Dynamic Bayeian Inference Networks and Hidden Markov Models for Modeling Learning Progressions over Multiple Time Points

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The current study examines the performance of a Bayesian Inference Network (BIN) for modeling Learning Progressions (LP) as a longitudinal design approach. Recently, Learning Progressions, defined by measurable pathways that a student may follow in building their knowledge and gaining expertise over time (National Research Council, 2007; Shin, Stevens, Short & Krajcik, 2009), have captured attention in mathematics and science education (Learning Progressions in Science Conference, 2009). While substantive, psychological, instructional, and task developmental aspects has been proposed in the LP framework, few assessment design frameworks have been designed to link the theory embodied in a progression, tasks that provide evidence about a student's level on that progression, and psychometric models that can link them. Specially, few psychometric models have been proposed to characterize the relationship between student performance and levels on learning progressions in a longitudinal design approach. This dissertation introduces an approach to modeling LPs over multiple time points using Bayesian Inference Networks, referred to as dynamic Bayesian Inference Networks (DBINs). The DBINs are a framework for modeling LPs over time by integrating the theory embodying LPs, assessment design, and interpretation of student performances. The technical aspects of this dissertation cover the fundamental concepts of the graphical model for constructing a DBIN. It is shown that this modeling strategy for change over multiple time points is equivalent to a hidden Markov model. An expectation-maximization (EM) algorithm is presented for estimating the parameters in the model. Two simulation studies are conducted that focus on the construction of a simple DBIN model and an expanded DBIN model with a covariate. The extension that incorporates a covariate for students is useful for studying the effect of instructional treatments, students' background, and motivation on a student's LP. An application illustrates the ideas with real data from the domain of beginning computer network engineering drawn from work in the Cisco Networking Academy.