The role of multiple modeling perspectives in students' learning of exponential growth

Carlos Castillo-Garsow

doi:10.3934/mbe.2013.10.1437

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2013, Volume 10, Issue 5&6: 1437-1453. Doi: 10.3934/mbe.2013.10.1437 open access

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The role of multiple modeling perspectives in students' learning of exponential growth

Carlos Castillo-Garsow^1,

1.
Mathematics Department, Kingston Hall 216, Eastern Washington University, Cheney, WA 99004-2418

Received: October 2012

Revised: May 2013

Published: August 2013

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Abstract

The exponential is among the most important family functions in mathematics; the foundation for the solution of linear differential equations, linear difference equations, and stochastic processes. However there is little research and superficial agreement on how the concepts of exponential growth are learned and/or should be taught initially. In order to investigate these issues, I preformed a teaching experiment with two high school students, which focused on building understandings of exponential growth leading up to the (nonlinear) logistic differential equation model. In this paper, I highlight some of the ways of thinking used by participants in this teaching experiment. From these results I discuss how mathematicians using exponential growth routinely make use of multiple --- sometimes contradictory --- ways of thinking, as well as the danger that these multiple ways of thinking are not being made distinct to students.

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Mathematics Subject Classification: Primary: 97M60, 97M30; Secondary: 92B05.

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