This article explores the power of language to either include or exclude certain groups of students from genuine opportunities for mathematical sense-making. The substantial increase worldwide in the number of students learning mathematics through a language other than their primary language makes this a particularly urgent issue. This paper…

Understanding and analyzing data is a crucial aspect of quantitative literacy in the 21st century, leading scholars and policy makers to push for more rigorous instruction in this area rooted in statistical investigation. In this study, we examine 144 upper-elementary mathematics lessons on data and statistics topics to assess the extent to which…

Although teachers are expected to teach with technology, they often are not prepared or supported to do so (Albion, Tondeur, Forkosh-Baruch, & Peeraer, 2015), a critical issue in mathematics education (Wilson, 2008). The study described in this article investigated why and how secondary mathematics teachers implemented virtual manipulative…

This study examined parent-child math talk within three contexts (formal learning; guided play; unguided play) in order to identify characteristics of activities supporting high-quality math engagement. Seventy-two dyads of parents and 4- and 5-year-olds were observed using a set of toy foods; instructions and materials varied across conditions.…

In this paper, we pursue a materialist approach to tool use to account for the material dimensions of learning mathematics with technology while decentralizing the human body from activity. We root this vision in theoretical advances on embodied mathematics learning and tool use that have been recently offered as alternatives to traditional…

This study explored how approximating the practice of mathematicians by communally negotiating the standards for proof mediates middle grade students' abilities to collaboratively construct mathematical arguments. Forty-seven eighth-grade students engaged in an instructional sequence wherein they, along with the instructors, negotiated communal…

How can teachers encourage productive struggle in mathematics and yet minimize the exposure to shame often associated with struggle? In this article, the authors offer constructive ways to position struggle in the classroom to minimize shame and promote doers of mathematics.

A question that confronts teachers of mathematics is how best to establish in their classrooms a space where students can participate more fully in the curriculum. This article explores the development of agency in the school mathematics classroom. Using data from a variety of classroom contexts, this article employs sociocultural constructs of…

Mathematics teacher educators' (MTEs') written feedback is an instantiation of teaching practice and provides information to support the developing understanding of prospective teachers (PTs), yet no research has been undertaken to characterize such feedback. Research on feedback forms, including written feedback, has focused on information…

When designing an instructional tool and using it in pedagogical activities, it is essential that designers and users understand what pedagogical affordances and constraints the tool provides to support its successful integration into targeted pedagogical activities. Toward this end, we developed "Pedagogical Affordance Analysis (PAA)."…

Multiplication and division are vital topics in upper level elementary school. A teacher's pedagogical content knowledge (PCK) influences both instruction and students' learning. However, there is currently little research examining teachers' PCK within this domain, particularly regarding professional education of future teachers. To help address…

Much of the research on the development of professional noticing expertise has focused on prospective teachers. We contend that we must investigate practicing teachers as well, and in particular practicing secondary teachers, because they bring with them years of teaching experience and are situated in unique contexts. Hence we studied the…

Understanding and analyzing data is a crucial aspect of quantitative literacy in the 21st century, leading scholars and policy makers to push for more rigorous instruction in this area rooted in statistical investigation. In this study, we examine 144 upper-elementary mathematics lessons on data and statistics topics to assess the extent to which…

Now in its fourth edition--with more than 50 new questions and a new chapter on financial literacy--this bestselling resource helps experienced and novice teachers effectively and efficiently differentiate mathematics instruction in K-grade 8. Math education expert Marian Small shows teachers how to get started and become expert at using two…

This article provides information to educational leaders about how to address the challenge of supporting students who are emergent multilingual--i.e., those identified as English Learners (ELs) by their schools--in middle grades mathematics classes. The ideas in this article draw on research and collaborations with hundreds of teachers across the…