Lizzy’s struggles with attaining fluency in multiplication tables

Many learners struggle to make the transition from addition and subtraction to multiplication and division, which hampers further progress in mathematics. In this article, I present a case study of one learner who struggled to attain fluency in multiplication by seven. The purpose of this study was to identify and explain how previous non-encapsulations related to addition and subtraction number bonds hampered her efforts in attaining fluency in the multiplication tables. Data for the study were generated from observations and interactions with the child, Lizzy, over a period of two years. The study employed a narrative analysis technique, while drawing upon the APOS (action, process, object, schema) framework together with the notion of conceptual embodiment. The findings suggest that Lizzy’s struggles were due to a non-encapsulation of the various number bond strings, which did not allow her to see patterns in addition by seven. By using an alternative intervention, Lizzy was able to use this strategy as a conceptual embodiment leading her to greater fluency in the seven-times table.