Strategic counting: A novel assessment of place-value understanding

Children's counting strategies reflect how much they understand the place-value structure of numbers. In Study 1, a novel task, namely the strategic counting task, elicited strategies from kindergarteners and first graders that showed a trend of increasing place-value knowledge – from perceiving number as an undivided entity to seeing it as a collection of independent groups of powers of ten. In Study 2, first-graders' strategic counting task scores at the end of fall semester were better predictors of year-end mathematical achievement than the traditional place-value tasks. In Study 3, a five-item subset of strategic counting was the best among 15 various cognitive predictors of end of second-grade mathematical achievement. Growth curve modeling revealed that low-mathematics achievers at the end of second grade had been lagging behind their peers in strategic counting since early first grade. Implications for early support for children with difficulties in place-value knowledge are discussed.