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ERIC Number: EJ1000870
Record Type: Journal
Publication Date: 2012-Nov
Pages: 5
Abstractor: ERIC
Reference Count: 6
ISSN: ISSN-0025-5769
Understanding the Derivative through the Calculus Triangle
Weber, Eric; Tallman, Michael; Byerley, Cameron; Thompson, Patrick W.
Mathematics Teacher, v106 n4 p274-278 Nov 2012
Typical treatments of the derivative do not clearly convey the idea that the derivative function represents the original function's rate of change. Revealing the relationship between a function and its rate-of-change function for static values of "x" does not facilitate productive ways of thinking about generating the rate-of-change function or allow students to anticipate the graphical behavior of the rate-of-change function by examining a graph of the original function. Accordingly, the authors propose the calculus triangle approach. This approach builds on Thompson's calculus research (Thompson 1994; Thompson and Silverman 2008), which introduces the derivative in a way that maintains the centrality of rate of change as a conceptual underpinning of derivative. By providing examples of the approach's use in novel and routine settings, the authors will show how it facilitates a mature understanding of the derivative. (Contains 4 figures.)
National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191-1502. Tel: 800-235-7566; Tel: 703-620-3702; Fax: 703-476-2970; e-mail:; Web site:
Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A