The "Grey Area": A Computational Approach to Model the Zone of Proximal Development

In this paper, we propose a computational approach to model the Zone of Proximal Development (ZPD) using predicted probabilities of correctness while students engage in reflective dialogue. We employ a predictive model that uses a linear function of a variety of parameters, including difficulty and student knowledge, as students use a natural-language tutoring system that presents conceptual reflection questions after they solve high-school physics problems. In order to operationalize our approach, we introduce the concept of the “Grey Area”, that is, the area of uncertainty in which the student model cannot predict with acceptable accuracy whether a student is able to give a correct answer without support. We further discuss the impact of our approach on student modeling, the limitations of this work and future work in systematically and rigorously evaluating the approach.