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Where is the rate in the rule?

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journal contribution
posted on 2008-10-01, 00:00 authored by Sandra Herbert
A well-developed understanding of rate is foundational to conceptual understanding of introductory calculus. Many students achieve procedural competence with the application of rules for differentiation without developing an awareness of the connection between derivative and rate. In addition, rate-related reasoning is needed to make informed decisions in many everyday applications of rate. This paper reports on additional data collected during interviews for a project investigating the different ways rate may be experienced by pre-calculus students. Many researchers (for example Kaput, 1999) have suggested that the conceptual understanding of function may be enhanced through the presentation and exploration of multiple representations of a variety of functions. In this paper, one section of each interview is considered in detail to evaluate the participants’ understanding in a specific rate context. Participants were asked to discuss a dynamic geometry simulation of a blind on two different windows one rectangular and the other not. Detailed analysis of the video-record of each participant’s interview provides insights into their perceptions of rate in several different representations. In the sections below, the conceptual framework is described; details of the interviews and the computer-based simulation are provided; and the analysis of the data is discussed.

History

Journal

Australian Senior Mathematics Journal

Volume

22

Issue

2

Pagination

28 - 36

Publisher

Australian Association of Mathematics Teachers Inc.

Location

Armidale, N.S.W.

ISSN

0819-4564

Language

eng

Publication classification

C1.1 Refereed article in a scholarly journal

Copyright notice

2008, Australian Association of Mathematics Teachers

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