Blokland, P., Giessen, C, & Tall, D. O. (2000). Graphic Calculus for Windows [Computer software). Available on the World Wide Web:http://www.vusoft.nl
Chae, S. D., & Tall, D. O. (in press). Aspects of the construction of conceptual knowledge in the case of computer aided exploration of period doubling. In C. Morgan & T. Rowlands (Eds.),Research in Mathematics Education: Vol. 3. Bristol, England: British Society for Research in the Learning of Mathematics, Faculty of Education.
Collis, K. F. (1972).A study of the relationship between formal thinking and combinations of operations. Newcastle, NSW: University of Newcastle.
Carmi, B. (1991). Limits. In D. O. Tall (Ed.),Advanced Mathematical Thinking (pp.153–166). Dordrecht, The Netherlands: Kluwer.
Crick, F. (1994).The astonishing hypothesis: The scientific search for the soul. London, England: Simon & Schuster.
Crowley, L. R. F. (2000).Cognitive structures in college algebra. Unpublished Ph.D. thesis, University of Warwick, England.
Douady, R. (1986), Jeu de cadres et dialectique outil-objet.Recherches en Didactique des Mathematiques, 7(2), 5–32.
Davis, R. B., Jockusch, E., & McKnight, C. (1978). Cognitive processes in learning algebra.Journal of Children’s Mathematical Behavior, 2(1), 10–320.
Dehaene, S. (1997).The number sense: How the mind creates mathematics. New York, NY: Oxford University Press.
DeMarois, P. (1998).Aspects and layers of the function concept. Unpublished doctoral thesis, University of Warwick, England.
Gleick, J. (1987).Chaos. New York, NY: Penguin.
Gray, E. M., & Pitta, D. (1997). Changing Emily’s images.Mathematics Teaching, 161, 38–51.
Gray, E., M, Pitta, D., Pinto, M. M. F., & Tall, D. O. (1999). Knowledge construction and diverging thinking in elementary and advanced mathematics.Educational Studies in Mathematics, 38
Gray, E. M. & Tall, D. O. (1991). Duality, ambiguity and flexibility in successful mathematical thinking. In F. Furinghetti (Ed.),Proceedings of the 15th annual conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 72–79). Assisi, Italy: Program Committee.
Gray, E. M. & Tall, D. O. (1994). Duality, ambiguity and flexibility: A proceptual view of simple arithmetic.Journal for Research in Mathematics Education, 26, 115–141.
Htillter, M., Monaghan, J. D., & Roper, T. (1993). The effect of computer algebra use on students’ algebraic thinking. In R. Sutherland (Ed.),Working Papers for ESRC Algebra Seminar. London, England: London University, Institute of Education.
Kieran C. (1981). Pre-algebraic notions among 12 and 13 year olds. In Equipe de Recherche Pedagogique Laboratoire I.M.A.G. (Ed.),Proceedings of the 5th annual conference of the International Group for the Psychology of Mathematics Education (pp. 158–164). Grenoble, France: Program Committee.
Lanford, O. E. (1982). A computer-assisted proof of the Feigenbaum conjectures.Bulletin of the American Mathematical Society
, 6, 427.CrossRef
Li, L., & Tall, D. O. (1993). Constructing different concept images of sequences and limits by programming. In I. Hirabayashi, N. Nohda, K. Shigematsu, & F.-L. Lin (Eds.),Proceedings of the 17th annual conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 41–48). Tsukuba, Japan: Program Committee.
Matz, M. (1980). Towards a computational theory of algebraic competence,Journal of Mathematical Behavior, 3 (1), 93–66.
Monaghan, J. D. (1986).Adolescents’ understanding of limits and infinity. Unpublished doctoral thesis, University of Warwick, England.
Monaghan, J., Sun, S., & Tall, D. O. (1994), Construction of the limit concept with a computer algebra system. In J. P. da Ponte & J. F. Matos (Eds.),Proceedings of the 18th annual conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 279–286). Lisbon, Portugal: Program Committee.
Pinto, M. M. F., (1998).Students’ understanding of real analysis. Unpublished doctoral thesis, University of Warwick, England.
School Mathematics Project (1991).Introductory calculus. Cambridge, England: Cambridge University Press.
Skemp, R. R. (1971).The psychology of learning mathematics. London, England: Penguin.
Still, S. (1993).Students’ understanding of limits and the effect of computer algebra systems. Unpublished M.Ed. thesis, Leeds University, England.
Tall, D. O. (1982). The blancmange flmction, continuous everywhere but differentiable nowhere.Mathematical Gazette
, 66, 11–22.CrossRef
Tall, D. O. (1985). Understanding the calculus.Mathematics Teaching, 110, 49–53.
Tall, D. O. (1993a). Interrelationships between mind and computer: Processes, images, symbols In D. L. Ferguson (Ed.),Advanced technol,ogies in the teaching of mathematics and science (pp. 385–413). New York, NY: Springer-Verlag.
Tall, D. A. (1993b). Real mathematics, rational computers and complex people. In Lum, L. (Ed.),Proceedings of the 5th annual international conference on Technology in College.Mathematics Teaching (pp. 243–258). Reading, MA: Addison-Wesley.
Tall, D. A. (1998). Information technology and mathematics education: Enthusiasms, possibilities & realities. In C. Alsina, J. M. Alvarez, M. Niss, A. Perez, L. Rico, & A. Sfard (Eds.),Proceedings of the 8th International Congress on Mathematical Education. (pp. 65–82). Seville: SAEM Thales.
Tall, D. A., Blokland, P., & Kok, D. (1990).A graphic approach to the calculus. Pleasantville, NY: Sunburst.
Tall, D. A. & Thomas, M. A. J. (1991). Encouraging versatile thinking in algebra using the computer.Educational Studies in Mathematics, 22
Tall, D. A., Thomas, M. A. J., Davis, G., Gray, E. M., & Simpson, A. (2000). What is the object of the encapsulation of a process.Journal ofMathematical Behavior, 18(2), 1–19.
Thomas, M. A. J. (1988).A conceptual approach to the early learning of algebra using a computer. Unpublished doctoral thesis, University of Warwick, England.
Williams, S. R. (1991). Models of limit held by college calculus students.Journal for Research in Mathematics Education, 22