| Yuk Fai Cheong
Michigan State University
A Bayesian analysis of school- and state-level correlates of the likelihood of the offering of eighth grade algebra for high school credits
FINAL REPORT:
This dissertation addressed two research objectives: one substantive, the other methodological. The first objective was to examine what school- and state-level factors may influence a public school's decision to offer eighth-grade algebra for high school credits. The analysis employed the data collected under the 1992 Trial State Assessment Program (TSAP) in mathematics of the National Assessment of Educational Progress (NAEP), and the state profile statistics compiled by the Council of Chief State School Officers (CCSSO) (CCSSO, 1993). The second, related objective was to develop and evaluate a fully Bayesian, multilevel approach that enables the study of public schools as distributors of learning opportunities in advanced mathematics.
The Bayesian, multilevel approach developed by Zeger and Karim (1991) was implemented via the Gibbs sampler (Gemen & Gemen, 1984; Gelfand & Smith, 1990). The algorithm was coded using the Interactive Matrix Language of the Statistical Analysis Systems (SAS/IML) (SAS Institute, Inc., 1989). The result of a small simulation study, which generated and analyzed data sets having similar structure to that of the TSAP, showed that the SAS/IML code performed well and the algorithm yielded reasonable inferences.
The tested code was used to fit two models studying the distribution of learning opportunities in mathematics. The results of the first unconditional model reveal significant state-to-state variation in the likelihood of the offering of eighth-grade algebra by public schools. The findings of the second model suggest that schools serving minority students and students of low social-economic status (SES), small schools, schools located in rural settings and states that spend less on education are comparatively less likely than other schools to offer algebra. The implication is that size, composition, and location of a school are linked to inequality in access to this educational resource. In these ways,the schooling system reinforces social, ethnic and geographic inequalities regarding the opportunities available for eighth-grade students to study algebra for high school credits.
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