Research on teachers' noticing of student mathematical thinking has typically focused on how a teacher attends to, interprets, and determines a response to an individual student contribution in isolation from the broader mathematical classroom context. This research focus is not nuanced enough, however, to fully account for the complex noticing…

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.

Facilitating whole-class discussions based on tasks that support inquiry and provide conceptual learning opportunities has been identified as a central, challenging task of teaching. We drew upon practice-based and interactionist research traditions to decompose how eight experienced Grades 5-7 mathematics teachers facilitated whole-class…

This study explores secondary-school mathematics teachers' noticing of Critical Events Associated with Argumentation (CEAs), moments when students' reasoning or interactions become evident, offering teachers opportunities to promote argumentation in the classroom. Thirty-one teachers analyzed a written classroom scenario, identifying CEAs,…

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…

Interest in teachers' moves to classroom discourse has started to increase since how teachers respond to students' thinking influences students' learning. The purpose of this study was to investigate the moves used by one sixth grade mathematics teacher at a public middle school in Turkey to support student reasoning in mathematics instruction and…

This paper reports findings related to the pursuit of describing a lived knowing for teaching mathematics. Specifically, we used an enactivist perspective to describe the knowing exhibited by three experienced high school teachers in their instructional actions while leading whole-class instruction on the topic of the equations of exponential…

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"…

Our study explores teaching practices that aim to promote students' learning to define an analytical object. A Calculus II instructor conducted a teaching experiment (TE) in which 11 students reinvented a formal definition of a limit over five class periods with the instructor's guidance. During the TE, the instructor's teaching practices were…

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…

The research on mathematical argumentation has mainly adopted a dialectic lens which focuses on understanding the abstract and logical development of reasoning in argumentation. However, this approach may have overlooked other key aspects of mathematical argumentation, including the unfolding of the meaning-making experience and process during…

This study addresses the need to better describe instructional strategies used by middle grades mathematics teachers. After coding 177 videos of grades 6-8 mathematics instruction for indications of effective instructional practices, we further analyzed 8 of the highly scored videos with specific attention to teachers' implementation of strategies…

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…