Statistics has been a content domain in the mathematics curriculum for decades. However, statistics is a distinct discipline from mathematics and there are important differences in how one should teach the two disciplines. In this article, the authors consider how these differences can inform an adaptation to the 5 Practices for Orchestrating…

These educators share the "how" and "why" behind their use of open middle tasks in the classroom. In this article, the authors share a type of mathematics task, called Open Middle, that exhibits the characteristics outlined above. The authors frequently use Open Middle tasks in their classrooms because they teach students that…

The study of mathematics is often described as the science of patterns (Resnik 1981), and the cognitive tasks involving the search, recognition, and assessment of patterns are fundamental to learning mathematics. Patterning activities lead students to a better understanding of dependent relations among representations, create a transparent way for…

Teachable moments are often thought of as serendipitous moments when children's ideas become visible and a teacher is able to take advantage of a specific idea to teach content (e.g., Glasswell and Parr 2009; Hyun and Marshall 2003; Virtue 2007). However, teachers cannot always wait for serendipity to create moments of authentic learning, which…

This article describes the two types of reasoning in fraction conceptions that students often use, "gap" and "missing piece," and one that the authors aspire their students to reach, "residual." Each of these types of reasoning are underpinned by a different conception of fractions. Students who use "gap…

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…

What tales would students tell about their mathematical experiences? Are they stories of triumph, boredom, despair, exhilaration, or, perhaps, all of these emotions? How do teachers access these stories to understand students' experiences and build from them? In this article, the authors describe a task, The Math Metaphor, and how it was used in a…

Inspired by the "Batman Equation" of 2011, this article presents a challenging and engaging process for graphing complicated designs from just a single parametric equation pair. Reinforces numerous analytic geometry skills. Works in popular graphing software such as Desmos or GeoGebra, or even graphing calculators.

This article discusses Experience First, Formalize Later (EFFL), an approach to teaching and learning that empowers students to build strong conceptual understanding of concepts, redefining how students experience mathematics class, and ultimately leading to more equitable learning opportunities. Traditional lecture-based models for mathematics…

Classroom stories show how using technology to investigate the wage gap provided opportunities to develop students' identities and agency and enabled a classroom culture of sharing and risk-taking. This article illustrates how technology can (a) support students' engagement in case-based reasoning by helping them organize and analyze data; (b)…

This article dives into the importance of engaging students in investigating the mathematics of businesses that pressure their members to recruit new members as a basis for success, also referred to as multi-level marketing (MLM). The mathematics behind these businesses are discussed, and a sample student task is given.

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.

An university in Chile developed a Digital Learning Routes (DLR) for three elective courses in the area of mathematics: (1) limits, derivatives, and integrals; (2) probabilities and descriptive and inferential statistics; and (3) three-dimensional geometry. A DLR is a sequence of e-learning activities that seeks to enable learners to build…

How would students feel when learning through the use of mathematical modeling? On investigation, this article reveals that students felt better prepared for assessments, learned valuable life skills, and saw the relevance of mathematics to their lives outside of the classroom.

Understanding exponential growth is a fundamental aspect of developing critical numeracy skills; however, typically, exponential growth is introduced in curricular documents to secondary students. Moreover, such introductions tend to be in the context of formal mathematical modeling, divorced from a sense of quantity. The authors argue that, given…