Grounding the Symbols for Place Value: Evidence From Training and Long-Term Exposure to Base-10 Models

Two experiments examined whether concrete models support place value learning. In Experiment 1 (N = 149), 7-year-olds were trained with either a) symbols alone or b) symbols and base-10 blocks. Children in both groups showed significant growth overall, but there were specific effects favoring one training type over another. Symbols-only training led to higher scores on a number line estimation task and was particularly effective among high-ability students, whereas blocks training led to better understanding of base-10 structure and was particularly effective among low-ability learners. In Experiment 2 (N = 68), Montessori students, for whom concrete models play a major role in mathematics instruction, also demonstrated better understanding of base-10 structure than did their matched peers enrolled in mainstream elementary schools.