Human one-on-one coaching involves complex multimodal interactions. Successful coaching requires teachers to closely monitor students' cognitive-affective states and provide support of optimal type, timing, and amount. However, most of the existing human tutoring studies focus primarily on verbal interactions and have yet to incorporate the rich…

The purpose of this paper is to integrate mathematical modeling and ecology by presenting an activity involving an authentic environmental problem, which is called "Pine Processionary Caterpillars Invasion." Adopting Mathematical Modeling and Education for Climate Action (EfCA) approaches, it was aimed to encourage pre-service teachers…

How can humans acquire relational representations that enable analogical inference and other forms of high-level reasoning? Using comparative relations as a model domain, we explore the possibility that bottom-up learning mechanisms applied to objects coded as feature vectors can yield representations of relations sufficient to solve analogy…

Most treatments of indirect effects and mediation in the statistical methods literature and the corresponding methods used by behavioral scientists have assumed linear relationships between variables in the causal system. Here we describe and extend a method first introduced by Stolzenberg (1980) for estimating indirect effects in models of…

This article addresses issues in model building and statistical inference in the context of student modeling. The use of probability-based reasoning to explicate hypothesized and empirical relationships and to structure inference in the context of proportional reasoning tasks is discussed. Ideas are illustrated with an example concerning…

Diagnostic score reports linking assessment outcomes to instructional interventions are one of the most requested features of assessment products. There is a body of interesting work done in the last 20 years including Tatsuoka's rule space method (Tatsuoka, 1983), Haertal and Wiley's binary skills model (Haertal, 1984; Haertal & Wiley, 1993),…