We expect that word knowledge accumulates gradually. This article draws on earlier approaches to assessing depth, but focuses on one dimension: richness of semantic knowledge. We present results from a study in which three distinct item types were developed at three levels of depth: knowledge of common usage patterns, knowledge of broad topical…

Spurred by a succession of reports pointing to the importance of algebra as a gateway to college, educators and policymakers embraced "algebra for all" policies in the 1990s and began working to ensure that students take the subject by 9th grade or earlier. A trickle of studies suggests that in practice, though, getting all students past…