Introducing the improved Heaviside approach to partial fraction decomposition to undergraduate students: results and implications from a pilot study

Abstract

Partial fraction decomposition is a useful technique often taught at senior secondary or undergraduate levels to handle integrations, inverse Laplace transforms or linear ordinary differential equations, etc. In recent years, an improved Heaviside's approach to partial fraction decomposition was introduced and developed by the author. An important feature of this approach is that there is no need to solve a system of linear equations or to use differentiations to find the unknown coefficients of the partial fractions. In order to study its potential application in mathematics education at the undergraduate level, a pilot study of tryout at the Hong Kong Institute of Education has been conducted. The data are collected via quizzes, questionnaires and face-to-face interviews. In this article, the results and implications will be discussed. In general, according to the responses and feedbacks from the instructors and students concerned, the improved Heaviside approach is suitable to be introduced at the undergraduate level, as an alternative to the method of undetermined coefficients described in common undergraduate mathematics textbooks.

Keywords:

• improved Heaviside approach
• cover-up technique
• partial fraction decomposition
• pilot study

Acknowledgements

The author would like to acknowledge that this study was supported by the Internal Research Grant of the HKIEd in 2010-11. Special thanks to Prof. Jinfa Cai for his valuable comments on the design of the quizzes and the questionnaires at the initial stage of this study. Finally, the author would like to thank the referees for their positive and valuable comments.