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…

Research commonly finds that urban teachers bring deficit views about students of color with them into classrooms, and professional development efforts focused on this critical problem have been met with limited success. Therefore, scholars have called for work that integrates content and equity as a way to challenge teachers' deficit views at the…

The students in Ms. Moscoso's second-grade class gather on the rug after recess, ready for one of their favorite math warm-ups: Choral Counting. Counting is an important part of doing mathematics throughout the school; students count collections (Schwerdtfeger and Chan 2007) and solve problems using a variety of strategies, many of which are…

In-depth analyses of six elementary mathematics classrooms (with varying student achievement) captured student and teacher interactions and documented the critical role of teacher follow-up in shaping opportunities for low-income students of color to engage in algebraic reasoning. This paper details the efforts of teachers as they, contrary to…

This case study of a third grade classroom details the ways that competence was jointly constructed by students and the teacher in relation to students' efforts to engage with each other's mathematical ideas. By creating consistent opportunities for students to share and make sense of others' ideas, and by supporting students to take up these…

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…

We analyze a particular pedagogy for learning to interact productively with students and subject matter, which we call “rehearsal.” Our goal is to specify a way in which teacher educators (TEs) and novice teachers (NTs) can interact around teaching that is both embedded in practice and amenable to analysis. We address two main research questions:…

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'…

It is commonly argued that teachers need ongoing engagement with ideas about using student reasoning, pedagogy, and subject matter if they are to make sense of the complex demands of current reforms in mathematics education. Drawing on similar arguments about the potential benefits of using student work to organize professional development, this…

The importance of student talk in mathematics classrooms figures prominently in curriculum and teaching standards. Student talk is a vehicle for increasing student learning and for helping teachers monitor student understanding and inform student instructional practices. Although researchers have begun to study the moves teachers may make to…

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…