Learning algebra is difficult for many students in part because of an emphasis on the memorization of abstract rules. Algebraic reasoners across expertise levels often rely on perceptual-motor strategies to make these rules meaningful and memorable. However, in many cases, rules are provided as patterns to be memorized verbally, with little overt…

Seeking the right level of help at the right time can support learning. However, in the context of online problem-solving environments, it is still not entirely clear which help-seeking strategies are desired. We use fine-grained data from 38 high school students who worked with the Geometry Cognitive Tutor for 2 months to better understand the…

A total of 136 eighth-grade math students from 2 Singapore schools learned from either productive failure (PF) or vicarious failure (VF). PF students "generated" solutions to a complex problem targeting the concept of variance that they had not learned yet before receiving instruction on the targeted concept. VF students…

There is a growing national recognition that teachers and teaching are at the heart of successful educational reform. However, few tools exist for measuring classroom instruction. The primary purpose of this article is to describe methods we developed to measure and study teaching, specifically while teachers were using a multimedia intervention…

Groups that created more correct ideas (correct contributions or CCs) might be more likely to solve a problem, and students' recent actions (micro-time context) might aid CC creation. 80 high school students worked in groups of 4 on an algebra problem. Groups with higher mathematics grades or more CCs were more likely to solve the problem. Dynamic…