Connecting concrete objects and abstract symbols promotes children’s place value knowledge
Andrea Marquardt Donovan, Emily R. Fyfe
Abstract
Children often learn abstract mathematics concepts with concrete manipulatives. The current study compared different ways of using specific manipulatives – base-ten blocks – to support children’s place value knowledge. Children (N = 112, M age = 6.88 years) engaged in place value learning activities in one of four randomly assigned conditions in a one-on-one tutoring setting: Concrete Only, Two-Step Fading, Three-Step Fading, and Fading-with-Comparison. Performance on a posttest measure was higher in the Two-Step and Three-Step Fading conditions relative to the Fading-with-Comparison condition, suggesting potential benefits of gradual, sequential transitions from concrete objects to written numerals. Children in the Concrete Only condition also exhibited high place value knowledge on the posttest. Finally, across conditions, children who exhibited knowledge of the connections between the base-ten-blocks and written number symbols had higher posttest and transfer test scores relative to children who did not exhibit knowledge of these connections.