This article investigates why students reported liking a student-driven learning design better than a highly guided design despite equivalent gains in knowledge assessments in both conditions. We created two learning designs based on the distinction in the literature between student-driven and teacher-led approaches. One teacher assigned each of…

The struggle with fraction learning in kindergarten through Grade 12 in the United States is a persistent problem and one of the major stumbling blocks to succeeding in higher mathematics. Research into this problem has identified several areas where students commonly struggle with fractions. While there are many theories of fraction learning,…

This article reports on an ethnographic study of a 10-year-old's pursuit of school-based mathematics across school and home to suggest that participating in school-based mathematics is a cross-setting phenomenon in at least 2 ways. First, I illustrate how accomplishing school-based mathematics literally extends into the home and how individuals…

This study examines the nature of teacher participation in the context of a video club. Video clubs are professional development meetings in which teachers watch and discuss excerpts of video from their classrooms. In this study, I adopt a situative perspective to examine how teachers develop in their participation to accomplish the goals of the…

This article extends and strengthens the knowledge in pieces perspective (diSessa, 1988, 1993) by applying core components to analyze how 5th-grade students with computational knowledge of whole-number multiplication and connections between multiplication and discrete arrays constructed understandings of area and ways of using representations to…