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

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 teac...

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Bibliographic Details
Published inEducational studies in mathematics Vol. 26; no. 2/3; pp. 229 - 274
Main Author Thompson, Patrick W.
Format Journal Article
LanguageEnglish
Published Kluwer Academic Publishers 01.03.1994
Subjects
Average rate of change
Calculus
Cognitive Development
College Students
Concept Formation
Difference quotients
Fundamental theorem of calculus
Fundamental theorems
Graduate Students
Higher Education
Imagery
Mathematical functions
Mathematics Education
Mathematics Education Research
Mathematics Instruction
Observation
Rate (Mathematics)
Rates of change
Riemann sums
Surface areas
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Summary: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.
ISSN:0013-1954
1573-0816
DOI:10.1007/BF01273664