One or More External Representations

Abstract

Use of base-10 decomposition strategy for addition in first grade is related to mathematics advantage in the later years (Geary et al., 2013), yet we know little about the strategy’s prevalence among first graders or factors contributing to its use. The present study sought to bridge this gap by testing 87 first graders in the greater Boston area. The results confirmed previous findings that showed that in the last 10 years first graders in the US have increased in frequency of base-10 decomposition. Children who had better knowledge of basic number facts used it more frequently, particularly on problems with smaller addends. Further, the study tested whether an instructional intervention would be effective in increasing reliance on base-10 decomposition. 61 of the original participants were selected to take part in an experimental intervention that taught them to execute the strategy while relying on external representations – sometimes known as manipulatives. Informed by two lines of research, the present study tested the hypothesis that the efficacy of the intervention may depend on whether one or multiple external representations are used for instruction. The results showed a dramatic increase in first graders’ mental base-10 decomposition use as a result of the intervention. Children grew in their use of the strategy at the same rates across genders, levels of basic arithmetic fluency, and working memory. Overall, the results showed that relying on multiple representations during instruction appears more beneficial to strategy use on mental arithmetic, but this benefit may be conditional on how well the children have mastered and abstracted the strategy. Implications to classroom interventions aimed to increase the use of advanced arithmetic strategies are discussed.