Providing learners with multiple representations of learning content has been shown to enhance learning outcomes. When multiple representations are presented across consecutive problems, we have to decide in what sequence to present them. Prior research has demonstrated that interleaving "tasks types" (as opposed to blocking them) can…

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…

This article describes research results based on multiple years of experimentation and real-world experience with an adaptive tutoring system named Wayang Outpost. The system represents a novel adaptive learning technology that has shown successful outcomes with thousands of students, and provided teachers with valuable information about…

In this paper we investigate how competition among tutees in the context of learning by teaching affects tutors' engagement as well as tutor learning. We conducted this investigation by incorporating a competitive Game Show feature into an online learning environment where students learn to solve algebraic equations by teaching a synthetic…

We present an inference algorithm for perturbation models based on Poisson regression. The algorithm is designed to handle unclassified input with multiple errors described by independent mal-rules. This knowledge representation provides an intelligent tutoring system with local and global information about a student, such as error classification…