Compound subtraction in non-decimal bases: Relative effectiveness of base-complement additions and decomposition algorithms

Abstract

The purpose of the study was to determine whether there was any significant difference in speed, accuracy, retention and transferability between the Decomposition (DEC) and the Base-Complement Additions (BCA) algorithms for performing compound subtraction in non-decimal bases. Fifty-nine students with a mean age of approximately 15 years from two Agona Swedru Junior High Schools in the Agona District participated in the study. The study employed the pretest-posttests non-equivalent design. The two schools were randomly assigned to the treatment groups. The data collected on the four achievement tests namely Pretest, Posttest, a Third test and Retention test administered were then studied and analysed by employing the t-test at 0.05 level of significance. From the study it was found out that the mean performance of the BCA group was significantly higher than the DEC group on measures of accuracy. There was no relationship between the BCA and the DEC groups on the measure of speed. The BCA group produced significantly better computational accuracy than the DEC group. The mean score of the BCA group in the retention measures were significantly higher than that of the DEC group. The third test which was the test for understanding and application of the two methods showed that the BCA group performed better than the DEC group though the difference was slightly significant. Based on the findings, it was established that BCA method has substantial gains over the DEC method and as such recommended that the BCA should thus be included in the Junior Hugh mathematics curriculum as alternative method of solving compound subtraction in non-decimal bases.

Keywords: Decomposition, base-complement additions, compound subtraction.