Instructors manage several tensions as they engage students in defining, conjecturing, and proving, including building on students' contributions while maintaining the integrity of certain mathematical norms. This paper presents a case study of a teacher-researcher who was particularly skilled in balancing these tensions in a laboratory setting.…

In this theoretical paper, we respond to a call for all Mathematics Education researchers to become equity researchers (Aguirre et al., 2017) by articulating how equity is foundational to making second-order models of students' mathematics. First, based on prior research, we view equity to be about power and respect. We define an act of equity as…

With a focus on the US, I briefly review the literature to examine current trends, and outline a typology of what is meant by educational research for teaching by, with and for teachers, followed by a discussion of why it is important for educators to engage in and commit to such research. The key question in this article is what kinds of research…

With this article, we aim to spur a conversation on research implementation in the context of collaborations of mathematics teachers and educational researchers, with a special interest in projects situated in university mathematics education. Implementation has been often discussed in relation to the education of school teachers, and we suggest…

The addressed question from the interface between theory and teaching practice of constructivism is discussed at the background of whereabouts of the Common Core (CCSS-M) constructivist-based mathematics curriculum. It concerns the formulation of constructivist methodology of teaching, whose existence is called in doubts by US constructivist…

Two broad categories of instructional practices, (a) explicitly attending to concepts and (b) fostering students' opportunities to struggle, have been consistently linked to improving students' mathematical learning and achievement. In this article, we describe an effort to build these practices into a framework that is useful for a diverse set of…

The NCTM Research Committee identifies key influences on mathematics education that are largely outside the domain of the academic world in which most mathematics education researchers live. The groups that are identified--including the media, companies and foundations, and other academic domains--affect the public's perception of mathematics and…

In this paper, we explore the ways in which learning more about research on students' experiences in mathematics classrooms has the potential to transform the work we do with teachers in teacher preparation, professional development, and research settings. We focus in particular on questions of student access to and participation in mathematics…

As the Better Math Teaching Network (BMTN) matured, different strategies for sharing network learning emerged. These strategies became more formalized and intentional as BMTN members developed tools and routines to spread the learning. Our multi-year evaluation sought to understand the affordances and constraints of each strategy. In the sections…

A problem identified in the literature around task design is the persistence of a gap between teacher intention and student activity. We show how principles designed around the making of distinctions and having an explicit language of mathematical thinking can eliminate the "gap" by guiding teacher planning, teacher actions in the…

This paper reports on the use of a reflective technique that incorporated video-stimulated recall to encourage reflection on practice. The author videotaped a series of mathematics lessons conducted by an experienced teacher, which were then collaboratively viewed and discussed, with the aim being to bring about changes in the teacher's practice.…

Mathematics teachers face a myriad of instructional obstacles. Since the early 1990s, mathematics education researchers have proposed the use of constructivist practices to counteract these ever-prevalent obstacles. While we do give credit to the choices of instructional activities the constructivist paradigm promotes, there are problems with its…

O'Connor and Penuel (2010) argue that viewing research in education as a human science requires explicit attention to social, cultural, historical, and institutional dimensions of human activity, to the agency of participants in learning research, and to the importance of incorporating "emic" perspectives that shift the voice of the…

This study compared no-no prompting procedures to simultaneous prompting procedures for 3 children with autism. Using a parallel treatments design, researchers taught rote math skills, receptive labels, or answers to "wh-" questions with both prompting systems. Results indicated that no-no prompting was effective in teaching all skills. By…

Through analyses of three dissertations completed by graduates of our Carnegie Project for the Education Doctorate-influenced program, this article offers insights into both the doctoral students' inquiries into their problems of practice and their faculty advisors' roles and expectations for them. Studying student dissertations provided the…