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The Mathematics Enthusiast

Authors

Robert Ely

Volume

9

Issue

3

Abstract

Research indicates that calculus students often imagine objects losing a dimension entirely when a limit is taken, and that this image serves as an obstacle to their understanding of the fundamental theorem of calculus. Similar imagery, in the form of “indivisibles”, was similarly unsupportive of the development of the fundamental theorem in the mid-1600s, unlike the more powerful subsequent imagery of infinitesimals. This parallel between student issues and historical issues suggests several implications for how to provide students with imagery that is more productive for understanding the fundamental theorem, such as the imagery of infinitesimals or the more modern quantitative limits approach, which relies heavily on quantitative reasoning.

First Page

303

Last Page

326

Included in

Mathematics Commons

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