From patterns to theories: Conditions for conceptual change

Journal of Mathematical Behavior

Volumn 19, Issue 2, 2000, Pages 247-271

  Maher, Carolyn A ^a   Martino, Amy M ^b  

^a State University of New Jersey   (United States)

^b Conover Road School ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041525918     PISSN: 07323123     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0732-3123(00)00047-x     Document Type: Article

References (25)

1. Alibert D., Thomas M. Research on mathematical proof. Tall D. Advanced mathematical thinking. 1991;215-230 Kluwer Academic Publishing, Dordrecht, The Netherlands.
2. Alston A., Maher C.A. Tracing Milin's building of proof by mathematical induction: a case study. Pence B. Proceedings of the Fifteenth Annual Meeting for the North American Chapter for the Psychology of Mathematics Education. vol. 2:1993;1-7. Pacific Grove, CA.
3. Balacheff N. The benefits and limits of social interaction: the case of mathematical proof. Bishop A.J., Mellin-Olsen J., van Dormole J. Mathematical knowledge: its growth through teaching. 1991;175-192 Kluwer Academic Publishing, Dordrecht, The Netherlands.
4. Bell A. A study of pupils' proof-explanations in mathematical situations. Educational Studies in Mathematics. 7:1976;23-40.
5. Davis P.J. The nature of proof. Carss M. Proceedings of the Fifth International Congress on Mathematical Education. 1986;Birkhauser, Boston.
6. Davis R.B., Maher C.A. The nature of mathematics: what do we do when we do mathematics? Davis R.B., Maher C.A., Noddings N. Constructivist views on the teaching and learning of mathematics. 1990;53-69 NCTM, Reston, VA.
7. Davis R.B., Maher C.A., Martino A. Using videotapes to study the construction of mathematical knowledge of individual children working in groups. Journal of Science, Education and Technology. 1(3):1992;177-189.
8. Fischbein, E. (1982). Intuition and proof. For the Learning of Mathematics, 3 (2), 9-18, 24.
9. Fischbein E. Intuition and the need for certitude. Fischbein E. Intuition in science and mathematics. 1987;3-13 Kluwer Academic Publishing, Dordrecht, The Netherlands.
10. Freudenthal H. Revisiting mathematics education: China lectures. 1991;47-55 Kluwer Academic Publishing, Dordrecht, The Netherlands.
11. Gaud D., Guichard J.P. Apprentissage de la demonstration. Petit. 4:1984;5-25.
12. Hanna G. Mathematical proof. Tall D. Advanced mathematical thinking. 1991;54-61 Kluwer Academic Publishing, Dordrecht, The Netherlands.
13. Kitcher P. The nature of mathematical knowledge. 1984;Oxford Univ. Press, New York.
14. Maher C.A., Martino A. Teachers building on children's thinking. Arithmetic Teacher. 39(7):1992;32-37.
15. Maher C.A., Martino A.M. Young children invent methods of proof: the "Gang of Four" Nesher P., Steffe L.P., Cobb P., Greer B., Goldin J. Theories of learning mathematics. 1996;431-444 Lawrence Erlbaum Associates, Hillsdale, NJ.
16. Maher C.A., Martino A.M. The development of the idea of mathematical proof: a 5-year study. Lester F. Journal for Research in Mathematics Education. 27(2):1996;194-214.
17. Martino, A. (1992). Elementary students' construction of mathematical knowledge: analysis by profile. Unpublished doctoral dissertation. Rutgers University.
18. Martino, A. M., & Maher, C. A. (1994). Teacher questioning which stimulates justification and generalization in mathematics. Presented at the 1994 Annual Meeting of the American Educational Research Association, New Orleans.
19. Movshovitz-Hadar N. Stimulating presentation of theorems followed by responsive proofs. For the Learning of Mathematics. 8(2):1988;12-19.
20. Senk S. How well do students write geometric proofs? Mathematics Teacher. 74:1985;19-26.
21. Steen L.A. Steen L.A. On the shoulders of giants: new approaches to numeracy. 1990;1-8 National Academy Press, Washington, DC. Mathematical Sciences Education Board, National Research Council.
22. Tall D.O. Cognitive aspects of proof, with special reference to the irrationality of the square root of 2. Proceedings of PME III. 1979;203-205. Warwick.
23. Tall D.O. Preface. Tall D. Advanced mathematical thinking. 1991;xiii-xv Kluwer Academic Publishing, Dordrecht, The Netherlands.
24. Tymoczko T. Making room for mathematicians in the philosophy of mathematics. Mathematical Intelligence. 8(3):1986;44-50.
25. Usiskin, Z. (1982). Van Hiele levels and achievement in secondary school geometry. CDASSG Project, SE 038 813.