Strategies are an important component of self-regulated learning frameworks. However, the characterization of strategies in these frameworks is often incomplete: (1) they lack an operational definition of strategies; (2) there is limited understanding of how students develop and apply strategies; and (3) there is a dearth of systematic and…

We often understand something only after we've had to teach or explain it to someone else. Learning-by-teaching (LBT) systems exploit this phenomenon by playing the role of "tutee." BELLA, our sixth-grade mathematics LBT systems, departs from other LTB systems in several ways: (1) It was built not from scratch but by very slightly…

In this paper we will describe a learning environment designed to foster conceptual understanding and reasoning in mathematics among younger school children. The learning environment consists of 48 2-player game variants based on a graphical model of arithmetic where the mathematical content is intrinsically interwoven with the game idea. The…

Intelligent tutors have become increasingly accurate at detecting whether a student knows a skill, or knowledge component (KC), at a given time. However, current student models do not tell us exactly at which point a KC is learned. In this paper, we present a machine-learned model that assesses the probability that a student learned a KC at a…