Strategies and Procedural and Conceptual Knowledge of Addition of Unlike Denominator Fractions: The Case of Grade 8 Children in Two Districts of the Central Region of Ghana

Abstract

This study investigated children’s knowledge of the addition of fractions with unlike denominators. It focussed on the strategies used by children to add fractions with unlike denominators. A cross-sectional survey of Grade 8 children in schools in two districts in Ghana was used. A test on the addition of fractions with unlike denominators was administered to 543 high-, average- and low-achieving children, and their responses were categorised based on the characterisation of correct strategies by Braithwaite et al. and Siegler and Pykes. Cluster bar charts and analysis of variance were used to analyse the data. The results showed that the children’s use of correct strategies for adding proper fractions with unlike denominators was higher than their use of correct strategies for adding improper fractions with unlike denominators. Thus, the children’s procedural knowledge of the addition of proper fractions with unlike denominators was higher than that of improper fractions with unlike denominators. Conceptual knowledge of the addition of fractions with unlike denominators was much lower than procedural knowledge of the same. The less advantaged (females, rural and low achievers) used fewer correct strategies and demonstrated less procedural and conceptual knowledge. Among other recommendations, curricula and classroom teaching should emphasise conceptual knowledge and its support for procedural knowledge of the addition of fractions with unlike denominators. Research interventions focussed on the less advantaged are advised.