Constructing a schema: The case of the chain rule?

Journal of Mathematical Behavior

Volumn 16, Issue 4, 1997, Pages 345-364

  Clark, Julie M ^b   Cordero, Francisco ^b   Cottrill, Jim ^a   Czarnocha, Bronislaw ^b   DeVries, David J ^b   St John, Denny ^b   Tolias, Georgia ^b   Vidakovic, Draga ^b  

^a GEORGIA STATE UNIVERSITY   (United States)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031498169     PISSN: 07323123     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0732-3123(97)90012-2     Document Type: Article

References (36)

1. Asiala, Mark, Brown, Anne, DeVries, David J., Dubinsky, Ed, Mathews, David, & Thomas, Karen. (1996). A framework for research and development in undergraduate mathematics education. Research in Collegiate Mathematics Education, 2, 1-32.
2. Asiala, Mark, Cottrill, Jim, Dubinsky, Ed, & Schwingendorf, Keith E. (1997). The development of students' graphical understanding of the derivative. Journal of Mathematical Behavior, 16 (4), 399-430.
3. Ayers, Thomas, Davis, George, Dubinsky, Ed, & Lewin, Philip. (1988). Computer experiences in learning composition of functions. Journal for Research in Mathematics Education, 19, 246-259.
4. Breidenbach, Daniel, Dubinsky, Ed, Hawks, Julie, & Nichols, Devilyna. (1992). Development of the process conception of function. Educational Studies in Mathematics, 23, 247-285.
5. Confrey, Jere, & Smith, Erick. (1994). Exponential functions, rates of change, and the multiplicative unit. Educational Studies in Mathematics, 26, 135-164.
6. Confrey, Jere, Smith, Erick, Piliero, Susan, & Rizzuti, Jan. (1991). The use of contextual problems and multi-representational software to teach the concept of functions (Final Project Report). Ithaca, NY: Cornell University.
7. Cottrill, Jim, Dubinsky, Ed, Nichols, Devilyna, Schwingendorf, Keith, Thomas, Karen, & Vidakovic, Draga. (1996). Understanding the limit concept: Beginning with a coordinated process schema. Journal of Mathematical Behavior, 15, 167-192.
8. Cuoco, Al. (1994). Multiple representations for functions. In J.J. Kaput & E. Dubinsky (Eds.), Research issues in undergraduate mathematics learning, MAA notes 33 (pp. 121-140). Washington, D.C.: Mathematical Association of America.
9. Dubinsky, Ed. (1991). Constructive aspects of reflective abstraction in advanced mathematics. In L.P. Steffe (Ed.), Epistemological foundations of mathematical experience (pp. 160-202). New York: Springer-Verlag.
10. Dubinsky, Ed, & Harel, Guershon. (1992). The nature of the process conception of function. In G. Harel and E. Dubinsky (Eds.), The concept of function: Aspects of epistemology and pedagogy, MAA notes 25 (pp. 85-106). Washington, D.C.: Mathematical Association of America.
11. Even, Ruhama. (1988). Pre-service teacher's conceptions of the relationships between functions and equations. In A. Borbás (Ed.), Proceedings of the 12th International Conference for the Psychology of Mathematics Education (pp. 304-311). Veszprém, Hungary: Ferenc Genzwein, OOK.
12. Even, Ruhama. (1993). Subject-matter knowledge and pedagogical content knowledge: Prospective secondary teachers and the function concept. Journal for Research in Mathematics Education, 24, 94-116.
13. Ferrini-Mundy, Joan, & Graham, Karen. (1994). Research in calculus learning: Understanding limits, derivatives, and integrals. In J.J. Kaput & E. Dubinsky (Eds.), Research issues in undergraduate mathematics learning, MAA notes 33 (pp. 31-45). Washington, D.C.: Mathematical Association of America.
14. Frid, Sandra D. (1992). Calculus students' sources of conviction. In B. Southwell, B. Perry, & K. Owens (Eds.), Space - The first and final frontier. Conference proceedings of the annual conference of the Mathematics Education Research Group of Australasia (15th, Richmond, New South Wales, Australia, July 4-8, 1992).
15. Goldenberg, E. Paul. (1988). Mathematics, metaphors, and human factors: Mathematical, technical, and pedagogical challenges in the educational use of graphical representation of functions. Journal of Mathematical Behavior, 7, 135-173.
16. Harel, Guershon & Kaput, James. (1991). The role of conceptual entities and their symbols in building advanced mathematical concepts. In D. Tall (Ed.), Advanced mathematical thinking (pp. 82-94). London: Riedel.
17. Hitt, Fernando. (1993). Internal and external representations related to the function concept. In J.R. Becker & B.J. Pence (Eds.), Proceedings of the Fifteenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 177-183). Pacific Grove, CA: San José State University.
18. Hsaio, F.S. (1984/85). A new CAI approach to teaching calculus. Computers in Mathematics and Science Teaching, 4(2), 29-36.
19. Lauten, A. Darien, Graham, Karen, & Ferrini-Mundy, Joan. (1994). Student understanding of basic calculus concepts: Interaction with the graphics calculator. Journal of Mathematical Behavior, 13, 225-237.
20. Mathews, John H. (1989). Teaching differentiation with muMATH. Journal of Computers in Mathematics and Science Teaching, 8(3), 50-53.
21. Orton, Anthony. (1983). Students' understanding of differentiation. Educational Studies in Mathematics, 14, 235-250.
22. Piaget, Jean, & Garcia, Rolando. (1989). Psychogenesis and the history of science (H. Feider, Trans.). New York: Columbia University Press. (Original work published 1983).
23. Schwarz, Baruch, & Bruckheimer, Maxim. (1990). The function concept with microcomputers: Multiple strategies in problem-solving. School Science and Mathematics, 90, 597-614.
24. Schwingendorf, Keith, Hawks, Julie, & Beineke, Jennifer. (1992). Horizontal and vertical growth of the student's conception of function. In G. Harel & E. Dubinsky (Eds.), The concept of function: Aspects of epistemology and pedagogy, MAA notes 25 (pp. 133-149). Washington, D.C.: Mathematical Association of America.
25. 4L: The Purdue calculus reform project. Proceedings of the Seventh Annual International Conference on Technology in Collegiate Mathematics (pp. 402-406). Reading, MA: Addison-Wesley.
26. Selden, John, Mason, Alice, & Selden, Annie. (1989). Can average calculus students solve nonroutine problems? Journal of Mathematical Behavior, 8, 45-50.
27. Selden, John, Selden, Annie, & Mason, Alice. (1994). Even good calculus students can't solve nonroutine problems. In J. J. Kaput & E. Dubinsky (Eds.), Research issues in undergraduate mathematics learning, MAA notes 33 (pp. 19-26). Washington, D.C.: Mathematical Association of America.
28. Tall, David O. (1986). Building and testing a cognitive approach to calculus using interactive computer graphics. Unpublished doctoral dissertation, University of Warwick, Warwick, UK.
29. Thomas, Karen. (1995). The fundamental theorem of calculus: An investigation into students' constructions. Unpublished doctoral dissertation, Purdue University, West Lafayette, IN.
30. Thompson, Patrick W. (1994a). Images of rate and operational understanding of the fundamental theorem of calculus. Educational Studies in Mathematics, 26, 229-274.
31. Thompson, Patrick W. (1994b). Students, functions, and the undergraduate curriculum. Research in Collegiate Mathematics Education, 1, 21-44.
32. Thoo, J. B. (1995). Compositions and the chain rule using arrow diagrams. PRIMUS, 5, 291-295.
33. Vidakovic, Draga. (1993). Differences between group and individual processes of construction of the concept of inverse function. Unpublished doctoral dissertation, Purdue University, West Lafayette, IN.
34. Vinner, Shlomo, & Dreyfus, Tommy. (1989). Images and definitions for the concept of function. Journal for Research in Mathematics Education, 20, 356-366.
35. White, Paul, & Mitchelmore, Michael. (1992). Abstract thinking in rates of change and derivative. In B. Southwell, B. Perry, & K. Owens (Eds.), Space - The first and final frontier. Conference proceedings of the annual conference of the Mathematics Education Research Group of Australasia (15th Richmond, New South Wales, Australia, July 4-8, 1992).
36. Wilson, Melvin R. (1994). One preservice secondary teacher's understanding of function: The impact of a course integrating mathematical content and pedagogy. Journal for Research in Mathematics Education, 25, 346-370.