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

Mallet, Daniel G. & McCue, Scott W. (2009) Constructive development of the solutions of linear equations in introductory ordinary differential equations. International Journal of Mathematical Education in Science and Technology, 40(5), pp. 587-595.

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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. Recognising 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 studies 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.

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2 citations in Scopus
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ID Code: 27799
Item Type: Journal Article
Additional Information: Publisher pdf removed to I: drive.
Keywords: differential equations, undergraduate, constructive, inquiry, oriented
DOI: 10.1080/00207390902759626
ISSN: 1464-5211
Subjects: Australian and New Zealand Standard Research Classification > EDUCATION (130000) > OTHER EDUCATION (139900) > Education not elsewhere classified (139999)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > PURE MATHEMATICS (010100)
Australian and New Zealand Standard Research Classification > EDUCATION (130000) > OTHER EDUCATION (139900)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > PURE MATHEMATICS (010100) > Ordinary Differential Equations Difference Equations and Dynamical Systems (010109)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Past > Schools > Mathematical Sciences
Copyright Owner: Copyright 2008 Taylor & Francis
Copyright Statement: This is an electronic version of an article published in [International Journal of Mathematical Education in Science and Technology]. [International Journal of Mathematical Education in Science and Technology] is available online at informaworldTM with the open URL http://www.tandf.co.uk/journals/titles/0020739X.asp
Deposited On: 08 Jan 2010 14:50
Last Modified: 01 Mar 2012 00:05

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