Visual representations can be effective for children's learning of place value but less is known about how they can support understanding of the relation between base-ten numeration units. We investigated the perceptual features in visual representations of quantities on children's understanding of the relations between tens and hundreds. First and second graders ( N = 137) were randomly assigned to four conditions in which they were presented with visual representations that differed by the (a) visibility of base-ten units in a quantity, and (b) presence of extraneous details. Participants indicated the number of tens in the representation, which required decomposing tens from the hundreds, or the number of hundreds, which required composing tens into hundreds. Decomposing was more challenging than composing, regardless of perceptual features, but performance was enhanced when the tens were visible. A post-hoc descriptive analysis showed that children relied on the number of units in their respective “places” without considering the tens embedded in the hundreds or those that could be composed into hundreds, suggesting a strong influence of school-based instruction. Teachers are encouraged to provide more opportunities for children to learn about base ten as a structured system of units with visual representations that make target units visible.
Barilaro et al. (Mon,) studied this question.