Teachers' noticing of students' mathematical thinking plays an important role in supporting student learning. Yet little is known about how online professional development (PD)--a growing setting for PD in the USA--can cultivate this noticing. Here, we explore the potential of using two online tools for engaging video to support K-2 teachers'…

One characteristic of high-quality mathematics teaching is supporting students in engaging in tasks of high cognitive demand. In this paper, we explore relationships between two elementary teachers' efforts to integrate computational thinking (CT) practices--abstraction, debugging, and decomposition--into their mathematics instruction and their…

A 12-episode constructivist teaching experiment with two pairs of elementary preservice teachers was conducted to examine how they reason distributively and proportionally. Specifically, I studied how prospective teachers reason with ratios as multiplicative comparisons. Prospective teachers solved different problems in one specific context (Step…

Given that early career elementary teachers face pressure to plan pedagogy that provides equitable opportunities to learn mathematics for understanding, it is important to consider their mathematics lesson planning practices. This study uses interview data to compare the planning practices of four early career teachers (ECTs) who consistently…

In this study, hypothetical samples of students' work on a task involving pattern generalizations were used to examine the characteristics of the ways in which 154 elementary prospective teachers (PSTs) paid attention to students' work in mathematics. The analysis included what the PSTs attended to, their interpretations, and their suggestions for…

This study aims to explore teacher noticing differences of the sampled US and Chinese elementary teachers from cross-cultural mathematics videos. A total of 34 expert teachers commented on 25 video clips online. We coded what and how teachers noticed from the videos both quantitatively and qualitatively. Findings reveal teachers' strong interests…

In this paper, we analyse a grade 8 (age 13-14) Japanese problem-solving lesson involving angles associated with parallel lines, taught by a highly regarded, expert Japanese mathematics teacher. The focus of our observation was on how the teacher used carefully planned board work to support a rich and extensive plenary discussion (neriage) in…

The measures of mathematical knowledge for teaching developed at the University of Michigan in the U.S., have been adapted and used in studies measuring teacher knowledge in several countries around the world. In the adaptation, many of these studies relied on comparisons of item parameters and none of them considered a comparison of raw data. In…

Over the past decade, teaching mathematics ambitiously has received increased attention. In this paper, we argue that to materialize this vision in contemporary classes we need to understand how practicing teachers experiment with certain aspects of this teaching and what challenges they encounter. Toward this end, we focus on an aspect of…

This study focused on the practice of selecting student strategies for whole-class discussions with teachers working toward a vision of instruction that is responsive to students' mathematical thinking. Selecting strategies is one of the "5 practices" identified in Smith and Stein's (5 practices for orchestrating productive mathematics…

This qualitative survey study set out to investigate in-service and pre-service primary school teachers' perceived barriers to and enablers for the integration of children's literature in mathematics teaching and learning in an Australian educational context. While research over the past three decades have documented pedagogical benefits of…

This study is an examination of 79 elementary prospective teachers' (PSTs') capacity for recognizing the core ideas involved in modeling fraction addition problems and their difficulties in solving and presenting the process of fraction addition using area, length, and set models. PSTs completed a written task in which they represented the process…

When teaching fractions, teachers make instructional decisions about if, when, and how to use the many different types of fraction models and manipulatives. In this study, we sought insights into their pedagogical reasoning with fraction representations via their preferences, both for solving tasks themselves and for teaching (in general and for…

This study investigates the potential of rehearsal interjections to provide opportunities for novice teachers and teacher educators to discuss topics related to teaching the practice of mathematical defining. Through analysis of video recordings of seven elementary novice teachers' rehearsals about geometric definitions, we identified the problems…

Studies of facilitators of professional development (PD) for mathematics teachers have been increasing in order to improve their preparation for conducting PD. However, specifications of what facilitators should learn often lack a conceptualization that captures facilitators' expertise for different PD content. In this article, we provide a…