Supporting Meaningful Use of Manipulatives in Kindergarten: The Role of Dual Representation in Early Mathematics

Abstract

Concrete objects (otherwise known as ``manipulatives'') are used often in elementary mathematicsMathematicsclassrooms. Teaching effectively with manipulativesManipulativesis in part contingent on the extent to which children acquire dual representation (DeLoache, 1995), the notion that the manipulatives are objects in their own right as well as objects that ``stand for'' target concepts. We explored the instructional conditions that support the developmentDevelopmentof children's dual representation of manipulativesManipulativesand the moderating effects of prior numeracyNumeracyknowledge. The participants were 12 kindergartenKindergartenstudents from two classrooms. Explicit instruction on using base ten blocks as representations of quantity was delivered over six lessons. The students' understanding of the blocks was assessed after each lesson and an application task measuring performance in a novel context was administered at the end of the unit. Meaningful use of the blocks increased steadily from lesson to lesson, with explicit instruction most beneficial for the students with lower prior knowledge. Students with higher prior knowledge were better able to transfer their learning and demonstrated superior performance on the application task.