Learning Time and Achievement: Evidence from a Nationwide Natural Experiment

Abstract

How much do students learn from an additional day of instruction? This paper uses the National Assessment of Educational Progress (NAEP) to measure achievement gains from additional instruction. I identify gains using demonstrably random variation in assessment dates, which gives some students more time to prepare for assessments. In mathematics, 4th and 8th grade students gain 0.80 and 0.40 standard deviations per year; in reading, gains are 0.50 and 0.25 standard deviations per year. Declining learning rates across grade levels cannot be explained by normalization, measurement error, or ceiling effects: these are ruled out with new evidence from self-reported sub- jective test difficulty, and from individual test questions and psychometric parameters. Measured learning rates may decline across grade levels because learning is slower, or for two other reasons related to test design: only part of what is tested is taught (tests are cumulative, as in Cascio and Staiger, 2012), or only part of what is taught is tested. Regardless of why learning rates differ across grades, an application demonstrates their value in interpreting other findings in the literature: measured in standard deviations, black-white achievement gaps are steady from 4th to 8th grade. But measured in units of time, black-white achievement gaps double from 4th to 8th grade, from 1 to 2 years to close the gap in math, and from 1.5 to 3 years to close the gap in reading.