Prior knowledge has long been recognized as an important predictor of learning, yet the term prior knowledge is often applied to related but distinct constructs. We define a specific form of prior knowledge, ancillary knowledge, as knowledge of concepts and skills that enable learners to gain the most from a target lesson. Ancillary knowledge is…

Instructors in STEM classrooms often frame students' interactions with technologies to help them learn content. For instance, in many STEM domains, instructors commonly help students translate physical 3D models into 2D drawings by prompting them to focus on (a) orienting physical 3D models and (b) generating 2D drawings. We investigate whether…

The effectiveness of an experimental middle school fraction intervention was evaluated. The intervention was centered on the number line and incorporated key principles from the science of learning. Sixth graders (N = 51) who struggled with fraction concepts were randomly assigned at the student level to the experimental intervention (n = 28) or…

In this paper, we describe our learning progressions approach to early algebra research that involves the coordination of a curricular framework, an instructional sequence, written assessments, and levels of sophistication describing the development of students' thinking. We focus in particular on what we have learning through this approach about…

Student models for adaptive systems may not model collaborative learning optimally. Past research has either focused on modeling individual learning or for collaboration, has focused on group dynamics or group processes without predicting learning. In the current paper, we adjust the Additive Factors Model (AFM), a standard logistic regression…