The Role of Extended Time and Item Content on a High‐Stakes Mathematics Test

The premise of a great deal of current research guiding policy development has been that accommodations are the catalyst for student performance differences. Rather than accepting this premise, two studies were conducted to investigate the influence of extended time and content knowledge on the performance of ninth‐grade students who took a statewide mathematics test with and without accommodations. Each study involved 1,250 accommodated students (extended time only) with learning disabilities and 1,250 nonaccommodated students demonstrating no disabilities. In Study One, a standard differential item functioning (DIF) analysis illustrated that the usual approach to studying the effects of accommodations contributes little to our understanding of the reason for performance differences across students. Next, a mixture item response theory DIF model was used to explore the most likely cause(s) for performance differences across the population. The results from both studies suggest that students for whom items were functioning differently were not accurately characterized by their accommodation status but rather by their content knowledge. That is, knowing students' accommodation status (i.e., accommodated or nonaccommodated) contributed little to understanding why accommodated and nonaccommodated students differed in their test performance. Rather, the data would suggest that a more likely explanation is that mathematics competency differentiated the groups of student learners regardless of their accommodation and/or reading levels.     

Spurious Latent Classes in the Mixture Rasch Model

Mixture Rasch models have been used to study a number of psychometric issues such as goodness of fit, response strategy differences, strategy shifts, and multidimensionality. Although these models offer the potential for improving understanding of the latent variables being measured, under some conditions overextraction of latent classes may occur, potentially leading to misinterpretation of results. In this study, a mixture Rasch model was applied to data from a statewide test that was initially calibrated to conform to a 3‐parameter logistic (3PL) model. Results suggested how latent classes could be explained and also suggested that these latent classes might be due to applying a mixture Rasch model to 3PL data. To support this latter conjecture, a simulation study was presented to demonstrate how data generated to fit a one‐class 2‐parameter logistic (2PL) model required more than one class when fit with a mixture Rasch model.