Professional noticing of children's mathematical thinking (Jacobs et al. in J Res Math Educ 41(2):169-202, 2010) is a construct that is used frequently to understand the ways in which teachers attend to, interpret, and respond to children's mathematical thinking. In this paper, we present our analysis of prospective elementary mathematics…

Regular contributors James and Toby Russo return with a sixth principle for educationally-rich mathematical games--almost all mathematical games have the potential to be transformed into an investigation. This article builds on their earlier piece with Leicha A Bragg (APMC 23(3), 30-34). [For "Five Principles of Educationally Rich…

Whole-class discussion of open mathematics tasks is an instructional practice K-12 mathematics educators report has the potential to engage all learners. Because this practice has not been extensively and systematically researched, this study aims to describe and analyze the engagement and experience of learners in open mathematics tasks. Drawing…

This study examines how elementary preservice teachers notice children's mathematical thinking and how this noticing influences the evaluation of technological resources. In particular, we explore the aspects of thinking to which preservice teachers attend and how they interpret evidence about children's thinking when using the Spatial-Temporal…

In classrooms, students engage in argumentation through justifying and generalizing. However, these activities can be difficult for teachers to conceptualize and therefore promote in their classrooms. In this article, we present the Student Discourse Observation Tool (SDOT) developed to support teachers in noticing and promoting student justifying…

This workbook is a companion to the "Community Math Night Facilitators' Toolkit. REL 2022-120" (ED615952), a comprehensive resource for elementary school educators to plan and implement a Community Math Night. A Community Math Night brings together educators, students, and their families to: (1) learn about, talk about, and have fun with…

Mathematics discourse is a teaching approach that encourages student discussion and reveals an understanding of concepts as students engage in mathematical reasoning and debate (Cobb 2006). Grabowski and Ke (2007) posit that students have significantly higher achievement and positive attitudes toward mathematics after participating in gaming…

In this paper we present a professional development course designed to impact on teachers' mathematical knowledge for teaching fractions. The main features of the course are the use of i) problem solving activities related with mathematical knowledge for teaching fractions ii) peer discussions and iii) monitor's interventions focused on answering…

This study examines how collective activity related to multiplication evolved over several class sessions in an elementary mathematics content course that was designed to foster prospective elementary teachers' number-sense development. We document how the class drew on as-if-shared ideas to make sense of multidigit multiplication in terms of…

In this article we explore young children's development of mathematical knowledge and reasoning processes as they worked two modelling problems (the "Butter Beans Problem" and the "Airplane Problem"). The problems involve authentic situations that need to be interpreted and described in mathematical ways. Both problems include tables of data,…