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.

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 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.

The ability to solve mathematical problems has been an interesting research topic for several decades. Intuition is considered a part of higher-level thinking that can help improve mathematical problem-solving abilities. Although many studies have been conducted on mathematical problem-solving, research on intuition as a bridge in mathematical…

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…

As mathematical patterns become more complex, students' conditional reasoning skills need to be nurtured so that students continue to critique, construct, and persevere in making sense of these complexities. This article describes a mathematical task designed around the online version of the game Mastermind to safely foster conditional reasoning.

Dude Perfect has one of the most popular YouTube channels in the United States. The task in this article is one of several activities the author has integrated into mathematics lessons in ways that engage students and that are connected to Dude Perfect videos (Stohlmann 2019). The author describes how he planned and implemented purposeful…

This article explores teaching practices described in NCTM's [National Council of Teachers of Mathematics'] "Principles to Actions: Ensuring Mathematical Success for All." Investigating and mitigating implicit bias in questions are discussed in this article, which is another installment in the series.

Conventional word problems can't help students build mathematical modeling skills. on their own. But they can be leveraged! We examined how middle and high school students made sense of word problems and offer strategies to question and extend word problems to promote mathematical reasoning.

Positioning students as competent is a teaching practice that uses specific, explicit affirmations to note that students have contributed something meaningful to the community of learners. It supports student agency in the mathematics classroom and contributes to the development of a positive mathematics identity. In this article, the authors…

The aim of this article is to inspire more teachers to explore the use of codable robots for teaching mathematics. The authors begin by discussing four benefits experienced by incorporating robots into middle school mathematics classes: (1) reasonable time frames; (2) authentic purposes for mathematics; (3) visual and nonevaluative feedback; and…

This article explores facilitating meaningful mathematics discourse, one of the research-based practices described in "Principles to Actions: Ensuring Mathematical Success for All." Two tools that can support teachers in strengthening their classroom discourse are discussed in this, another installment in the series.

Engaging in argumentation can lead to an increase in the development of critical-thinking skills, not to mention academic achievement, emotional maturity, and academic and communication skills. If argumentation is such an effective format for developing rigorous academic ideas, how might it be used in discussion-oriented classrooms to engage…