Effective mathematics teaching practices include not only probing student thinking and selecting student strategies to share but also facilitating discourse and encouraging reflection about important mathematical ideas (National Council of Teachers of Mathematics [NCTM], 2014, pp. 36-37). Encouraging students to use precise academic vocabulary to…

In this article, the authors share their favorite "Construct It!" activity, which focuses on rate of change and functions. The initial approach to instruction was procedural in nature and focused on making use of formulas. Specifically, after modeling how to find the slope of the line given two points and use it to solve for the…

In this article, the authors describe an algebra 2 class activity, called the Exponent Maze, that had students practice many mathematics problems, display their creativity, and work together collaboratively by creating their own mazes. The authors discuss how they introduced the activity, what the students created, and how creating mazes can be…

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.

Mathematical modeling tasks can engage students in ways in which they see themselves as mathematicians capable of using mathematics to solve real-world and complex problems. As mathematics teacher educators and researchers, the authors collaborated with two 5th-grade teachers, Liz and Anna (pseudonyms), focusing on equitable practices that foster…

Language is a conduit for communicating and understanding mathematical ideas. In this article, the authors describe how literacy relates to modes of reading, writing, speaking, and listening. They then share a strategy for supporting student literacy in mathematics--judicious telling--and provide examples of what this approach looks like in the…

Purposeful questioning is one of the most important elements to promote successful mathematics understanding (National Council of Teachers of Mathematics, 2014; Ontario Ministry of Education, 2011). Questioning helps teachers to elicit, interpret, and respond to student thinking (Stein et al., 2008) and supports students' understanding,…

Children are having fewer embodied social interactions outside (Haidt, 2024). Thus, there is a need to create embodied activities that turn students' attention to each other and nature (Barwell et al., 2022) and that build from their interests (Frankenstein & Powell, 2023). Using a socio-ecological framework that centers on relationships among…

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…

Making sense of algebraic expressions in context is multifaceted and extends beyond representing real-world situations using algebra. As part of Project MathTalk, the authors created videos that feature a pair of Grade 9 algebra 1 students coming to understand algebraic expressions in context. The students found three aspects of making sense of…

This article encourages promoting a sense of belonging in the field of mathematics for children of all backgrounds by using multicultural children's literature to teach the subject. Doing so challenges inequitable structures while also connecting learners authentically to the increasingly diverse world around them, empowering their…

Teachers' actions matter greatly in the mathematics classroom, but it is not always clear what guides their actions or from where they come. As teachers strive to create rich and engaging learning environments, how they capitalize on a particular moment is often unclear. Sometimes just identifying potential pathways to take can be challenging. In…

In this article, the authors share two examples of student engagement in visible, mathematical thinking through a Chalk Talk within the four walls of the classroom, as well as the connected spaces of online learning. Five steps for facilitating the Chalk Talk are outlined, with descriptions of teacher moves for each step. The silent thinking…

Mathematics learning requires student vulnerability because students are expected to persist in making sense of complex problems despite their uncertainty. For Black students specifically, societal and educational narratives about mathematics learning and participation may implicitly communicate messages to them that they do not belong. This…

The purpose of this article is to describe and illustrate learning trajectories (LTs) and introduce a new, comprehensive set of resources that support teaching meaningfully and joyfully. An LT for a topic has three parts: (1) a mathematical goal; (2) a developmental progression of levels of thinking; and (3) teaching practices (environments,…