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ERIC Number: EJ837534
Record Type: Journal
Publication Date: 2008
Pages: 20
Abstractor: As Provided
Reference Count: 0
ISSN: ISSN-0732-3123
Hidden Lessons: How a Focus on Slope-Like Properties of Quadratic Functions Encouraged Unexpected Generalizations
Ellis, Amy B.; Grinstead, Paul
Journal of Mathematical Behavior, v27 n4 p277-296 2008
This article presents secondary students' generalizations about the connections between algebraic and graphical representations of quadratic functions, focusing specifically on the roles of the parameters a, b, and c in the general form of a quadratic function, y = ax[superscript 2] + bx + c. Students' generalizations about these connections led to a surprising finding: two-thirds of the students interviewed identified the parameter a as the "slope" of the parabola. Analysis of qualitative data from interviews and classroom observations led to the development of three "focusing phenomena" in the classroom environment that inadvertently supported a focus on slope-like properties of quadratic functions: (a) the use of linear analogies, (b) the rise over run method, and (c) viewing "a" as dynamic rather than static. (Contains 10 figures and 1 table.)
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Publication Type: Journal Articles; Reports - Research
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A