Modeling a cognitive tool for teaching the addition/subtraction of common fractions

The case study reported here models a Cognitive Tool (CT) for primary school children to learn common fraction addition/subtraction with unlike denominators. In the study, we developed a CT based on a cognitive task analysis of the domain. We then observed how 12 learners used this CT to understand fraction operations based on a knowledge of fraction equivalence. Results of the study indicate that the support offered by the CT aids learners with higher ability in mathematics to produce cognitive residues. The graphical partitioning model helps to link the concrete operations of partitioning with the abstract idea of a common denominator required for adding/subtracting fractions with unlike denominators. However, learners who have failed to develop the knowledge of fraction equivalence, which includes the concept of equivalence and the ways of finding it, cannot gain much from working with the CT. A model of affordances for improving the design of the CT to meet the diverse needs of learners is discussed.