Intuitions and schemata in mathematical reasoning

Educational Studies in Mathematics

Volumn 38, Issue 1-3, 1999, Pages 11-50

  Fischbein, Efraim ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0008785255     PISSN: 00131954     EISSN: 15730816     Source Type: Journal    
DOI: 10.1007/978-94-017-1584-3_2     Document Type: Article

References (38)

1. Balzan, M.: 1997, 'Difficulties in Understanding the Concept of Sets', Masters Thesis, Tel Aviv University, Tel Aviv, Israel (in Hebrew).
2. Bastick, T.: 1982, Intuition: How we Think and Act, John Wiley & Sons, Chichester, England.
3. Bergson, H.: 1954, Creative Evolution (translated by A. Mitchell), Macmillan, London.
4. Bruner, J.: 1965, The Process of Education, Harvard University Press, Cambridge, MA.
5. Bunge, M.: 1962, Intuition and Science, Prentice Hall Inc., Englewood Cliffs.
6. Carey, S.: 1985, Conceptual Change in Childhood, MIT Press, Cambridge, MA.
7. Clark, F. B. and Kamii, C.: 1996, 'Identification of multiplicative thinking in children in grades 1-5', Journal for Research in Mathematics Education 27, 45-51.
8. Clement, J., Brown, D. E. and Zietsman, A.: 1989, 'Not all preconceptions are misconceptions: Finding 'anchoring conceptions' for grounding instruction on students' intuitions', International Journal for Science Education 11, 554-565.
9. Descartes, R.: 1967, The Philosophical Works (Vol. 1), (translated by E. S. Haldane and G. R. T. Ross), The University Press, Cambridge, MA.
10. DiSessa, A. A.: 1988, Knowledge in pieces, in G. Forman and P. B. Putall (eds.), Constructivism in Computer Age, Erlbaum, Hillsdale, NJ, pp. 49-70.
11. Fischbein, E.: 1963, Conceptele Figurale [The figural concepts], in Roumanian Bucharest, Editura Academiei, R.S.R.
12. Fischbein, E.: 1975, The Intuitive Sources of Probabilistic Thinking in Children, D. Reidel, Dordrecht, The Netherlands.
13. Fischbein, E.: 1978, 'Schemes virtuels et scheme actifs dans l'apprentissage des scinces', Revue Française de Pédagogie, 119-125.
14. Fischbein, E.: 1987, Intuition in Science and Mathematics, D. Reidel, Dordrecht, The Netherlands.
15. Fischbein, E. and Grossman, A.: 1997, 'Schemata and intuitions in combinatorial reasoning', Educational Studies in Mathematics 34, 21-47.
16. Fischbein, E. and Nachlieli, T.: 1997, Concepts and Figures in Geometrical Reasoning, submitted.
17. Fischbein, E. and Schnarch, D.: 1997, 'The evolution with age of probabilistic, intuitively based misconceptions', Journal for Research in Mathematics Education 28, 96-105.
18. Fischbein, E., Tirosh, D. and Hess, P.: 1979, 'The intuition of infinity', Educational Studies in Mathematics 10, 3-40.
19. Fischbein, E., Tirosh, D. and Melamed, U.: 1981, 'Is it possible to measure the intuitive acceptance of a mathematical statement?' Education Studies in Mathematics 12, 491-512.
20. Flavell, J.: 1963, The Developmental Psychology of Jean Piaget, Van Nostrand, Reinhold Co., New York.
21. Gelman, R. S. and Gallistel, C. R.: 1978, The Child's Understanding of Number, Harvard University Press, Cambridge, MA.
22. Hahn, H.: 1956, 'The crisis of intuition', in J. Newman (ed.), The World of Mathematics, Simon and Schuster, New York, v.3, pp. 1957-1976.
23. Kant, I.: 1980, Critique of Pure Reason, (translated by N.K. Smith), Macmillan, London.
24. Kline, M.: 1980, Mathematics: The Loss of Certainty, Oxford University Press, New York.
25. McCloskey, M., Washburn, A. and Felch, L.: 1983, 'Intuitive physics. The straight-down belief and its origin', Journal of Experimental Psychology: Learning, Memory and Cognition 9, 636-649.
26. Piaget, J.: 1980, Experiments in Contradiction, University of Chicago Press, Chicago and London.
27. Piaget, J., Inhelder, B. and Szeminska, A.: 1960, La Géomé trie Spontanée de l'Enfant, Press Universitaire de France, Paris.
28. Reber, A. S.: 1995, Dictionary of Psychology, Penguin Books, London.
29. Resnick, L. B.: 1987, 'The development of mathematical intuitions', in M. Perlmater (ed.), Minnesota Symposium of Child Psychology, Erlbaum, Hillsdale, NJ, p. 159-194.
30. Rumelhart, D. E.: 1980, 'Schemata: The building blocks of cognition', in R. T. Spiro, B. C. Bruce and W. F. Brewer (eds.), Theoretical Issues in Reading Comprehension, Erlbaum, Hillsdale, NJ.
31. Spinoza, B.: 1967, Ethics and Treatise on the Correction of the Understanding, (translated by A. Boyle), Everyman's Library, London.
32. Stavy, R. and Tirosh, D.: 1996, 'The role of intuitive rules in science and mathematics education', European Journal of Teacher Education, 19, 109-119.
33. Stavy, R., Tirosh, D. and Tsamir, P.: 1997, 'Intuitive rules and comparison tasks: The grasp of vertical angles', in G. Makrides (ed.), Mathematics Education and Applications, Cyprus Pedagogical Institute, Nicosia, Cyprus, pp. 269-276.
34. Thurston, V. P.: 1990, 'Mathematical education', Notices of the American Mathematical Society 137, 850-884.
35. Tirosh, D.: 1991, The role of students' intuitions of infinity in teaching the Cantorian theory, in D. Tall (ed.), Advanced Mathematical Thinking, Kluwer, Dordrecht, The Netherlands, pp. 199-214.
36. Westcott, M. R.: 1968, Towards a Contemporary Psychology of Intuition, Holt Rinehart and Winston, New York.
37. Wilkening, F.: 1980, 'Development of dimensional integration in children's perceptual judgment: Experiments with area, volume and velocity', in F. Wilkening, J. Becker and T. Trabasco (eds.), Information Integration by Children, Lawrence Erlbaum, Hillsdale, NJ.
38. Zamir, T.: 1996, 'Combinatorial intuitions', Masters Thesis, Tel Aviv University, Tel Aviv, Israel (in Hebrew).