All students want to talk about ideas that interest them, but often, multilingual learners are not offered high-challenge, high-support opportunities to connect everyday experiences to mathematical ideas. We describe a single class period that connects students' everyday opinions with two-way tables and notions of independence.

Using teaching representations is one of the common means for preparing pre-service mathematics teachers (PSTs) to learn how to teach mathematics meaningfully. However, turning PSTs' attention to the mathematical objects that students engage with during the lesson is a challenging pursuit. This paper suggests using the Realization Tree Mediator…

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…

This paper aims to broaden the scope of the construct concept image by addressing the mathematically oriented notion of "solution of an algebraic equation." The notion solution of an algebraic equation is not mathematical per se, but it is most prevalent in mathematical communications and in mathematics education. The paper describes…

Mathematical concepts have been a consensus goal for decades, yet there is little consensus on what is meant by the terms "mathematical concept" and "mathematical understanding." This article attempts to discuss these terms in a way that can be of practical use to teachers. Greater clarity on "mathematical concept"…

In this paper, we introduce a new interpretive framework, which we call Bodymarking, to aid in describing and interpreting activity (e.g., individuals' gestures, gaze, and interaction with materials in the environment) in the classroom. We apply the framework to video recordings of mathematics lessons to explain how it can be used and offer some…

Over three decades ago, National Council of Teachers of Mathematics (NCTM, 1991) proposed that "for students to develop the ability to formulate problems, to explore, conjecture, and reason logically, to evaluate whether something makes sense, classroom discourse must be founded on mathematical evidence" (p. 34). As math interventionists…

Statistics has been a content domain in the mathematics curriculum for decades. However, statistics is a distinct discipline from mathematics and there are important differences in how one should teach the two disciplines. In this article, the authors consider how these differences can inform an adaptation to the 5 Practices for Orchestrating…

This article shares a paper presented as the keynote for the Terry L. Wood Memorial Conference that was held virtually on May 20, 2022. This paper starts with a reference to the project, The Coordination of a Psychological and Sociological Perspective, that was funded by the Spencer Foundation. The results of the research in this project are…

In this article, the authors describe the two interpretations of mathematical expressions, as a process and as a product. They begin with an initial discussion of Tall's (2013) interpretations of expressions and connect this to state standards. Next, they describe the different interpretations of algebraic expressions based on their work with…

This paper introduces a model built upon the Method of Varying Inquiry, offering a didactical approach to problem posing and solving activities that stimulates inquiry-based learning in mathematics classrooms. The model combines the inquiry-based framework with the variation theory and with specific didactical and theoretical elements (the…

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…

One way to emphasize students' strengths when reasoning verbally is through number talks. During a number talk, a teacher facilitates a 5- to 15-minute conversation during which students have the opportunity to engage in mental mathematics and verbally explain and justify their reasoning regarding how they make sense of numerical computations.…

The COVID-19 pandemic has affected student learning; according to the National Assessment of Educational Progress (2022), scores for students in the United States have shown a decline in mathematics. . One way educators can strengthen students' current mathematical knowledge and bridge to new content is through Number Talks. Number Talks are brief…

What is a teacher to do when students share an idea with underlying mathematics that is different from that of the student contribution being discussed? Could such situations be avoided to begin with? In this article, the authors share strategies that can help teachers better keep the mathematics related to the student contribution under…