Despite significant investments over the past decade in the expansion and improvement of preschool programs, too many children, particularly poor children, enter kindergarten behind their peers. Because it is critical that voluntary pre-kindergarten (VPK) classrooms offer educational programs that both address the needs and developmental levels of…

Although learning mathematics certainly depends upon accurate understanding of the facts of multiplication, it requires much more. This study examines the relationship between a meaningful understanding of arithmetic operations and the mastery of basic facts. The study began with a joke about a mistaken mathematical fact. The children appreciated…