Email filters classify new messages as either spam or not spam based on word frequency, syntax, and metadata. A "classifier" is an algorithm that maps input data into categories based on distinguishing characteristics, or "features." Features can be raw data or attributes derived from that data. "Feature engineering"…

Baseball. Subway line. Maps. A flower. Each of these contexts involves some form of varying motion or constant change over time: the bi-directional motion of a fly ball, the speed of a subway car, or the growth of a flower until bloom. This article does not highlight students' calculus problem-solving abilities, but rather describes a set of…

How can elementary students use Google Slides to enhance their math problem-solving skills and creativity? Usable Math offers slideshows that pose a problem, provide hints, and ultimately reveal a solution. The intent of these slideshows is to provide extended opportunities to understand and practice mathematics skills. In this fourth-grade…

A sense of belonging in mathematics--feeling accepted and valued in the field (Good et al., 2012)--is a powerful predictor of student success. However, many students, particularly those from marginalized backgrounds, often lack this feeling as a result of limited representation in curricula and school cultures (Barbieri & Miller-Cotto, 2021).…

Social media artifacts, such as memes, offer a rich opportunity to amplify and explore mathematical discourse in a new way that is responsive to this generation of students. This article summarizes a list of activities developed by the Math Meme Team, a group of interdisciplinary educators and researchers that aims to not only analyze and…

The Cell Phone modeling task centers on a Fermi real-world estimation question. The task and rubric can be used at different grade levels to focus on the modeling process and classroom community. Finding time and space to engage students, especially novice modelers, in mathematical modeling can be a challenge, yet the benefits of modeling are…

In this article, the authors focus on using board work to scaffold what they call "joint sense making," because effective mathematics instruction is, at its heart, characterized by teachers and students engaging collaboratively in making sense of mathematical ideas (National Council of Teachers of Mathematics, 2009, 2014). This sense…

Understanding negative numbers can be challenging for many students, as these concepts may seem less tangible than counting objects, which are commonly represented by positive numbers. In addition, the multiplication of two negative numbers resulting in a positive might appear inconsistent and puzzling to young learners who are used to seeing the…

Every educator knows the sinking feeling of a lesson gone wrong. As teachers look around the room and realize that many of their students are just not getting it, they often feel like failures. However, the struggle students experience as they persevere through high-quality challenging tasks is not a sign of failure, but rather a key aspect of…

Digital curricula can constrain teachers with ready-made instructional materials. The authors used Mathematics Teaching Practices (MTPs) to modify a digital curriculum to engage students in more thoughtful and meaningful lessons. In this article, the authors visit one of their third-grade classrooms, in which they used the prescriptive digital…

Representing and recording student thinking in public spaces during mathematics discussions is challenging work. In this article, the authors articulate why skillfully recording and representing during discussions matters. The authors share principles for recording student thinking in the moment and share an activity structure to use with…

In this article, the author presents a short teaching sequence to show how to introduce young students in grades 3 (ages 8-9) and 4 (ages 9-10) to using digital tools for exploring larger and multivariate data sets. The teacher guided the young students from creating bar graphs in small data sets on embodied cognition and enactive levels to…

If the goal is to move beyond the shape of the graph to consider the dynamic aspects of functions, students need to explore dynamic representations of functions. To address this, the authors combined the use of a dynamic representation of function with the instructional routine, Which One Doesn't Belong? [WODB]. In this article, they briefly…

Generalizing, conjecturing, representing, justifying, and refuting are integral parts of algebraic thinking and mathematical thinking in general (Lannin et al., 2011). The activity described in this article makes a case for generalizing as an overall mindset for any introductory algebra or geometry class by illustrating how generalization problems…

This article describes how to build a classroom community by building representations and visualizations of data related to students' names. The goal of this task was to allow students to get to know each other's identities better by collecting and analyzing data about their names and exploring the connection between names and identities. The task…