Differences in mathematics achievement according to opportunity to learn: A 4pL item response theory examination

We examine student performance on mathematics items from the 2012 Program for International Student Assessment. Utilizing a 4 parameter logistic Item Response Theory model, we were particularly interested in estimating the probability of a student who was relatively high achieving incorrectly responding to mathematics items as related to having more or less opportunity to learn as rated by the student. Results indicate that students who were similarly high achieving yet had less opportunity to learn were significantly less likely to correctly respond to an item as compared to those who had more opportunity to learn. When accounting for these item-level differences in OTL in mathematics, socioeconomic status was longer related to academic achievement.