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Computer-based learning environments offer the potential for innovative assessments of student knowledge and personalized instruction for learners. However, there are a number of challenges to realizing this potential. Many psychological models cannot be directly deployed in instructional systems or may pose computational challenges. While learners' interactions with virtual environments encode significant information about their understanding, existing statistical tools are insufficient for interpreting these interactions. This research develops computational models of teaching and learning and combines these models with machine learning algorithms to interpret learners' actions and customize instruction based on these interpretations. This approach results in frameworks that can be adapted to a variety of educational domains, with the frameworks clearly separating components that can be shared across tasks and components that are customized based on the educational content. Using this approach, this dissertation addresses three major questions: (1) How can one diagnose learners' knowledge from their behavior in games and virtual laboratories? (2) How can one predict whether a game will be diagnostic of learners' knowledge? and (3) How can one customize instruction in a computer-based tutor based on a model of learning in a domain? The first question involves automatically assessing student knowledge via observed behavior in complex interactive environments. These environments require students to plan their behavior and take multiple actions to achieve their goals. Unlike in many traditional assessments, students' actions are not independent given their knowledge. I develop a Bayesian inverse planning framework for inferring learners' knowledge from observing their actions. The framework is a variation of inverse reinforcement learning and uses Markov decision processes to model how people choose actions given their knowledge. Through behavioral experiments, I show that this framework can infer learners' stated beliefs, with accuracy similar to human observers. I extended the inverse planning framework to diagnose students' algebra skills from worked solutions to linear equations, separating different sources of mathematical errors. Preliminary experiments using data collected in an online algebra tutor demonstrate that Bayesian inverse planning provides a good fit for the majority of participants' behaviors, and that its diagnoses are consistent with results of a more conventional assessment. The results of the previous studies showed that in many cases, little information about learners' understanding may be gained because their actions are ambiguous. I developed an optimal game design framework to predict how much information will be gained by observing players' actions in a game, extending optimal experiment design methods. It can limit the trial and error necessary to create games for education and behavioral research by suggesting game design choices. Behavioral results from a concept learning game demonstrate that the predicted information gain is correlated with the actual information gain and that the best designs can result in twice as much information as an uninformed design. The final part of this dissertation considers how to personalize instruction in a computer tutor, balancing assessment and introduction of new material. There may be a cost to time spent on assessment, as the time could have been spent allowing the learner to work through new material; however, this time spent on assessment may also be beneficial by providing information to allow the computer to choose material more effectively. I show that partially observable Markov decision processes can be used to decide what pedagogical action to choose based on a model of the domain and the learner. The resulting automated instructional policies result in faster learning of numeric concepts than baseline policies.

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