Improving Understanding In Ordinary Differential Equations Through Writing in a Dynamical Environment

Improving understanding in ordinary differential equations through writing in a dynamical environment
Author: Samer Habre

Teaching Mathematics and Its Applications, Vol. 31, No. 3 (2012), pp. 153–166

Published by: Oxford University Press

Tag: Other topics in differential equations

Abstract: During the last few decades there has been an emphasis on getting students to represent mathematics symbolically, verbally, graphically, and numerically. In addition, there has been a strong movement to extend writing across the curriculum. As a result, many mathematics departments now integrate a writing component into their undergraduate curriculum. In this article, the author argues that a writing component in an ordinary differential equations course can be used to strengthen student understanding of numeric, symbolic, verbal, and graphical representation of a concept and build an interconnection between the different representations.

Traditionally, differential equations courses have been taught by classifying the different types of equations and teaching a method of solution. In other words, we might classify a first-order equation as separable or linear and then give a method of solution. The author points out that this method does little to advance a student’s modeling or qualitative analysis skills. Furthermore, this approach does not build connections. Students may understand how to generate a symbolic solution of a differential equation but not see the connection to the direction field of the equation.

The author conducted an experiment with the students in his differential equations class. Students were asked on two exams and the final exam to write about differential equations. For example, students were asked to match direction fields with equations in one problem and to write a short explanation to justify their choice. Initially, students viewed the writing component as something alien; however, the writing component over the course of the semester did lead to better conceptual understanding.

Summary by Thomas W. Judson, Stephen F. Austin State University, September 10, 2014.

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