In this commentary, the author reflects on four studies that have greatly expanded the knowledge base on effective interventions in mathematics, and he provides four rigorous experimental studies of approaches for students likely to experience difficulties learning mathematics over a large grade-level span (pre-K to 4th grade). All of the…

This article argues that an important source of the difficulties posed by particular concepts and theories is the narrow range of "types of causal models" with which most learners are familiar. Most learners are familiar with relatively simple styles of causal models, but many concepts and theories in science depend on styles…