The First Step to Learning Place Value: A Role for Physical Models?

Abstract

Very few questions have cast such an enduring effect in cognitive science as the question of “symbol-grounding”: Do human-invented symbol systems have to be grounded to physical objects to gain meanings? This question has strongly influenced research and practice in education involving the use of physical models and manipulatives. However, the evidence on the effectiveness of physical models is mixed. We suggest that rethinking physical models in terms of analogies, rather than groundings, offers useful insights. Three experiments with 4- to 6-year-old children showed that they can learn about how written multi-digit numbers are named and how they are used to represent relative magnitudes based on exposure to either a few pairs of written multi-digit numbers and their corresponding names, or exposure to multi-digit number names and their corresponding physical models made up by simple shapes (e.g., big-medium-small discs); but they failed to learn with traditional mathematical manipulatives (i.e., base-10 blocks, abacus) that provide a more complete grounding of the base-10 principles. These findings have implications for place value instruction in schools and for the determination of principles to guide the use of physical models.