"Assumptions" play a fundamental role in disciplinary mathematical practice, especially concerning the relativity of truth. However, much is still unclear about ways to help students recognize key aspects of this role. In this paper, we propose a set of principles for task design to introduce students to the role of assumptions in…

Engaging historiography and interpreting secondary sources represent essential elements of historians' work that have been largely ignored in favor of primary source reading in high school history classrooms in the United States. To understand whether and how students apply their historical reasoning skills to secondary sources, we asked…

This study compares a problem-solving account of discovery through writing, which attributes discovery to strategic rhetorical planning and assumes discovery is associated with better quality text, to a dual-process account, which attributes discovery to the combined effect of 2 conflicting processes with opposing relationships to text quality.…

Social skills involved in leadership were examined in a problem-solving activity in which 252 Chinese 5th-graders worked in small groups on a spatial-reasoning puzzle. Results showed that students who engaged in peer-managed small-group discussions of stories prior to problem solving produced significantly better solutions and initiated…

This article focuses on how the representational properties of manipulatives affect the strategies children employ in problem solving. Two studies examined the effect of physical materials on 4-7-year-old children's problem solving strategies in a numerical (i.e., additive composition) task. The first study showed how children not only identified…

Deictic linking gestures, hand and arm motions that physically embody links being communicated between two or more objects in the shared communicative environment, are explored in a cross-cultural sample of mathematics instruction. Linking gestures are specifically examined here when they occur in the context of communicative analogies designed to…

This study explored the extent to which parents were able to scaffold their children's Self-Regulated Learning (SRL) in the context of authentic academic tasks and attempted to identify specific dimensions within the parent-child interaction (socioemotional and instructional) that were related to children's SRL. Fifteen Chilean parents and their…

This study demonstrates an existence proof for "productive failure": engaging students in solving complex, ill-structured problems without the provision of support structures can be a productive exercise in failure. In a computer-supported collaborative learning setting, eleventh-grade science students were randomly assigned to one of…