An investigation into the concreteness of manipulatives in mathematical instruction: Do the object and its label matter?

Abstract

Manipulatives are often used to help children master mathematical concepts. The present study investigated whether concreteness of the object and concreteness of the language used to describe it mattered for effectiveness. Two hundred and twenty-five kindergarten children were taught how to solve equal sharing problems with one of the four methods: concrete-object-concrete-language, concrete-object-generic-language, generic-object-concrete-language, generic-object-generic-language. Their knowledge of equal sharing was pre- and post-tested. Results of the 2×2×2 mixed-design ANOVA suggested that there was a significant interaction effect between the concreteness of object and concreteness of language on the differences in equal sharing knowledge across the two tests. Follow-up analysis revealed that children showed greater improvement in knowledge when incongruent methods (i.e., concrete-object-generic-language, generic-object-concrete-language) were adopted. These findings suggest that when teaching mathematics with manipulatives, early childhood educators should use generic language to label concrete manipulatives, but concrete language to label generic manipulatives.