The fundamental cycle of concept construction underlying various theoretical frameworks

ZDM - International Journal on Mathematics Education

Volumn 37, Issue 6, 2005, Pages 468-475

  Pegg, John ^a   Tall, David ^b  

^a UNIVERSITY OF NEW ENGLAND   (Australia)

^b UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 58449105010     PISSN: 18639690     EISSN: 18639704     Source Type: Journal    
DOI: 10.1007/BF02655855     Document Type: Article

References (29)

1. Biggs, J. & Collis, K. (1982). Evaluating the Quality of Learning: the SOLO Taxonomy. New York: Academic Press.
2. Biggs, J. & Collis, K. (1991). Multimodal learning and the quality of intelligent behaviour. In H. Rowe (Ed.), Intelligence, Reconceptualization and Measurement (pp. 57-76). New Jersey: Laurence Erlbaum Assoc.
3. Bruner, J. S. (1966). Towards a Theory of Instruction. New York: Norton.
4. Case, R. (1992). The Mind's Staircase: Exploring the conceptual underpinnings of children's thought and knowledge. Hillsdale, NJ: Erlbaum.
5. Crick, F. (1994). The Astonishing Hypothesis. London: Simon & Schuster.
6. Czarnocha, B., Dubinsky, E., Prabhu, V., & Vidakovic, D. (1999). One theoretical perspective in undergraduate mathematics education research. In Orit Zaslavsky (Ed.), Proceedings of the 23rd Conference of the International Group for the Psychology of Mathematics Education (1, 95-110). Haifa, Israel.
7. Davis, R.B. (1984). Learning Mathematics: The cognitive science approach to mathematics education. Norwood, NJ: Ablex.
8. Dienes, Z. P. (1960). Building Up Mathematics. London: Hutchinson.
9. Dubinsky, E. (1991). Reflective Abstraction in Advanced Mathematical Thinking. In David O. Tall (Ed.), Advanced Mathematical Thinking (pp. 95-123). Kluwer: Dordrecht.
10. Edelman, G. M. & Tononi, G. (2000). Consciousness: How Matter Becomes Imagination. New York: Basic Books.
11. Fischer, K. W. & Knight, C. C. (1990). Cognitive development in real children: Levels and variations. In B. Presseisen (Ed.), Learning and thinking styles: Classroom interaction. Washington: National Education Association.
12. Gray, E. M., Pitta, D., Pinto, M. M. F., & Tall, D. O. (1999). Knowledge construction and diverging thinking in elementary & advanced mathematics. Educational Studies in Mathematics. 38, 1-3, 111-133.
13. Gray, E. M. & Tall, D. O. (1991). Duality, Ambiguity and Flexibility in Successful Mathematical Thinking. In Fulvia Furinghetti (Ed.), Proceedings of the 13th Conference of the International Group for the Psychology of Mathematics Education (2, 72-79). Assisi, Italy.
14. Gray, E. M. & Tall, D. O. (1994). Duality, ambiguity and flexibility: a proceptual view of simple arithmetic. Journal for Research in Mathematics Education, 26, 2, 115-141.
15. Gray, E. M. & Tall, D. O. (2001). Relationships between embodied objects and symbolic procepts: an explanatory theory of success and failure in mathematics. In Marja van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education (3, 65-72). Utrecht, The Netherlands.
16. Greeno, J. (1983). Conceptual Entities. In D. Gentner & A. L. Stevens (Eds.), Mental Models (pp. 227-252). Hillsdale, NJ: Lawrence Erlbaum Associates.
17. Gruber, H. E. & Voneche, J. J. (1977). The Essential Piaget. New York: Basic Books, Inc.
18. Halford, G. S. (1993). Children's understanding: The development of mental models. Hillsdale: NJ: Lawrence Erlbaum
19. Lakoff, G. & Nunez, R. (2000). Where Mathematics Comes From. New York: Basic Books.
20. Lave, J. & Wenger E. (1991). Situated Learning: Legitimate peripheral participation. Cambridge: CUP.
21. Pegg, J. (1992). Assessing students' understanding at the primary and secondary level in the mathematical sciences. In J. Izard & M. Stephens (Eds.), Reshaping Assessment Practice: Assessment in the Mathematical Sciences under Challenge (pp. 368-385). Melbourne: Australian Council of Educational Research.
22. Pegg, J. (2003). Assessment in Mathematics: a developmental approach. In J.M. Royer (Ed.), Advances in Cognition and Instruction (pp. 227-259). New York: Information Age Publishing Inc.
23. Pegg, J. & Davey, G. (1998). A synthesis of Two Models: Interpreting Student Understanding in Geometry. In R. Lehrer & C. Chazan, (Eds.), Designing Learning Environments for Developing Understanding of Geometry and Space. (pp. 109-135). New Jersey: Lawrence Erlbaum.
24. Piaget, J. & Garcia, R. (1983). Psychogenèse et Histoire des Sciences. Paris: Flammarion.
25. Sfard, A. (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.
26. Poynter, A. (2004). Effect as a pivot between actions and symbols: the case of vector. Unpublished PhD thesis, University of Warwick.
27. Tall, D. O., Gray, E., M, Ali, M, Crowley, L, DeMarois, P., McGowen, M., Pitta, D., Pinto, M., Thomas, M., & Yusof, Y. (2000). Symbols and the Bifurcation between Procedural and Conceptual Thinking. The Canadian Journal of Science, Mathematics and Technology Education, 1, 80-104.
28. Tall, D. O. (2004). Thinking through three worlds of mathematics. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (4, 158-161). Bergen, Norway.
29. Van Hiele, P.M. (1986). Structure and Insight: a theory of mathematics education. New York: Academic Press.