Conceptual change in mathematics: From rational to (un)real numbers

European Journal of Psychology of Education

Volumn 12, Issue 2, 1997, Pages 131-145

  Lehtinen, Erno ^a   Merenluoto, Kaarina ^a   Kasanen, Eero ^b  

^a Turku University   (Finland)

^b HELSINKI SCHOOL OF ECONOMICS   (Finland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031507194     PISSN: 02562928     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF03173081     Document Type: Article

References (37)

1. Bell, E. (1937). Men of mathematics. New York: Simon and Schuster.
2. Bell, E. (1945). The development of mathematics. New York: McGraw-Hill.
3. Boyer, C.B. (1959). The history of the calculus and its conceptual development. New York: Dover.
4. Boyer, C.B. (1968). The history of mathematics. New York: John Wiley & Sons.
5. Carey, S. (1985). Conceptual change in childhood. Cambridge, MA: MIT Press.
6. Carey, S., & Spelke, E. (1994). Domain-specific knowledge and conceptual change. In L.A. Hirschfeld & S.A. Gelman (Eds.), Mapping the mind: Domain specificity in cognition and culture (pp. 162-200). Cambridge, MA: Cambridge University Press.
7. Chi, M.T.H. (1992). Conceptual change within and across ontological categories: Examples from learning and discovery in science. In R Giere (Ed.), Cognitive models of science: Minnesota studies in the philosophy of science (pp. 129-160). Minneapolis, MN: University of Minnesota Press.
8. Chi, M.T.H., Slotta, J.D., & de Leeuw, N. (1994). From things to processes: A theory of conceptual change for learning science concepts. Learning and Instruction, 4, 27-43.
9. Danzig, T. (1954). Number, the language of science. New York: Macmillan.
10. di Sessa, A. (1988). Knowledge in pieces. In G. Forman & P.B. Pufall (Eds.), Constructivism in the computer age (pp. 49-70). Hillsdale, NJ: Erlbaum.
11. Draglin, A.G. (1990). Intuitionism. In Encyclopaedia of mathematics, vol. 5 (pp. 158-161), Dordrect: Kluwer academic publishers.
12. Sessa, A. (1993). Towards an epistemology of physics. Cognition and Instruction, 10, 105-225.
13. Duit, R. (1995). The constructivist view: A fashionable and fruitful paradigm for science education research and practice. In L.P. Steffe & J. Gale (Eds.), Constructivism in education (pp. 271-285). Hillsdale, NJ: Lawrence Erlbaum.
14. English, L.D., & Halford, G.S. (1995). Mathematics educations: Models and processes. Mahwah, NJ: Lawrence Erlbaum.
15. Gallistel, C.R., & Gelman, R. (1992). Preverbal and verbal counting and computation. Cognition, 44, 43-74.
16. Gelman, R. (1990). First principles organize attention to and learning about relevant data: Number and the animate-inanimate distinction as examples. Cognitive Science. 14, 79-106.
17. Gelman, R., & Brenneman, K. (1994). First principles can support both universal and culture-specific learning about number and music. In L.A. Hirschfeld & S.A. Gelman (Eds.), Mapping the mind: Domain specificity in cognition and culture (pp. 369-390). Cambridge, MA: Cambridge University Press.
18. Hilbert, D. (1926). Ueber das Unendlich. Mathematische Annalen, 95, 161-190. (On infinity)
19. Kline, M. (1967). Mathematics for the nonmathematician. New York: Dover Publications.
20. Kline, M. (1972). Mathematics in western culture. London: Penguin Books.
21. Kline, M. (1972). Mathematical thought from ancient to modern times. New York: Oxford University Press.
22. Kuhn, T.S. (1962). The structure of scientific revolutions. Chicago: University of Chigago Press.
23. Kuhn, T.S. (1991). Scientific revolutions. In R. Boyd, P. Gasper, & J.D. Trout (Eds.), The philosophy of science (pp. 139-157). Cambridge, MA: MIT Press.
24. Lehtinen, E., & Repo, S. (1996). Activity, social interaction, and reflective abstraction: Learning advanced mathematical concepts in a computer environment. In S. Vosniadous, E. De Corte, R. Glases, & H. Mandl (Eds.), International perspectives on the design of technology-supported learning environments (pp. 05-128). Hillsdale, NJ: Lawrence Erlbaum.
25. Maula, E., & Kasanen, E. (1989). Chez Fermat A.D. 1937. Philosophica. 43, 127-162.
26. Ohlsson, S., & Lehtinen, E. (in press). Abstraction and the acquisition of complex ideas. International Journal of Educational Research.
27. Parsons, C. (1967). Mathematics, the foundations of. In W. Edwards (Ed.) Encyclopedia of philosophy, vol. 5 (pp. 192-213). New York: The Macmillan Company.
28. Piaget, J. (1952). The child's conception of number. London: Routledge and Kegan Paul.
29. Piaget, J., & Garcia, R. (1989). Psychogenesis and the history of science. New York: Columbia University Press.
30. Schnotz, W., & Preuss, A. (1995). Task-dependent construction of mental models as a basis for conceptual change. Friedrich-Schiller-Univeristy of Jena, Department of Educational Psychology: Research Report 6.
31. Stoffe, L.P., von Glasersfeld, E., Richards, J., & Cobb, P. (1983). Children's counting types. Philosophy, theory, and application. New York: Praeger.
32. Stern, E., & Maverech, Z.R. (in press). Children's understanding of successive halving in different contexts. Journal of Experimental Child Psychology.
33. von Glasersfeld, E. (1991). Abstraction, Re-Presentation, and Reflection: An interpretation of experinece and Piaget's approach. In L.P. Steffe (Ed.), Epistemological foundations of mathematical experience (pp. 45-67). New York: Springer-Verlag.
34. Vosniadou, S. (1994a). Capturing and Modeling the process of conceptual change. Learning and Instruction, 4, 45-69.
35. Vosniadou, S. (1994b). Universal and culture-specific properties of children's mental models on the earth. In L.A. Hirschfeld & S.A. Gelman (Eds.), Mapping the mind: Domain specificity in cognition and culture (pp. 412-430). Cambridge, MA: Cambridge University Press.
36. Vosniadou, S,. & Brewer, W.F. (1992). Mental models of the earth: A study of conceptual change in childhood. Cognitive Psychology, 24, 535-585.
37. Wang, H. (1974). From mathematics to philosophy. London: Routledge & Kegan Paul.