The number line has been proposed as a central construct used by students to solve a range of mathematics problems. Given the capacity of number lines to represent all real numbers and to be used in a variety of contexts, there have been calls to increase the use of number lines in mathematics instruction. However, due to the recency of these…

In this article, the authors share one approach to Number Talks that may help more students participate, increase access to and learning of mathematics, and provide some variation in routines. Number Talks are commonplace in the elementary mathematics classroom, thanks to Parker and Humphreys (e.g., 2018) and Parrish (e.g., 2011). They are a…

Visuospatial representations of numbers and their relationships are widely used in mathematics education. These include drawn images, models constructed with concrete manipulatives, enactive/embodied forms, computer graphics, and more. This paper addresses the analytical limitations and ethical implications of methodologies that use broad…

Mathematics Anxiety (MA) is an increasing challenge for mathematics educators and is a barrier to mathematical learning. Through reflection on the implementation of a lesson sequence designed to elicit regular use of explicit metacognitive questions (EMQ's), this paper explores the impact of the incorporation of self-regulated learning (SRL)…

In this article, the authors provide some insight into how teachers can potentially facilitate among students' representations and activities on mathematical tasks: between or among -- (1) student representations and the context; (2) multiple forms of student representations; and (3) processes in student representations. The authors use the…

Mathematical modeling and applications are an important part of curriculum and considered to be important for students' current and future lives. In this contribution, we focus on mathematical modeling from a cognitive prospective. Following embedding the cognitive perspective within the discourse of mathematical modeling, we describe some of the…

The purpose of this study was to identify and categorize in-the-moment teaching moves which support productive general social norms and sociomathematical norms during dialogic instruction by drawing on transcripts of classroom episodes. To understand how teachers construct in-the-moment teaching moves, this paper is grounded in a revised version…

We believe that developing cultural competencies can help students learn mathematics and conversely that learning mathematical content can help students learn about themselves and others. Using frameworks introduced by Rendón (2009) and Gutiérrez (2018), we present a five-part bundle of activities for undergraduate differential equations course…

In the area of early literacy, the children learned new vocabulary to describe the attributes of triangles and shapes. Through math talk and class discussions, the children also learned about listening to others, turn taking, and voicing their ideas. Although the children described in this article were generally competent in the English language…

The purpose of this article is to demonstrate how students' mathematics identities were developed and how their agency was fostered through the use of a mathematical action technology (MAT), Desmo, during stages of learning beyond noticing and wondering. The authors describe how they enacted an eighth-grade mathematics lesson depicting students…

Early intervention and identity-building can promote the idea among students that everyone is a math person. Natalie Parker-Holliman and Tenisha Marcel-Herbert share practical tools and strategies that schools and teachers can use to build students' confidence and strengthen their mathematical foundation. They highlight the significance of culture…

Reading mathematics problems can frustrate students to the point of shutting down. Although Pólya's four-step plan is a well-known problem-solving framework, the author's students benefited from a more concrete and detailed approach: chunking the reading. In this article, the author describes an approach to problem solving used with eighth-grade…

Many mathematics students require support for learning challenges, such as those invoked by mathematics anxiety. Support for these learning challenges is imparted through personal interactions between the student and the instructor, support staff or their peers. The online delivery of mathematics classes and support meetings reduced the quality of…

The beginning of the school year is a time of intense work for students and teachers, especially if it means learning mathematics in new ways (Ruef 2016). Students need guidance and support if they are shifting beliefs about what it means to do mathematics. This article shows how Torres and her students co-created new ways to be good at…

It is widely acknowledged that communicating mathematical thinking is complex, difficult, and often messy. In this article, the authors explore how mathematical thinking is communicated, providing examples of strategies for teachers and students to use in the mathematics classroom.