Adding or subtracting fractions: Relative effectiveness of the LCM and the equivalent fractions methods

Abstract

The purpose of the study was to compare the efficiency of the Equivalent Fractions (EF) method and the Least Common Multiple (LCM) method of doing the addition and subtracting of fractions on measures of accuracy and retention. All the 230 Form One students of Kaneshie '3' JSS and Kaneshie '1' JSS in the Okaikwei Sub - Metropolitan Area of the Greater Accra Region were involved in the study. Kaneshie' 3' JSS had two streams with an enrolment of 110 students, whilst the Kaneshie ' l' JSS with two streams had 120 students. The existing assembled classes of these Form One students were used in the study intact. The pretest - posttest nonequivalent - groups design was used. The data- collecting instrument developed by the investigator comprised three achievement tests designated pretest, posttest and retention test with co-efficicients of reliability of 0.87, 0.79 and 0.86 (Cronbach Alpha Formula) respectively. A day after the administration of the pretest, the two sets of different groups was taught their respective treatment methods by their respective regular mathematics teachers. A day after the last day of teaching the posttest was administered. After a two _ week period with no instructions in the two methods a retention test was administered. The first six out of the ten hypotheses were analysized by the analysis of covariance, whilst the dependent t-test was used to test the remaining four. The major findings of this study were as follows: 1. There was no significant difference between the mean scores of JSS Form One students who used the EF method and the LCM method on tasks involving the addition and subtraction of fractions on the posttest. 2. There was no significant difference bet\veen the mean scores of .ISS Form One students who used the EF method and the LCM method on the addition of fractions on the posttest. .3. There was no significant difference between the mean scores ofJSS Form One students who used the EF method and the LCM method on subtraction of fraction tasks on the posttest. 4. There was significant difference between the mean scores of the pretest and the posttest for students who used the EF method on the addition and subtraction of fractions. 5. There was no significant difference between the mean scores of the pretest and the posttest for students who used the LCM method on the addition and subtraction of fractions. 6. There was no significant difference between the mean scores of the posttest and retention test for the EF Group. Based on these findings it was recommended that curriculum developers improve upon the content of both EF and the LCM methods in the JSS and the primary school syllabuses, textbooks, teacher's handbooks and handouts. It was recommended that in-service training courses on the two methods be organised for classroom teachers; and teacher-training institutions include the exploration of theses methods in their programmes in order to expose student teachers to them.