A calculus graphing schema

Journal for Research in Mathematics Education

Volumn 31, Issue 5, 2000, Pages 557-578

  Baker, Bernadette ^a   Cooley, Laurel ^b   Trigueros, María ^c  

^a DRAKE UNIVERSITY   (United States)

^b CITY UNIVERSITY OF NEW YORK   (United States)

^c INSTITUTO TECNOLÓGICO AUTÓNOMO DE MÉXICO   (Mexico)

Author keywords

Calculus; Cognitive theory; College mathematics; Conceptual knowledge; Constructivism; Epistemology; Piaget; Qualitative methods

Indexed keywords

EID: 24944558573     PISSN: 00218251     EISSN: None     Source Type: Journal    
DOI: 10.2307/749887     Document Type: Article

References (17)

1. Asiala, M., Brown, A., DeVries, D. J., Dubinsky, E., Mathews, D., & Thomas, K. (1996). A framework for research and curriculum development in undergraduate mathematics education. In J. Kaput, A. H. Schoenfeld, & E. Dubinsky (Eds.), Research in collegiate mathematics education II (pp. 1-32). Providence, RI: American Mathematical Society and Washington, DC: Mathematical Association of America.
2. Asiala, M., Cottrill, J., Dubinsky, E., & Schwingendorf, K. E. (1997). The development of students' graphical understanding of the derivative. Journal of Mathematical Behavior, 16, 399-431.
3. Aspinwall, L., Shaw, K. L., & Presmeg, N. C. (1997). Uncontrollable mental imagery: Graphical connections between a function and its derivative. Educational Studies in Mathematics, 33, 301-317.
4. Clark, J. M., Cordero, F., Cottrill, J., Czarnocha, B., DeVries, D. J., St. John, D., Tolias, G., & Vidakovic, D. (1997). Constructing a schema: The case of the chain rule? Journal of Mathematical Behavior, 16, 345-364.
5. Fauvel, J., & Gray, J. (Eds.). (1987). The history of mathematics: A reader. London: Macmillan Press.
6. Ferrini-Mundy, J., & Graham, K. (1994). Research in calculus learning: Understanding limits, derivatives, and integrals. In E. Dubinsky & J. Kaput (Eds.), Research issues in undergraduate mathematics learning (pp. 19-26). Washington, DC: Mathematical Association of America.
7. McDonald, M. A., Mathews, D., & Strobel, K. (in press). Understanding sequences: A tale of two objects. In E. Dubinsky, J. Kaput, & A. H. Schoenfeld (Eds.), Research in collegiate mathematics education IV. Providence, RI: American Mathematical Society and Washington, DC: Mathematical Association of America.
8. Orton, A. ( 1983). Students' understanding of differentiation. Educational Studies in Mathematics, 14, 235-250.
9. Piaget, J. (1971). Psychology and epistemology (A. Rosin, Trans.). New York: Grossman. (Original work published in 1970)
10. Piaget, J. (1972). The principles of genetic epistemology (W. Mays, Trans.). London: Routledge and Kegan Paul. (Original work published 1970)
11. Piaget, J., & Garcia, R. (1989). Psychogenesis and the history of science (H. Feider, Trans.). New York: Columbia University Press. (Original work published 1983)
12. Piaget, J., & Garcia, R. (1996). Psicogenesis y historia de la ciencia [Psychogenesis and the history of science] (7th ed.). Mexico City, Mexico: Siglo Veintiuno Editores.
13. Selden, J., Selden, A., & Mason, A. (1994). Even good calculus students can't solve non-routine problems. In E. Dubinsky & J. Kaput (Eds.), Research issues in undergraduate mathematics learning (pp. 31-45). Washington, DC: Mathematical Association of America.
14. Slavit, D. (1995). A growth-oriented route to the reification of function. In D. T. Owens, M. K. Reed, & G. M. Millsaps (Eds.), Proceedings of the seventeenth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 284-290). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.
15. Thompson, P. W. (1994). Images of rate and operational understanding of the fundamental theorem of calculus. Educational Studies in Mathematics, 26, 229-274.
16. Vergnaud, G. (1996). La theorie des champs conceptuels [The theory of conceptual fields]. In J. Brun (Ed.), Didactique des mathematiques (pp. 197-242). Geneva, Switzerland: Delachaux et Niestle.
17. Vinner, S. (1992). The function concept as a prototype for problems in mathematics learning. In E. Dubinsky & G. Harel (Eds.), The concept of function: Aspects of epistemology and pedagogy (pp. 195-213). Washington, DC: Mathematical Association of America.