Self-Monitoring of Attention Versus Self-Monitoring of Performance: Examining the Differential Effects Among Students with Emotional Disturbance Engaged in Independent Math Practice

Although students with emotional disturbance are commonly known for their social behavior deficits, they often have academic deficits as well. Unfortunately, most of the intervention research and many of the practices used with this population focus upon their social behavior deficits and fail to recognize the need to improve their academic skills. Therefore, there is a need for identifying research-based interventions that focus on ameliorating social and academic deficits often exhibited by students with emotional disturbance. The purpose of this study was to examine the differential effects of self-monitoring of attention versus self-monitoring of performance on the academic and social behaviors of three minority students identified as having emotional disturbance while independently engaged in practicing mathematical calculations. The findings suggest that students with emotional disturbance may perform better socially and academically during math practice while self-monitoring their academic performance. Social validity data also suggest that students rated self-monitoring of academic performance more favorably than self-monitoring of attention. In addition, all target students in this study exhibited levels of on-task behavior more similar to their peers while self-monitoring academic performance compared to self-monitoring attentive behavior.     

Analyzing the Rate at Which Languages Lose the Influence of a Common Ancestor

Analyzing the rate at which languages change can clarify whether similarities across languages are solely the result of cognitive biases or might be partially due to descent from a common ancestor. To demonstrate this approach, we use a simple model of language evolution to mathematically determine how long it should take for the distribution over languages to lose the influence of a common ancestor and converge to a form that is determined by constraints on language learning. We show that modeling language learning as Bayesian inference of n binary parameters or the ordering of n constraints results in convergence in a number of generations that is on the order of n log n. We relax some of the simplifying assumptions of this model to explore how different assumptions about language evolution affect predictions about the time to convergence; in general, convergence time increases as the model becomes more realistic. This allows us to characterize the assumptions about language learning (given the models that we consider) that are sufficient for convergence to have taken place on a timescale that is consistent with the origin of human languages. These results clearly identify the consequences of a set of simple models of language evolution and show how analysis of convergence rates provides a tool that can be used to explore questions about the relationship between accounts of language learning and the origins of similarities across languages.     

Assessing Mathematics Misunderstandings via Bayesian Inverse Planning

Online educational technologies offer opportunities for providing individualized feedback and detailed profiles of students' skills. Yet many technologies for mathematics education assess students based only on the correctness of either their final answers or responses to individual steps. In contrast, examining the choices students make for how to solve the equation and the ways in which they might answer incorrectly offers the opportunity to obtain a more nuanced perspective of their algebra skills. To automatically make sense of step-by-step solutions, we propose a Bayesian inverse planning model for equation solving that computes an assessment of a learner's skills based on her pattern of errors in individual steps and her choices about what sequence of problem-solving steps to take. Bayesian inverse planning builds on existing machine learning tools to create a generative model relating (mis)-understandings to equation solving choices. Two behavioral experiments demonstrate that the model can interpret people's equation solving and that its assessments are consistent with those of experienced teachers. A third experiment uses this model to tailor guidance for learners based on individual differences in misunderstandings, closing the loop between assessing understanding, and using that assessment within an educational technology. Finally, because the bottleneck in applying inverse planning to a new domain is in creating the model of possible student misunderstandings, we show how to combine inverse planning with an existing production rule model to make inferences about student misunderstandings of fraction arithmetic.