The widespread concern about mathematics achievement has drawn extensive research attention to what skills predict later academic achievement. There is clear and consistent evidence that math achievement at school entry is the strongest predictor of later school success and educational attainment. Early childhood math achievement can thus have…

Although basing instruction on a learning trajectory (LT) is often recommended, there is little direct evidence to support the premise of a "LT approach"--that to be maximally meaningful, engaging, and effective, instruction is best presented one LT level beyond a child's present level of thinking. The present report serves to address…