Numerical understanding and arithmetic skills are easier to acquire for whole numbers than fractions. The "integrated theory of numerical development" posits that, in addition to these differences, whole numbers and fractions also have important commonalities. In both, students need to learn how to interpret number symbols in terms of…

This study documents the magnitude of the gaps in student performance for public school students in Pennsylvania and estimates the economic consequences of those education performance gaps. Although Pennsylvania is one of the top-scoring states on the 2013 National Assessment of Educational Progress (NAEP) on average, the achievement gaps between…