Background: Groupwork is a desirable activity in mathematics classrooms for the opportunity it creates for collaborative reasoning and interdependence. Correlations between group-level processes and outcomes have helped characterize the features of more successful groups, but group-level constructs can obscure how students negotiate ideas. This…

Most research on mathematical play and learning is focused on early childhood. This study examines how mathematical play and learning manifest in older children in a mathematical videogame designed by the first author, "Rolly's Adventure." We examined how players experienced mathematical play as they played "Rolly's Adventure,"…

This study uses a new communicational lens that conceptualizes the activity of learning mathematics as interplay between mathematizing and identifying in order to study how the emotional, social, and cognitive aspects of learning mathematics interact with one another. The proposed framework is used to analyze the case of Idit, a girl who started…

Increasingly, instructional improvement efforts include teacher communities as part of their overall strategy, yet the relationship between teachers' talk and professional learning remains underspecified. Using a discourse perspective on learning, this article compares opportunities to learn (OTLs) in the collaborative conversations of 3…

This article investigates how affluent students made sense of social justice issues that were embedded in mathematics learning activities. I present 2 case studies of such activities at the intermediate and secondary levels in 2 different schools. The analysis draws on video records and classroom artifacts and applies the theoretical framework of…

In this article we contribute a perspective on mathematical embodied cognition consistent with a phenomenological understanding of perception and body motion. It is based on the analysis of 4 selected episodes in 1 session of an undergraduate mathematics class. The theme of this particular class session was the geometric interpretation of the…

Many studies have tested external supports for promoting productive collaboration, but relatively few have examined what features characterize naturally productive collaborative tasks. Two lines of research have come to distinct conclusions on the primary task feature associated with productive collaboration: demonstrability versus complexity.…

In a study with ninth-grade mathematics students on learning the concept of variance, students experienced either direct instruction (DI) or productive failure (PF), wherein they were first asked to generate a quantitative index for variance without any guidance before receiving DI on the concept. Whereas DI students relied only on the canonical…

This paper replicates and extends my earlier work on productive failure in mathematical problem solving (Kapur, doi:10.1007/s11251-009-9093-x, 2009). One hundred and nine, seventh-grade mathematics students taught by the same teacher from a Singapore school experienced one of three learning designs: (a) traditional lecture and practice (LP), (b)…