We contribute to the understanding of teacher noticing by focusing on what a teacher may notice in students' mathematical contributions in the context of problem-based lessons. Complementing approaches to research on noticing that focus on individual teachers' perceptual, cognitive, or situated skills, this conceptual article offers four…

The aim of this paper is to discuss preservice mathematics teachers' in-the-moment noticing of mathematical opportunities and how they reflected on those opportunities both orally and in writing. A faculty-school collaboration program was set up to enable preservice teachers to work with students in a school setting throughout a year. Ten…

In this article, the authors share two examples of student engagement in visible, mathematical thinking through a Chalk Talk within the four walls of the classroom, as well as the connected spaces of online learning. Five steps for facilitating the Chalk Talk are outlined, with descriptions of teacher moves for each step. The silent thinking…

New Visions for Public Schools is in the third year of supporting a network of 18 New York City public schools to address uneven student success in Algebra 1. One of the ways New Visions is helping schools achieve greater equity in algebra is by supporting them to use a shared curriculum. But how is it known if the shared curriculum is making a…

An important step to achieving a sustainable department culture that encourages innovation in teaching is the alleviation of the isolation that teaching faculty experience. Decreasing this isolation should be accomplished in a manner that respects all instructors' classroom practices while simultaneously exposing faculty to new ideas. In this…

Observing teaching with a practiced, professional eye can yield valuable insights into the specific learning opportunities that students are (or are not) provided. However, recent policy initiatives have emphasized using formulaic rubrics and checklists to rate teacher behaviors and evaluate their use of particular instructional moves. Rather than…

This paper discusses the challenges and lessons learned from conducting observations to measure the quality of classroom practice for a large-scale study of elementary teachers' mathematics instruction. Specifically, this paper shares our process for obtaining valid data for quality of elementary mathematics instruction; what we learned can inform…

Two groups of mathematics faculty, one from a four-year college and one from a two-year college, redesigned their respective introductory college mathematics courses following presentation of observational data regarding how faculty had been teaching the courses. This presentation emphasised how infrequently faculty teaching introductory college…

Implicit bias is an issue that all instructors must face in their classrooms; this article describes an academic development method to help instructors address it. The method centres on EQUIP (https://www.equip.ninja), a free, web-based application for performing classroom observations that provides data disaggregated by social markers.…

Equity in mathematics classroom discourse is a pressing concern, but analyzing issues of equity using observational tools remains a challenge. In this article, we propose equity analytics as a quantitative approach to analyzing aspects of equity and inequity in classrooms. We introduce a classroom observation tool that focuses on relatively…

The desire to understand our questioning practices as relational led us to use collaborative self-study to construct images of our questioning practice within our mathematics teacher education practices. In a prior exploration of written feedback we had begun to consider how our practices supported relationships with preservice teachers. As a…

Surface area and volume computations are the most common applications of integration in calculus books. When computing the surface area of a solid of revolution, students are usually told to use the frustum method instead of the disc method; however, a rigorous explanation is rarely provided. In this note, we provide one by using geometric…

In "Principles to Actions: Ensuring Mathematical Success for All," NCTM (2014) defines productive struggle as students delving "more deeply into understanding the mathematical structure of problems and relationships among mathematical ideas, instead of simply seeking correct solutions" (p. 48). Hiebert and Grouws (2007, p. 387)…

In this paper we discuss our development and use of a conjecture map for a large research project on the design and implementation of an online professional development model. Following Sandoval's (2014) model, we built the conjecture map to reflect our high-level conjectures (overarching goals of the project), the embodiment of the learning…

Mathematics education has benefited from qualitative methodological approaches over the past 40 years across diverse topics. Although the number, type, and quality of qualitative research studies in mathematics education has changed, little is known about how a collective body of qualitative research findings contributes to our understanding of a…