Enhancing Mathematics Understanding through Visualization: The Role of Dynamical Software
Authors: Karen Keene and Chris Rasmussen
Appears in: "Sometimes Less is More: Examples of Student-Centered Technology as Boundary Objects in Differential Equations", Chapter 2
Published by: IGI Global
, Hershey, PA 2013
Stable URL: http://www.igi-global.com/chapter/sometimes-less-more/80256
Tag: First order equations, system of two first order equations
Abstract: Boundary objects are defined as material things that interface two or more communities of practice, in this case the classroom community and the mathematics community. The authors provide three extended examples of these objects as used in a first semester differential equations classroom to illustrate how students’ mathematical activity and understanding may advance as they interact with the software. The first example centers on the students' beginning experience with a tangent vector field applet. As the students learn more about solutions to differential equations, the second example, using the same applet, leads to a statement of the uniqueness theorem. In the third example, students develop a non-technological visualization task that introduces solutions to systems of differential equations with numerical approximation, and the associated images in 3-space and 2-space. Particularly nice is the note that the students tended to identify the 3D xyt trajectory as the "mother curve".
This chapter provides a number of new ideas for increasing student understanding and retention of concepts, with applets designed for this purpose, as opposed to the more usual software designed by experts already fluent in the mathematics. Some of the tools in IDE (Interactive Differential Equations) by Hu Hohn et al are designed with the same goals; Keene and Rasmussen's ideas fit those tools as well.
Reviewed by Beverly H. West, Cornell University, October 3, 2013