When thinking about digital equity, often what comes to mind are issues of access to digital technologies. Although that is a divide that must be conquered, once students have access to digital technologies, the next step is to ensure that they wield these technologies in such ways that they help to address the existing inequities in mathematics…

Helping students reach a clear understanding of the cause-and-effect relationship between changes in parameter and the graph of an equation is the focus of the activity outlined in this article. The behavior of phase shifts has been regarded as counterintuitive for many people, and often, because of this, conflict between student intuition and…

This article examines a common proportional reasoning problem used in schools, often referred to as the Orange Juice task. The authors show how these six strategies described by Nikula (e.g., Unitizing, Norming, etc.) and one additional strategy can be used to either solve or make progress in the Orange Juice task. The article presents work from…

Eliciting and using student thinking (NCTM 2014) is a foundational pedagogical skill that informs the decisions teachers make during instruction. It informs the questions teachers pose, the focus of small-group and whole-class discussions, and even the small adjustments teachers make during a well-planned lesson. To use student thinking to…

The goal of this article is to give examples of high school students exploring parameters of quadratic functions using different tools as a catalyst to discuss the pros and cons and demonstrate the mathematical power of each. The authors illustrate how teachers' learning goals should navigate them toward a productive option.

Aside from being culturally relevant, artificial intelligence is also supporting companies in making business decisions. Consequently, "workforce needs have shifted rapidly," resulting in a demand for applicants who are skilled in "data, analytics, machine learning, and artificial intelligence" (Miller and Hughes 2017). This…

When discussing mobile learning (or M-Learning), many educators tend to focus on the affordances of the technology. In this article, the authors feature the M-Learning Framework as a way to view the effective use of mobile devices. The framework includes three key features: (1) authenticity; (2) personalization; and (3) collaboration. These…

The contexts of the problems educators choose can affect students' mathematical identities by affecting their abilities to relate to the mathematics (Middleton, Jansen, and Goldin 2017). Moreover, these choices send powerful messages to students about the relevancy of mathematics to their own lives (Felton 2010). Eliciting and drawing on student…

Valid proofs need not be in the traditional two-column format. This classroom activity allows students to explore, discuss, and use specialized facts to create a general statement of truth.

The use of digital technologies (calculators, computers, simulations, etc.) is recommended for teaching and learning mathematics (NCTM 2000; NGA Center and CCSSO 2010). Given these recommendations, technology has been increasingly integrated into the mathematics classroom for decades. The authors began asking themselves about the nature of…

Perceptually rich concrete manipulatives benefit mathematics learning. Because students should be challenged to consider connections between two-dimensional (2D) and three-dimensional (3D) perspectives of conics (NCTM 2000), this article describes hands-on teaching techniques that promote this type of student reasoning. This article aims to (1)…

As 2020 draws to a close, so does this first volume of Mathematics Teacher: "Learning and Teaching PK-12" ("MTLT"). Ascribing to a digital-first philosophy, the articles comprising this first volume included digital assets such as classroom videos, author introductions, and digital applications (e.g., Desmos apps) and addressed…

Two of the Standards for Mathematical Practice (SMP) in the Common Core State Standards for Mathematics (CCSSM; NGA Center and CCSSO 2010), "Look for and use structure" (SMP 7) and "Look for and express regularity in repeated reasoning" (SMP 8), are particularly abstract and sometimes clear only in the mind. For a given…

As algebra teachers, the authors explore the following question in this article: "How can algebra 1, algebra 2, and precalculus teachers support students to develop algebraic reasoning and understanding of structure that can serve them in day-to-day algebraic computation?" The article shows how the algebraic identity "(a +…