwood, NJ.
7. Dienes Zoltan P. Building up mathematics. 1960;Hutchinson Educational, London.
8. Drake Susan M. Guided imagery and education: Theory, practice and experience. Journal of Mental Imagery. 20:1996;1-58.
9. Dubinsky Ed Reflective abstraction. Tall David O. Advanced mathematical thinking. 1991;Kluwer Academic Publishing, Dordrecht.
10. France N., Hieronymus A.N., Lidquist E.F. Richmond test of basic skills. 1974;NFER-Nelson, Windsor.
11. Geary D.C. Children's mathematical development. 1994;American Psychological Association, Washington.
12. Gray Eddie An analysis of diverging approaches to simple arithmetic: Preference and its consequences. Educational Studies in Mathematics. 22:1991;551-574.
13. Gray Eddie, Pitta Demetra Number processing: Qualitative differences in thinking and the role of imagery. Puig Luis, Guitiérrez Angel Proceedings of XX International Conference for the Psychology of Mathematics Education. Vol. 4:1996;155-162. Valencia, Spain.
14. Gray Eddie, Tall David O. Duality, ambiguity and flexibility: A proceptual view of simple arithmetic. Journal for Research in Mathematics Education. 25(2):1992;115-141.
15. Kamii Constance Young children reinvent arithmetic. 1985;Teachers College Press, New York.
16. Kosslyn Stephen M. Image and mind. 1980;Harvard Univ. Press, Cambridge, MA.
17. Paivio Alan Dual coding theory: Retrospect and current status. Canadian Journal of Psychology. 45:1991;255-287.
18. Piaget Jean The child's conception of number. 1965;Routledge & Kegan Paul, London. (Gattengo, C., Hodgson, F.M., trans.).
19. Piaget Jean Genetic epistemology. 1971;Columbia Univ. Press, New York. (Eleanor Duckworth, trans.).
20. Piaget Jean Comments on mathematical education. Howson A. Geoffrey Developments in mathematical education. Proceedings on the Second International Conference on Mathematics Education:1973;Cambridge Univ. Press, Cambridge.
21. Piaget Jean The equilibrium of cognitive structures. 1985;Harvard Univ. Press, Cambridge, MA.
22. Piaget Jean, Inhelder Barbel Mental imagery in the child. 1971;Basic, New York.
23. Pirie Susan, Kieran Tom Growth in mathematical understanding: How can we characterise it and how can we represent it? Educational Studies in Mathematics. 26:1994;165-190.
24. Pitta, Demetra. (1998). Beyond the obvious: Mental representations and elementary arithmetic. Unpublished Ph.D., Mathematics Education Research Centre, University of Warwick.
25. Pitta Demetra, Gray Eddie M. Nouns, adjectives and images in elementary mathematics. Puig Luis, Guitiérrez Angel Proceedings of XX International Conference for the Psychology of Mathematics Education. Vol. 3:1996;35-42. Valencia, Spain.
26. Pitta Demetra, Gray Eddie M. In the Mind ... What can imagery tell us about success and failure in arithmetic? Makrides Gregory A. Proceedings of the First Mediterranean Conference on Mathematics. 1997;29-41. Nicosia, Cyprus.
27. Pylyshyn Zenon W. What the mind's eye tells the mind's brain. Psychological Bulletin. 80:1973;1-24.
28. Seron Xavier, Pesenti Mauro, Noël Marie-Pascal, Deloche Gérard, Cornet Jacques-André Images of numbers, or "When 98 is upper left and 6 sky blue" Cognition. 44:1992;159-196.
29. Sfard Anna On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics. 22:1991;1-36.
30. Skemp Richard S. Relational understanding and instrumental understanding. Mathematics Teaching. 77:1976;20-26.
31. Steffe Less P., von Glaserfeld Ernst, Richards John, Cobb Paul Children's counting types: Philosophy, theory and applications. 1983;. Preagar, New York.
32. Tall David O., Vinner Shlomo Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics. 12:1981;151-169.
33. Thomas Noel, Mulligan Joanne, Goldin Gerald A. Children's representation of the counting sequence 1-100: Cognitive structural development. Puig Luis, Guitiérrez Angel Proceedings of XX International Conference for the Psychology of Mathematics Education. Vol. 4:1996;307-314. Valencia, Spain.
34. Thornton Carol A. Solution strategies: Subtraction number facts. Educational Studies in Mathematics. 21:1990;241-263.
35. Tulving Endel How many memory systems are there? American Psychologist. 40:1985;385-398.