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«University of Nebraska - Lincoln DigitalCommons of Nebraska - Lincoln Dissertations and Theses in Statistics Statistics, Department of 8-2010 ...»

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0.4 0.2 0.2 0.0 0.0 Upper Quartile for the Curve-of-Factors (solid), CA Z-score (dash) and MA Z-score (dotted) Models with Complete and Missing Tests, and MA/CA Z-score (dot-dash) Model with Missing Tests for Specific True Percentiles and Years factors model when all tests are given tends toward that of the alternative Z-score models when a test is missing in both years one and four. With regards to estimating a teacher’s true percentile, assuming a curve-of-factors model structure from which the data are originally simulated loses its statistical advantages, such as smaller RMSE, when tests are missing in some of the years. The results from the Z-score models are not noticeably different from one another for both the complete and missing tests cases. This is expected, because the only difference between a student’s mean-centered MA and CA scores for a given year is the random measurement error, assumed to have constant variance across test and year. The lack of differences between Z-score models in the complete and missing tests cases is also expected. Because only one test can be used as the response in each year, having only one test in a given year instead of two is not consequential. Overall, the curve-of-factors model does not have drastically better performance relative to the alternative Z-score approach, even though the curve-offactors model is the structure from which the data are simulated. Additional studies should use simulation to investigate how the estimation of teacher effects and their corresponding percentiles change under other assumed model structures and alternative weighting schemes for teacher effect variance components across years, as well as different ratios of teacher effect variance to error variance, such as those used by Lockwood et al. (2002), in various complete and incomplete test scenarios.

Chapter 5 Conclusions Value-added modeling techniques estimate the contribution of educational factors, such as teachers, to growth in student achievement, while allowing for the possibility to control for the effect of non-educational factors. Several value-added models for estimating teacher effects have been proposed as alternatives to current testbased accountability procedures, such as adequate yearly progress (AYP), but each has its respective advantages and disadvantages. Although these methods have the potential to identify highly effective teachers, teacher effect estimates are sensitive to different modeling specifications, including the persistency of teacher effects. Furthermore, several statistical and psychometric issues exist, and sensitivity of teacher effects to such issues still needs to be explored.

This dissertation includes three chapters that provide an introduction to valueadded methodology and discuss the estimation of teacher effects. Because value-added analyses require high-quality longitudinal data that are often not available, Chapters 3 and 4 proposed methodology for analyzing less-than-ideal student assessment data.

Specifically, Chapter 3 described how to use a value-added model when longitudinal student achievement data are not on a single developmental scale. Although the Z-score approach has limitations, it is an appropriate alternative to using raw data when analyzing less-than-ideal student achievement data across a mixture of norm- and criterion-referenced tests over time. This chapter addressed issues arising when using a layered, longitudinal linear mixed model to analyze gains in standardized scores, including weighting considerations for variance components. Additionally, this chapter proposed methods for estimating teacher effects on student learning before and after teacher participation in professional development programs. Although the specific example used in this chapter did not indicate the Math in the Middle Institute had a significant impact on participating teachers’ effects on student learning, the instruments may not have been designed to detect such changes. Additionally, teacher change from professional development may take time to show an impact on student learning. It is also possible other factors impact a teacher’s instruction and his or her ability or perceived ability to change in ways that align with the professional development program (Kromminga, in progress). When utilizing this methodology, determining whether the goals of the program align with what the instruments assess and acknowledging any existing limitations is essential.

Chapter 4 applied curve-of-factors methodology in a value-added context to extend the analysis of student achievement data to situations in which multiple tests with potentially different scales are given each year in a particular subject. Instead of estimating a teacher’s effect on changes in a student’s scores over time, the curve-offactors model allowed the estimation of a teacher’s effect on changes in some common, latent trait measured by the multiple instruments across years. In the simulation study, the behavior of the curve-of-factors model when all tests were given tended toward that of the alternative Z-score models when a test was missing in both years one and four. With regards to estimating a teacher’s true percentile, assuming a curve-of-factors model structure from which the data were originally simulated lost its statistical advantages, such as smaller RMSE, when tests were missing in some of the years. In general, the curve-of-factors model did not have drastically better performance relative to the alternative Z-score approach, even though the curve-of-factors model was the structure from which the data were simulated.

Together, these two approaches address concerns surrounding the estimation of value-added teacher effects when analyzing less-than-ideal student achievement data.

However, considerations should be made when defining what teacher effects really describe, and teacher effect estimates should be linked to other valid measures of teacher effectiveness. Although standardized tests can provide useful information about a student’s content knowledge in a particular subject, they can only measure a few of the many skills teachers help shape and influence in their students. Teacher evaluation should reflect these many areas of instruction and learning and not be based solely on students’ performance on achievement tests. The uncertainty associated with value-added teacher effect estimates suggests such estimates should not be used in isolation of other measures for high-stakes evaluation purposes and decisions. Instead, value-added teacher effects could be one of many different aspects used for teacher development purposes, fostering high quality teaching and motivating informed improvements in education.

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