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

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.

Longitudinal Comparison of Montessori versus Non-Montessori Students’ Place-Value and Arithmetic Knowledge

“…Further, a recent study found no differences between East Asian and American kindergartners' use of base-10 representations in children with less than one year of formal instruction (Vasilyeva et al, 2015), despite these differences being well documented at the end of first grade, after more than one year of formal instruction (e.g., Miura et al, 1993). The Montessori mathematics curriculum places great emphasis on base 10 and place value using a series of materials (e.g., golden beads, stamp game, bead frames) that highlight these concepts, even with children as young as 3 years (Laski, Jor'dan, Daoust, & Murray, 2015;Lillard, 2005;Montessori & Simmonds, 1917). Thus, it seemed plausible that differences in young children's understanding of base 10 and place value may exist based on whether they had experienced Montessori mathematics instruction between the ages of 3 and 6 years.…”

Applications and props: the impact on engagement and understanding

“…McNeil and Jarvin (2007) weigh up both sides of the debate on the effective use of mathematical manipulatives, though the counterevidence they provide focuses mainly on the "cognitive resources" of children and so is harder to reconcile with the abilities of adults in higher education. We believe that other recommendations, such as principles (c) and (d) described by Laski, Jor'dan, Daoust, and Murray (2015), are in line with the use of manipulatives within the scope of this module, with their other principles again focussing on the cognitive capabilities of children rather than adults. If used in the right way, physical objects can be used to represent abstract ideas in physical form to "help students deeply understand the math they are learning and needing to apply to our everyday life" (Furner and Worrell, 2007).…”

Place Values And Three-Digit Subtraction By Hand-On Activities

“…This relating activities could help students have meaningful understanding of the place values and the operations. The understanding could help students improve ability to solve problems, creative thinking, and learning outcomes [12] [13].…”