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Images of Rate and Operational Understanding of the Fundamental Theorem of Calculus

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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.

Keywords

Average Rate Teaching Experiment Fundamental Theorem Circular Cross Section Functional Covariation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1994

Authors and Affiliations

  1. 1.Center for Research in Mathematics and Science EducationSan Diego State UniversitySan DiegoUSA

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