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…

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…

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…

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;…

When one sets out to solve a mathematics problem, a feeling of satisfaction and accomplishment comes with finding the answer and knowing it is correct. In contrast, a student performing the correct process to solve an algebra equation and getting an answer such as 3 = 0 may be left perplexed and not understanding what--if anything--he or she did…

In this article, the authors explain how they leveraged the popularity of the "Star Wars" franchise to introduce a task steeped in popular culture as a fun way to engage their students in investigating complex mathematics that have real-life connections to careers in toy design and engineering design in general. The authors share various…

Too often, statistical inference and probability are treated in schools like they are unrelated. In this paper, we describe how we supported students to learn about the role of probability in making inferences with variable data by building models of real world events and using them to simulate repeated samples.

Argumentation is an important mathematical practice, highlighted by research and policy documents that describe ways to structure reform-oriented classrooms (Nardi and Knuth 2017; NCTM 2000; NGA Center and CCSSI 2010). Participating in argumentation can enhance students' mathematics learning as they make sense of mathematical ideas, provide…

The beginning of the school year is a time of intense work for students and teachers, especially if it means learning mathematics in new ways (Ruef 2016). Students need guidance and support if they are shifting beliefs about what it means to do mathematics. This article shows how Torres and her students co-created new ways to be good at…