Artigue, M. (1991). Analysis. In D. O. Tall (Ed.), *Advanced mathematical thinking* (pp. 167–198). Dordrecht: Kluwer.

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.

Blokland, P., Giessen, C., & Tall, D. O. (2000).

*Graphic calculus for windows*. Retrieved September 24, 2008 from

http://www.vusoft2.nl.

Chae, S. D. (2002). *Imagery and construction of conceptual knowledge in computer experiments with period doubling*. Unpublished PhD, University of Warwick.

Cornu, B. (1991). Limits. In D. O. Tall (Ed.), *Advanced mathematical thinking* (pp. 153–166). Dordrecht: Kluwer.

Donald, M. (2001). *A mind so rare*. New York: Norton.

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.

Heath, T. L. (1921). *History of Greek mathematics volume 1*. Oxford: Oxford University Press. (Reprinted Dover Publications 1963).

Hughes-Hallett, D., Gleason, A. M., McCallum, W. G., et al. (2007). *Calculus: Single and multivariable*. New York: Wiley.

Keisler, H. J. (1976). *Elementary calculus: An infinitesimal approach*. Boston: Prindle, Weber and Schmidt.

Kepler, J. (1858–1871). *Opera Omnia* (Vol. 8) (ed. C. von Frisch). Frankfurt: Heyder & Zimmer.

Leibniz, G. W. (1849–1860). Mathematische Schriften (7 vols) (ed. C. I. Gerhardt, Berlin and Halle).

Robinson, A. (1966). *Non-standard analysis*. Amsterdam: North Holland.

Stewart, J. (2003). *Calculus* (5th ed.). Belmont: Thomson.

Stewart, I. N., & Tall, D. O. (1977). *Foundations of mathematics*. Oxford: Oxford University Press.

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.

Tall, D. O. (1980b). Looking at graphs through infinitesimal microscopes, windows and telescopes.

*Mathematical Gazette,*
*64*, 22–49. doi:

10.2307/3615886.

CrossRefTall, D. O. (1981). Comments on the difficulty and validity of various approaches to the calculus. *For the Learning of Mathematics,*
*2*(2), 16–21.

Tall, D. O. (1985). Understanding the calculus. *Mathematics Teaching,*
*110*, 49–53.

Tall, D. O. (1986). *Building and testing a cognitive approach to the calculus using interactive computer graphics.* Unpublished PhD, University of Warwick, Coventry.

Tall, D. O. (1991a). The psychology of advanced mathematical thinking. In D. O. Tall (Ed.), *Advanced mathematical thinking* (pp. 3–21). Dordrecht: Kluwer.

Tall, D. O. (1991b). *Real functions and graphs for the BBC computer*. Cambridge: Cambridge University Press.

Tall, D. O. (2004). The three worlds of mathematics. *For the Learning of Mathematics,*
*23*(3), 29–33.

Tall, D. O. (2008). The transition to formal thinking in mathematics. *Mathematics Education Research Journal,*
*20*, 5–24.

Tall, D. O., & Schwarzenberger, R. L. E. (1978). Conflicts in the learning of real numbers and limits. *Mathematics Teaching,*
*82*, 44–49.