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…

Background: This study considers the moment-bymoment mathematics discourse of teachers and students and the relationship of these discourses to student learning. I focus on the discursive constructs of responsiveness to students' mathematical thinking and the intellectual work in teacher and student discourse. Responsiveness to students'…

The current study examined the effectiveness of self-explanation prompts, visual signaling cues, and a combination of the two features on middle school students' (N = 202) algebra learning. Also explored were the differential effects of features for students with faulty conceptual knowledge (evidenced by a higher prevalence of making errors during…

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…

This article explores an alternative strategy for designing hybrid instructional environments. Rather than bridging home or community funds of knowledge with school learning, I propose designing disruptions to typical school practices to invite students to recruit out-of-school resources meaningful and sensible to them in order to grapple with…

This article investigates the coconstruction of student identity and engagement in the case of a 9th grader in a project-based algebra classroom that afforded students a great deal of autonomy. The focal student, Terrance, utilized classroom resources to serve both project-related and social functions as he interacted with his peers during…

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…