Refinements in mathematics undergraduate students' reasoning on completed infinite iterative processes

Educational Studies in Mathematics

Volumn 78, Issue 2, 2011, Pages 165-180

  Radu, Iuliana ^a   Weber, Keith ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

Advanced mathematical thinking; Infinite iterative processes; Infinity; Mathematics education; Undergraduate mathematics education

Indexed keywords

EID: 80053307080     PISSN: 00131954     EISSN: 15730816     Source Type: Journal    
DOI: 10.1007/s10649-011-9318-1     Document Type: Article

References (20)

1. Brown, A., McDonald, M. A.,& Weller, K. (2008). Step by step: Infinite iterative processes and actual infinity. In F. Hitt, D. Holton, P. Thompson (Eds.), Research in Collegiate Mathematics Education VII. Providence: Amer. Math. Soc.
2. Cobb, P., Confrey, J., deSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9-13.
3. Confrey, J., & Costa, S. (1996). A critique of the selection of "mathematical objects" as central metaphor for advanced mathematical thinking. International Journal of Computers for Mathematical Learning, 1, 139-168.
4. Dubinsky, E., Weller, K., Mcdonald, M. A., & Brown, A. (2005). Some historical issues and paradoxes regarding the concept of infinity: An APOS analysis: Part 2. Educational Studies in Mathematics, 60, 253-266.
5. Dubinsky, E., Weller, K., Stenger, C., & Vidakovic, D. (2008). Infinite iterative processes: The Tennis Ball Problem. European Journal of Pure and Applied Mathematics, 1(1), 99-121.
6. Ely, R. (2007). Nonstandard models of arithmetic found in student conceptions of infinite processes. In T. Lamberg, & L. R. Weist (Eds.), Proceedings of the 29th Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 116-119). Stateline (Lake Tahoe), NV: University of Nevada, Reno.
7. Falk, R., & Ben-Lavy, S. (1989). How big is an infinite set? Exploration of children's ideas. In S. Vergnaud, G., J. Rogalski, & M. Artigue (Eds.), Proceedings of the Thirteenth Annual Conference of the International Group for the Psychology of Mathematics Education 1 (pp. 252-259). Paris: G. R. Didactique.
8. Fischbein, E. (1963). Conceptele figurale. Bucuresti: Editura Academiei R. S. R.
9. Fischbein, E., Tirosh, D., & Hess, P. (1979). The intuition of infinity. Educational Studies in Mathematics, 10(1), 3-40.
10. Gravemeijer, K. (1998). Developmental research as a research method. In A. Sierpinska & J. Kilpatrick (Eds.), Mathematics education as a research domain: A search for identity (pp. 277-296). The Netherlands: Kluwer.
11. Lakoff, G., & Núñez, R. E. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York: Basic Books.
12. Mamolo, A., & Zazkis, R. (2008). Paradoxes as a window to infinity. Research in Mathematics Education, 10(2), 167-182.
13. Piaget, J., & Inhelder, B. (1956). The child's conception of space. London: Routledge & Kegan Paul.
14. Radu, I. (2009) To infinity and beyond: Toward a local instruction theory for completed infinite iteration. Doctoral dissertation, Rutgers University, New Jersey, USA. http://hdl. rutgers. edu/1782. 2/rucore10001600001. ETD. 000051893. Accessed 1 Apr 2011.
15. Radu, I., & Weber, K. (2011) Formalizing the state at infinity of completed infinite iteration (in press).
16. Stenger, C., Vidakovic, D., & Weller, K. (2005) Student's conceptions of infinite iteration: A follow-up study. Presented at the SIGMAA on RUME conference, Phoenix, AZ, February 24-27.
17. Tall, D. (1980). The notion of infinite measuring number and its relevance in the intuition of infinity. Educational Studies in Mathematics, 11(3), 271-284.
18. Tirosh, D., & Tsamir, P. (1996). The role of representations in students' intuitive thinking about infinity. International Journal of Mathematics Education in Science and Technology, 27, 33-40.
19. Wagner, J. F. (2006). Transfer in pieces. Cognition and Instruction, 24(1), 1-71.
20. Wheeler, M. M., & Martin, W. G. (1988). Explicit knowledge of infinity. In M. Behr, C. Lacampagne, & M. M. Wheeler (Eds.), Proceedings of the Tenth Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 312-318). DeKalb, IL.