Exploring two methods of partial fraction decomposition on students’ performance / Jong Li Ling and Kuan Siaw Vui

Different partial fraction decomposition (PFD) methods may drive students to explore and understand partial fractions and thus, improve their mastery in PFD performance. Hence, this study explored the effectiveness of using two different methods, namely the improved version of the Heaviside method and the undetermined coefficients method, in performing PFD of the proper partial fraction. Literature showed that most of the instructors employed the undetermined coefficients method, and little is known about the effectiveness of employing other methods on students'
performance. This study used a quasi-experimental approach with a pre-test and post-test interval. Purposive sampling was employed as all the participants are from science stream, have completed Calculus I course, and learnt PFD. A total of 148 undergraduates from two faculties of a Malaysian public university were purposefully chosen for this study. The pre-test and post-test scores of PFD for three categories of factors in the denominator using the two methods were collected. Then, the statistical results of pre-test and post-test were examined using IBM SPSS 21. The mean scores of the tests were analysed using paired sample t-tests and analysis of covariance. The findings revealed that students who used the improved version of the Heaviside method outperformed those who used the undetermined coefficients method in performing the PFD of proper rational functions for distinct linear factor and irreducible quadratic factor in the denominators. However, the performance for both methods was insignificantly different for solving PFD of proper rational functions concerning repeated linear factor in the denominator. This study provides valuable insights into the choice of PFD methods employed by instructors in bringing out the best in students' performance.