Students' participation in a differential equations class: Parametric reasoning to understand systems
Abstract
Dynamical systems as a content area in mathematics is growing in importance. New technology enables mathematicians and scientists to model the real world with systems of rate of change equations that are interrelated and based on time. One goal of this study is to report the results of an investigation on how students develop and use parametric reasoning as one basis for understanding dynamical systems of differential equations in an inquiry-oriented differential equations class. The need to understand how students reason parametrically with time and grow to understand this new aspect of mathematics provides significance for this study. This research study provides evidence that students already have understandings of time and rate from earlier experience and from their instruction recovering solutions to single ordinary differential equations and they use this to build their conceptions and understandings of solutions to systems of differential equations. The study also provides case studies of two students' mathematical activity as they learn systems of differential equations. Finally, the study uses a new construct of "advancing mathematical activity" and the mathematical practices of symbolizing, algorithmatizing, justifying, and experimenting to document how students enculturate into the larger mathematical community.
Degree
Ph.D.
Advisors
Wood, Purdue University.
Subject Area
Mathematics education
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