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"Secondary teachers across the United States are being asked to use formative assessment data to inform their classroom instruction. At the same time, critics of US government’s No Child Left Behind legislation are calling the bill “No Child Left Untested”. Among other things, critics point out that every hour spent assessing students is an hour lost from instruction. But, does it have to be? What if we better integrated assessment into classroom instruction and allowed students to learn during the test? This dissertation emphasizes using the intelligent tutoring system as an assessment system that just so happens to provide instructional assistance during the test. Usually it is believed that assessment get harder if students are allowed to learn during the test, as it’s then like trying to hit a moving target. So, my results are somewhat shocking that by providing tutoring to students while they are assessed I actually improve the assessment of students’ knowledge. Most traditional assessments treat all questions on the test as sampling a single underlying knowledge component. Yet, teachers want detailed, diagnostic reports to inform their instruction. Can we have our cake and eat it, too? In this dissertation, I provide solid evidence that a fine-grained skill model is able to predict state test scores better than coarser-rained models, as well as being used to give teachers more informative feedback that they can reflect on to improve their instruction. The contribution of the dissertation lies in that it established novel assessment methods to better assess students in intelligent tutoring systems. Through analyzing data of more than 1,000 students across two years, it provides strong evidence implying that it is possible to develop a continuous assessment system that can do all three of these things at the same time: 1) accurately and longitudinally assesses students, 2) gives fine grained feedback that is more cognitively diagnostic, and 3) saves classroom instruction time by assessing students while they are getting tutoring. "

In this paper I propose Bayesian estimation of a nonlinear panel data model with a fractional dependent variable (bounded between 0 and 1). Specifically, I estimate a panel data fractional probit model which takes into account the bounded nature of the fractional response variable. I outline estimation under the assumption of strict exogeneity as well as when allowing for potential endogeneity. Furthermore, I illustrate how transitioning from the strictly exogenous case to the case of endogeneity only requires slight adjustments. For comparative purposes I also estimate linear specifications of these models and show how quantities of interest such as marginal effects can be calculated and compared across models. Using data from the state of Florida, I examine the relationship between school spending and student achievement, and find that increased spending has a positive and statistically significant effect on student achievement. Furthermore, this effect is roughly 50% larger in the model which allows for endogenous spending. Specifically, a $1,000 increase in per-pupil spending is associated with an increase in standardized test pass rates ranging from 6.2-10.1%.

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.