StevensIMooreK.C.-TheFerrisWheelandJustificationsofCurvature2016PMENA.pdf

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See discussions, stats, and author profiles for this publication at: The Ferris Wheel and Justifications of CurvatureConference Paper· October 2016CITATIONS4READS2852 authors:Some of the authors of this publication are also working on these related projects:Advancing ReasoningView projectAdvancing reasoningView projectIrma E. StevensUniversity of Georgia24PUBLICATIONS49CITATIONSSEE PROFILEKevin C. MooreUniversity of Georgia71PUBLICATIONS724CITATIONSSEE PROFILEAll content following this page was uploaded by Irma E. Stevens on 29 May 2018.The user has requested enhancement of the downloaded file.
The Ferris Wheel and Justifications of Curvature Irma E. Stevens & Kevin C. Moore University of Georgia Stevens, I. E., & Moore, K. C. (2016). The Ferris wheel and justifications of curvature. In M. B. Wood, E. E. Turner, M. Civil, & J. A. Eli (Eds.), Proceedings of the 38th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 644-651). Tucson, AZ: The University of Arizona. Available at:
Mathematical Processes 644Wood, M. B., Turner, E. E., Civil, M., & Eli, J. A. (Eds.). (2016). Proceedings of the 38th annual meeting of the North American Chapter of the International Group for the Pyschology of Mathematics Education. Tucson, AZ: The University of Arizona. THE FERRIS WHEEL AND JUSTIFICATIONS OF CURVATURE Irma E. Stevens Kevin C. Moore University of Georgia University of Georgia [email protected] [email protected] This report discusses the results of semi-structured clinical interviews with ten prospective secondary mathematics teachers who were provided with dynamic images of Ferris wheels. We asked the students to graph the relationship between the distance a rider traveled around the Ferris wheel and the height of the rider from the ground. We focus on the different quantitative and non-quantitative ways of thinking in which students engaged to justify the curvature of their drawn graphs. We also discuss how these ways of thinking relate to reasoning covariationally about directional change and amounts of change. Keywords: Modeling, Cognition, Problem Solving Introduction Authors of the Common Core State Standards for Mathematics (CCSSM) (National Governors Association Center for Best Practices, 2010) recommended that educators provide students with repeated and sustained opportunities to model situations via constructing and comparing relationships including those involving constant and changing rates of change. Researchers have also shown that quantitative reasoning (i.e., the analysis of a situation into a quantitative structure (Thompson, 2011)) and covariational reasoning (i.e., students conceiving situations as composed of measurable attributes that vary in tandem (Carlson, M. P., Jacobs, S., Coe, E., Larsen, S., & Hsu, E., 2002)) are critical for numerous K-16 topics (Ellis, 2007; Johnson, 2015; Moore & Carlson, 2012). These researchers have

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