Abstract
Manipulatives are ubiquitous in early childhood classrooms; yet, findings regarding their efficacy for learning mathematics concepts are inconsistent. In this article, we present four general principles that have emerged from cognitive science about ways to ensure that manipulatives promote learning when used with young children. We also describe how Montessori instruction offers a concrete example of the application of these principles in practice, which may, in turn, explain the high levels of mathematics achievement among children who attend Montessori programs during early childhood. The general principles and concrete examples presented in this article should help early childhood programs maximize the benefits of using manipulatives for developmentally appropriate mathematics instruction.
Highlights
Walk into any early childhood classroom and you are sure to see mathematics manipulatives
In particular, has generated a considerable amount of knowledge that could be useful for improving instruction so that all young children can acquire the mathematics knowledge necessary for success, as described in National Council of Teachers of Mathematics (NCTM) standards and Common Core standards (Laski, Reeves, Ganley, & Mitchell, 2013; NCTM, 2006; National Governors Association Center for Best Practices, Council of Chief State School Officers, 2010; Newcombe et al, 2009; Siegler, 2003)
Despite the widespread use of manipulatives in early childhood mathematics instruction, research examining the efficacy of manipulatives for mathematics instruction is inconsistent
Summary
Walk into any early childhood classroom and you are sure to see mathematics manipulatives. From our review of the literature, four general principles emerged: (a) use a manipulative consistently, over a long period of time; (b) begin with highly transparent concrete representations and move to more abstract representations over time; (c) avoid manipulatives that resemble everyday objects or have distracting irrelevant features; and (d) explicitly explain the relation between the manipulatives and the math concept.
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