Beyond One-Size Fits All: Using Heterogeneous Models to Estimate School Performance in Mathematics
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This dissertation explored the academic growth in mathematics of a longitudinal cohort of 21,567 Oregon students during middle school on a state accountability test. The student test scores were used to calculate estimates of school performance based on four different accountability models (percent proficient [PP], change in PP, multilevel growth, and growth mixture). On average, 72% of Oregon eighth graders were proficient in mathematics in 2012, 71% in the average school, and 6% more students in this cohort demonstrated mathematics proficiency compared to 2011. The two-level unconditional multilevel growth model estimated the average intercept (Grade 6) to be 228.4 (SE = 0.07) scale score points with an average middle school growth rate of 5.40 scale points per year (SE = 0.02) on the state mathematics test. Student demographic characteristics were a statistically significant improvement on the unconditional model. A major shortcoming of this research, however, was the inability to find successful model convergence for any three-level growth model or any growth mixture model. A latent class growth analysis was used to uncover groups of students who shared common growth trajectories. A five-latent class solution best represented the data with the lowest BIC and a significant LMR p. Two of the latent classes were students who had high achievement in Grade 6 and demonstrated high growth across middle school and a second group with low sixth grade achievement that had below average growth in middle school. Student-level demographic predictors had statistically significant relations with growth characteristics and latent class membership. In comparing school performance based on the four different models, it was found that, although statistically correlated, the models of school performance ranked schools differently. A school’s percentage of proficient students in Grade 8 correlated moderately (r = [.60, .70]) with growth over the middle school years as estimated by the growth and LCGA models. About 70% to 80% of schools ranked more than 10 percentiles differently for every pairwise comparison of models. These results, like previous research call into question whether currently used models of school performance produce consistent and valid descriptions of school performance using state test scores.