Although reformers have embraced learning trajectories (LT, also called learning progressions) as an important tool for improving mathematics education, the efficacy and assumptions of LT-based instruction are largely unproven. The aim of a recently completed research project was to fill this void. Fulfilling this aim was more challenging than…

A substantial literature documents the benefits of early childhood education and formal preschool experiences on children's school readiness, with low-income and otherwise disadvantaged children benefitting the most from these programs. However, these academic benefits often fade out as children age, and most disappear by the end of kindergarten…