Within-task actions can provide additional information on student competencies but are challenging to model. This paper explores the potential of using a cognitive model for decision making, the Markov decision process, to provide a mapping between within-task actions and latent traits of interest. Psychometric properties of the model are explored, and simulation studies report on parameter recovery within the context of a simple strategy game. The model is then applied to empirical data from an educational game. Estimates from the model are found to correlate more strongly with posttest results than a partial-credit IRT model based on outcome data alone.

Watching another person take actions to complete a goal and making inferences about that person's knowledge is a relatively natural task for people. This ability can be especially important in educational settings, where the inferences can be used for assessment, diagnosing misconceptions, and providing informative feedback. In this paper, we develop a general framework for automatically making such inferences based on observed actions; this framework is particularly relevant for inferring student knowledge in educational games and other interactive virtual environments. Our approach relies on modeling action planning: We formalize the problem as a Markov decision process in which one must choose what actions to take to complete a goal, where choices will be dependent on one's beliefs about how actions affect the environment. We use a variation of inverse reinforcement learning to infer these beliefs. Through two lab experiments, we show that this model can recover people's beliefs in a simple environment, with accuracy comparable to that of human observers. We then demonstrate that the model can be used to provide real-time feedback and to model data from an existing educational game.

We discuss our present knowledge of the flow and stability of helium II between concentric cylinders. The flow problem for helium II leads us to consider the formation of quantized vortices in the uniform rotation of helium II in an open bucket as well as quantized circulation states and vortices in a rotating annulus. We then consider how to treat the first appearance of vortices in the presence of shear, which allows us to characterize the basic flow which must be examined for stability. The results suggest an explanation for heretofore unexplained experiments. Future directions for research on the stability of helium II are suggested.

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Despite large literature on Cross-Cultural Competence (3C) there is a gap in understanding learning processes and mechanisms by which people arrive at successful 3C. We present a novel perspective for 3C learning and decision-making in innovative assessment contexts. We use Mindset theory (i.e., believing ability is fixed or changeable) because it is shown to be a powerful motivator for general learning and performance and in cross-cultural contexts. We propose the notion of cultural mindsets – beliefs, affect, and cognition that govern how people adapt, learn, and update cultural information. To understand how cultural mindset affects learning and performance, we apply computational cognitive modeling using Markov decision process (MDP). Using logfile data from an interactive 3C task, we operationalize behavioral differences in actions and decision making based on Mindset theory, developing cognitive models of fixed and malleable cultural mindsets based on mechanisms of initial beliefs, goals, and belief updating. To explore the validity of our theory, we develop computational MDP models, generate simulated data, and examine whether performance patterns fit our expectations. We expected the malleable cultural mindset would be better at learning the cultural norms in the assessment, more persistent in cultural interactions, quit less before accomplishing the task goal, and would be more likely to modify behavior after negative feedback. We find evidence of distinct patterns of cultural learning, decision-making, and performance with more malleable cultural mindsets showing significantly greater cultural learning, persistence, and responsiveness to feedback, and more openness to exploring current cultural norms and behavior. Moreover, our model was supported in that we were able to accurately classify 83% of the simulated records from the generating model. We argue that cultural mindsets are important mechanisms involved in effectively navigating cross-cultural situations and should be considered in a variety of areas of future research including education, business, health, and military institutions.