At Mayfield Middle School, in order to create personalized and more meaningful learning experiences for the students, it was realized that a typical, traditional schedule was not always conducive to the types of learning experiences teachers wanted to create. Teachers had great ideas for projects and practices that would incorporate more critical…

One of the greatest conceptual difficulties faced by middle level mathematics students is developing a rich understanding of irrational numbers that includes recognizing that irrational numbers are truly real numbers with an exact value and an exact place on the number line. Developing a deep conceptual understanding of irrational numbers is…

Metacognition supports students in successfully working through struggle by equipping them with the tools to maintain an awareness of what they are doing and to change directions when needed to overcome obstacles. Thus, it is of little surprise that effective problem solvers spend a significant amount of time analyzing tasks relative to the amount…

Our aim is to contribute to the body of research on learning trajectories (LTs) in mathematics by making visible a process for articulating a hypothetical learning trajectory implicit in a widely adopted, reform-based, middle-grades mathematics curriculum. In doing so, we highlight considerations, decisions, and challenges we faced as part of this…

Using question 28 from the May Problems to Ponder in volume 114, the author and her seventh- and eighth-grade students launched into a discussion of creativity, linearity, piecewise, and recursive definitions of functions. This pattern to ponder provided rich mathematical opportunities for all students in her middle school classroom.

Area should be experienced, not simply calculated. This task invites students to physically experience areas and the spatial relationships between them, as well as their own community.

Effective teaching requires enjoyable classroom tasks aimed at promoting students' learning of mathematics meaningfully, and previous research has demonstrated that the use of origami activities in mathematics classrooms can help achieve that goal. In this article, the authors describe their "LOVE MATH" one-straight-cut letter origami…

The National Academy of Education (NAEd) Civic Reasoning and Discourse project aims to support civic reasoning and discourse in the schools by helping teachers across disciplines to prepare youth in the United States to examine and discuss complex issues in ways that are thoughtful, developmentally appropriate, and respectful of others' opinions…

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…

Throughout the learning process, English learners should meaningfully engage with both their peers and the mathematics. How do mathematics teachers provide the "just-right" supports for English learners to insure this happens? What scaffolds are best? How do teachers make adjustments to these scaffolds based on the needs of the…

Many teachers use problems set in real or imaginary contexts to make mathematics engaging, but these problems can also be used to anchor conceptual understanding. By constructing an understanding of mathematical ideas through solving problems in contexts that make sense to students, they have a better chance of actually understanding those…

Spirograph® is a classic drawing toy that has intriguing connections with mathematics. Inspired by earlier articles in "Mathematics Teacher" on the classic drawing toy that targeted higher grade levels, the authors adopt and create activities that make Spirograph mathematics accessible to middle-grade learners.

Many teachers reported improved skills in using technology as a direct result of teaching virtually during the pandemic (Bushweller, 2020). The authors wondered which uses of technology would continue as teachers transitioned back into face-to-face classrooms. Recognizing that mere incorporation of technology into instruction does not guarantee…

Data-based individualization (DBI) is a framework that allows educators to make timely and informed decisions about student progress in academics or behavior. In this article, we focus on the DBI framework as applied to math intervention within a tiered support model for students experiencing math difficulty. We review how DBI starts with an…

The concept of a learner's identity in mathematics is complex and multifaceted. Based on a review of the relevant research, the authors believe most factors that influence one's mathematical identity fall within these four categories: (1) past mathematics experiences; (2) personal beliefs and efficacy; (3) future self-representation and belonging;…