Informed by a constructivist-based, student-adaptive pedagogical approach, this study explores the benefits of teacher-learner discourse moves for the mathematics learning of students with learning disabilities (LD). During a constructivist teaching experiment for nurturing the multiplicative reasoning and problem solving of five third-grade…

Learning analysts often consider whether learning processes across time are related (1) to one another or (2) to learning outcomes at higher levels. For example, are a group's temporal sequences of talk (e.g., correct evaluation [right arrow] correct, new idea) during its problem solving related to its group solution? I show how to address these…

We explore development of elementary preservice teachers' reflective practices as they solved problems encountered while teaching in a reading clinic. Written reflections (N = 175) were collected across 8 weeks from 23 preservice teachers and analyzed to investigate relationships among problem exploration, teaching adaptations, and problem…

This paper conceptualizes spatial literacy as consisting of three overlapping domains: visualization, reasoning, and communication. By considering these domains, this study explores different aspects of spatial literacy to better understand how a group of mathematics teachers reasoned about spatial tasks. Seventy-five preservice and inservice…

Given international use of video-based reflective discussions in teacher education, and the limited knowledge about whether teachers apply learning from these discussions, we explored teachers' learning of new ideas about pedagogy and their self-reported application of this learning. Nine inservice and 48 preservice teachers participated in…

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…

The micro-time context of group processes (such as argumentation) can affect a group's micro-creativity (new ideas). Eighty high school students worked in groups of four on an algebra problem. Groups with higher mathematics grades showed greater micro-creativity, and both were linked to better problem solving outcomes. Dynamic multilevel analyses…

Sixteen middle school students ranked the lengths of various paths in problem-solving interviews. Every student invoked at least one of four intuitions that originated from their everyday experiences: compression, detour, complexity, and straightness. Students continued to use their inadequate intuitions in the posttest before applying learned…

Rudeness and status can affect group-problem-solving processes. A new statistical method for analyzing group processes was used to analyze predictors of agreement and solution score. In successful groups, agreement was affected positively by academic status and negatively by justifications. In unsuccessful groups, however, agreement was affected…

This study tested a model of teacher interventions (TIs) conducted during cooperative learning to examine how they affected students' subsequent time on-task (TOT) and problem solving. TIs involved groups of ninth-grade students working on an algebra problem; videotaped lessons were transcribed and analyzed. Results showed that teachers initiated…

Metaphorical reasoning explains how people can interpret abstract representations through a complex activity and then apply them to new problems. In particular, metaphors can facilitate both conceptual understanding and problem solving by: (1) intuitively justifying mathematical operations, (2) integrating mathematical knowledge, (3) enhancing the…

Discusses group problem solving processes, how status can harm group problem solving, and how the politeness of students' criticisms reflects status. Reports on analyses of the determinants of group solutions, perceived leadership, and biased evaluations during collaborative problem solving in which students attempted to solve an algebra problem.…

Differences among students can yield rich benefits as well as pose difficult problems during collaborative learning. Students can draw on diverse individual experiences to exchange information, to understand different expressions of shared commonalities, and to construct new possibilities jointly. However, they also face the potential pitfalls of…

This study investigated how different components of teacher/teaching assistant interventions improved or reduced student motivation. The study was part of a larger project in which ethnically diverse students were videotaped during their 5 algebra classes for 6 weeks in their urban public high school. A total of 40 students (10 groups of 4) from 5…

Eighty ninth graders who solved an algebra problem in groups of four showed status effects at the individual level. The students had filled out preactivity questionnaires about mathematical status and social status and a postactivity leadership questionnaire. Hierarchical regressions and path analyses show that, at the group level, solution score…