Comparing Three Methods of Geometrical Approach in Visualizing Differential Equations

Comparing Three Methods of Geometrical Approach in Visualizing Differential Equations This paper concerns “planes-coordination” and “long-term-prediction” difficulties. These are specifically the case when students attempt to visualize solution curves of autonomous differential equations for predicting the long-term behavior of various initial conditions. To address these issues, a study was conducted in which three different methods, namely Standard, Traditional, and Dynamic, were implemented in three different classrooms, to allow a comparison of these methods regarding their effectiveness to overcome these difficulties. Forty-eight students participated in the study and each class had four instructional sessions taken by the first author. Of the four sessions, the first two were the same for all three classes. Then a pre-test was administered 2 weeks after the second session. For the next two sessions, an educational intervention was implemented for the two experimental groups. A post-test was administered 3 weeks after the fourth session. Analysis of the data collected via pre- and post-tests revealed that a) both the Traditional and the Dynamic groups showed enhanced performance in the sample solution curve-drawing, and b) the Dynamic group displayed improvement in long-term prediction performance. The conclusion is that an educational intervention can have a positive impact on students’ advancement in this area. The concluding remark is that there might be a link between “planes-coordination” and “long-term-prediction” difficulties. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Research in Undergraduate Mathematics Education Springer Journals

Comparing Three Methods of Geometrical Approach in Visualizing Differential Equations

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Publisher
Springer International Publishing
Copyright
Copyright © 2017 by Springer International Publishing AG
Subject
Education; Mathematics Education; Learning and Instruction
ISSN
2198-9745
eISSN
2198-9753
D.O.I.
10.1007/s40753-017-0061-6
Publisher site
See Article on Publisher Site

Abstract

This paper concerns “planes-coordination” and “long-term-prediction” difficulties. These are specifically the case when students attempt to visualize solution curves of autonomous differential equations for predicting the long-term behavior of various initial conditions. To address these issues, a study was conducted in which three different methods, namely Standard, Traditional, and Dynamic, were implemented in three different classrooms, to allow a comparison of these methods regarding their effectiveness to overcome these difficulties. Forty-eight students participated in the study and each class had four instructional sessions taken by the first author. Of the four sessions, the first two were the same for all three classes. Then a pre-test was administered 2 weeks after the second session. For the next two sessions, an educational intervention was implemented for the two experimental groups. A post-test was administered 3 weeks after the fourth session. Analysis of the data collected via pre- and post-tests revealed that a) both the Traditional and the Dynamic groups showed enhanced performance in the sample solution curve-drawing, and b) the Dynamic group displayed improvement in long-term prediction performance. The conclusion is that an educational intervention can have a positive impact on students’ advancement in this area. The concluding remark is that there might be a link between “planes-coordination” and “long-term-prediction” difficulties.

Journal

International Journal of Research in Undergraduate Mathematics EducationSpringer Journals

Published: Oct 24, 2017

References

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