Background: Current efforts to promote reasoning, problem solving, and discussion are often framed as advancing equity, but scholarship suggests individual students' opportunities to learn can vary considerably in classrooms that attempt to take up these approaches to teaching mathematics. Noticing students' mathematical strengths and positioning…

Educators, researchers, and policy makers recognize that student participation in classroom mathematics conversations, especially explaining one's own thinking and engaging with others' ideas, can promote students' mathematics learning. However, precisely "how" participating in these ways supports learning has not often been examined in…

Understanding how learning environments productively mobilize children's ideas as resources for participation in joint activity is an ongoing focus of research on classroom instruction. We investigated whole-class mathematics conversations in which multiple students participated in ways previous research suggests are consequential for learning. We…

Compelling research evidence shows benefits for student learning from explaining one's ideas and engaging with the ideas of others. However, whether certain patterns of group interaction may engender this productive student participation is unknown. Using data from two third grade mathematics classrooms, and over the course of six days during a…

Eliciting, responding to, and advancing students' mathematical thinking all lie at the heart of great teaching. In this article, the authors describe a formative assessment approach that teachers can use to learn more about their students' mathematical thinking and inform their instructional decisions. This assessment approach draws on a widely…

Sociocultural perspectives on learning highlight varied conceptions of what it means to know and do mathematics, and in turn what it means to be mathematically competent. This work presents a dynamic conceptualization of competence--what counts as competent mathematical activity is negotiated and constructed within learning environments, and…

Educators, researchers, and policy makers increasingly recognize that participation in classroom mathematics discussions, especially engaging with others' ideas, can promote students' mathematics understanding. How teachers can promote students' high-level engagement with others' ideas, and the challenges teachers face when trying to do so, have…

Engaging students as active participants in mathematics classroom discussions has great potential to promote student learning. Less well understood is how teachers can promote beneficial student participation, and how teacher-student interaction relates to student achievement. This study examined how the kinds of teacher practices that may…

Cognitively Guided Instruction (CGI) researchers have found that while teachers readily ask initial questions to elicit students' mathematical thinking, they struggle with how to follow up on student ideas. This study examines the classrooms of three teachers who had engaged in algebraic reasoning CGI professional development. We detail teachers'…

A yearlong experimental study showed positive effects of a professional development project that involved 19 urban elementary schools, 180 teachers, and 3735 students from one of the lowest performing school districts in California. Algebraic reasoning as generalized arithmetic and the study of relations was used as the centerpiece for work with…

Investigated changes over four years for three elementary teachers participating in Cognitively Guided Instruction (CGI), which emphasized students' mathematical thinking and supported teachers through workshops, mentoring, and collaboration. Interviews and observations indicated that CGI allowed teachers to engage in ongoing practical inquiry…

Investigated gender differences in problem-solving and computational strategies used by 44 boys and 38 girls as they progressed from grades 1 to 3. Found no gender differences in solving number fact, addition/subtraction, or nonroutine problems but strong gender differences in strategies used to solve problems. Discusses the use of invented…

Considers implications of the findings of the study by E. Fennema and others that boys in the primary grades use different mathematics problem-solving strategies than girls and suggests that equitable mathematics instruction may require specific attention to gender differences and underachieving groups. (SLD)