## Abstract

Conceptual analyses of Newton's use of the Fundamental Theorem of Calculus and of one 7th-grader's understanding of distance traveled while accelerating suggest that concepts of rate of change and infinitesimal change are central to understanding the Fundamental Theorem. Analyses of a teaching experiment with 19 senior and graduate mathematics students suggest that students' difficulties with the Theorem stem from impoverished concepts of rate of change and from poorly-developed and poorly coordinated images of functional covariation and multiplicatively-constructed quantities.

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Research reported in this paper was supported by National Science Foundation Grants No. MDR 89-50311 and 90-96275, and by a grant of equipment from Apple Computer, Inc., Office of External Research. Any conclusions or recommendations stated here are those of the author and do not necessarity reflect official positions of NSF or Apple Computer. Also, I wish to thank Paul Cobb and Guershon Harel for their helpful reactions to an earlier draft of this article.

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Thompson, P.W. Images of rate and operational understanding of the fundamental theorem of calculus.
*Educ Stud Math* **26**, 229–274 (1994). https://doi.org/10.1007/BF01273664

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DOI: https://doi.org/10.1007/BF01273664