Images of rate and operational understanding of the fundamental theorem of calculus

Patrick W. Thompson

Research output: Contribution to journalArticlepeer-review

154 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)229-274
Number of pages46
JournalEducational Studies in Mathematics
Volume26
Issue number2-3
DOIs
StatePublished - Mar 1994

ASJC Scopus subject areas

  • Mathematics(all)
  • Education

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