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Manipulatives are ubiquitous in early childhood classrooms; yet,findings regarding their efficacy for learning mathematics concepts are inconsistent. Inthis article, we present four general principles that have emerged from cognitivescience about ways to ensure that manipulatives promote learning when used with youngchildren. We also describe how Montessori instruction offers a concrete example of theapplication of these principles in practice, which may, in turn, explain the high levelsof mathematics achievement among children who attend Montessori programs during earlychildhood. The general principles and concrete examples presented in this article shouldhelp early childhood programs maximize the benefits of using manipulatives fordevelopmentally appropriate mathematics instruction

What Makes Mathematics Manipulatives Effective? Lessons From Cognitive Science and Montessori Education