Dynamic mathematics and the blending of knowledge structures in the calculus

ZDM - International Journal on Mathematics Education

Volumn 41, Issue 4, 2009, Pages 481-492

  Tall, David O ^a  

^a UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77957873862     PISSN: 18639690     EISSN: 18639704     Source Type: Journal    
DOI: 10.1007/s11858-009-0192-6     Document Type: Article

References (23)

1. Artigue, M. (1991). Analysis. In D. O. Tall (Ed.), Advanced mathematical thinking (pp. 167-198). Dordrecht: Kluwer.
2. Asiala, M., Brown, A., DeVries, D., Dubinsky, E., Mathews, D., & Thomas, K. (1996). A framework for research and curriculum development in undergraduate mathematics education. Research in Collegiate Mathematics Education II. CBMS Issues in Mathematics Education, 6, 1-32.
3. Blokland, P., Giessen, C., & Tall, D. O. (2000). Graphic calculus for windows. Retrieved September 24, 2008 from http://www. vusoft2.nl.
4. Chae, S. D. (2002). Imagery and construction of conceptual knowledge in computer experiments with period doubling. Unpublished PhD, University of Warwick.
5. Cornu, B. (1991). Limits. In D. O. Tall (Ed.), Advanced mathematical thinking (pp. 153-166). Dordrecht: Kluwer.
6. Donald, M. (2001). A mind so rare. New York: Norton.
7. Gray, E. M., & Tall, D. O. (2001). Relationships between embodied objects and symbolic procepts: An explanatory theory of success and failure in mathematics. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 65-72). Utrecht, The Netherlands.
8. Heath, T. L. (1921). History of Greek mathematics volume 1. Oxford: Oxford University Press. (Reprinted Dover Publications 1963).
9. Hughes-Hallett, D., Gleason, A. M., McCallum, W. G., et al. (2007). Calculus: Single and multivariable. New York: Wiley.
10. Keisler, H. J. (1976). Elementary calculus: An infinitesimal approach. Boston: Prindle, Weber and Schmidt.
11. Robinson, A. (1966). Non-standard analysis. Amsterdam: North Holland.
12. Stewart, J. (2003). Calculus (5th ed.). Belmont: Thomson.
13. Stewart, I. N., & Tall, D. O. (1977). Foundations of mathematics. Oxford: Oxford University Press.
14. Tall, D. O. (1980a). Intuitive infinitesimals in the calculus. Abstracts of short communications, Fourth International Congress on Mathematical Education, Berkeley. Retrieved September 24, 2008 from http://www.warwick.ac.uk/staff/David.Tall/pdfs/dot1980c-intuitive-infls.pdf.
15. Tall, D. O. (1980b). Looking at graphs through infinitesimal microscopes, windows and telescopes. Mathematical Gazette, 64, 22-49. doi:10.2307/3615886.
16. Tall, D. O. (1981). Comments on the difficulty and validity of various approaches to the calculus. For the Learning of Mathematics, 2(2), 16-21.
17. Tall, D. O. (1985). Understanding the calculus. Mathematics Teaching, 110, 49-53.
18. Tall, D. O. (1986). Building and testing a cognitive approach to the calculus using interactive computer graphics. Unpublished PhD, University of Warwick, Coventry.
19. Tall, D. O. (1991a). The psychology of advanced mathematical thinking. In D. O. Tall (Ed.), Advanced mathematical thinking (pp. 3-21). Dordrecht: Kluwer.
20. Tall, D. O. (1991b). Real functions and graphs for the BBC computer. Cambridge: Cambridge University Press.
21. Tall, D. O. (2004). The three worlds of mathematics. For the Learning of Mathematics, 23(3), 29-33.
22. Tall, D. O. (2008). The transition to formal thinking in mathematics. Mathematics Education Research Journal, 20, 5-24.
23. Tall, D. O., & Schwarzenberger, R. L. E. (1978). Conflicts in the learning of real numbers and limits. Mathematics Teaching, 82, 44-49.