Constructive development of the solutions of linear equations in introductory ordinary differential equations

Authors: Mallet, DG; McCue, SW

Source: International Journal of Mathematical Education, Volume 40, Number 5, January 2009 , pp. 587-595(9)

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Abstract:

The solution of linear ordinary differential equations (ODEs) is commonly taught in first-year undergraduate mathematics classrooms, but the understanding of the concept of a solution is not always grasped by students until much later. Recognizing what it is to be a solution of a linear ODE and how to postulate such solutions, without resorting to tables of solutions, is an important skill for students to carry with them to advanced courses in mathematics. In this study, we describe a teaching and learning strategy that replaces the traditional algorithmic, transmission presentation style for solving ODEs with a constructive, discovery-based approach where students employ their existing skills as a framework for constructing the solutions of first and second-order linear ODEs. We elaborate on how the strategy was implemented and discuss the resulting impact on a first-year undergraduate class. Finally, we propose further improvements to the strategy as well as suggesting other topics which could be taught in a similar manner.

Keywords: teaching differential equations; undergraduate mathematics; constructive problem solving; inquiry-oriented learning

Document Type: Research article

DOI: http://dx.doi.org/10.1080/00207390902759626

Affiliations: 1: School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland 4001, Australia

Publication date: 2009-01-01

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