The Cell Phone modeling task centers on a Fermi real-world estimation question. The task and rubric can be used at different grade levels to focus on the modeling process and classroom community. Finding time and space to engage students, especially novice modelers, in mathematical modeling can be a challenge, yet the benefits of modeling are…

The purpose of this article is to demonstrate how students' mathematics identities were developed and how their agency was fostered through the use of a mathematical action technology (MAT), Desmo, during stages of learning beyond noticing and wondering. The authors describe how they enacted an eighth-grade mathematics lesson depicting students…

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…

Tasks involving real-world contexts offer opportunities for teachers to engage students in mathematical practices (Standards for Mathematical Practice; NGA Center and CCSSO 2010). The practice of reasoning abstractly and quantitatively requires students to decontextualize and contextualize a task. Decontextualizing a task involves representing it…

When a Year 7 student physically reacted to a prompt of another student by anxiously drumming the desk with his ruler, exclaiming "uuuuhh", the initial thought of the observing researcher, Laura, was: "this is an interesting account". This started a reflective journey of first applying robust research methodologies to the…

The incorporation of intentional mathematical discussions can be used as a tool to increase engagement and ensure instruction is equitable. In this article, the authors share how the implementation of the five practices (Smith and Stein 2011) can reveal potential implicit biases during critical instructional moments, and they provide tools and…

Mathematical paradoxes often produce awe and wonder in the mathematics classroom. In this classroom episode, I share a paradoxical task, based on Simpson's Paradox, and its power as an intervention for a child diagnosed with ADHD. The Paradox leveraged his strengths to help him build understandings in proportional reasoning.

Advancement of self-regulation during complex problem solving and the development of strategical reasoning are among the central educational goals linked to 21st century skills. In this paper we introduce the notion of "Stepped Tasks", which are specially designed in Top-Down structure to achieve these goals in mathematics instruction.…

This article presents a model of intercultural learning that may be used in the planning and implementation of citizenship education in foreign/second/world language teaching. The Cycle model of intercultural learning aims at the development of global citizenship and comprises four phases: noticing, comparing, reflecting and interaction. Among the…

Because financial literacy is an important skill for middle-grades students, this article suggests numerous personal financial literacy tasks for use in the mathematics classroom. Also provided are specifics for implementing one of these tasks to address mathematical content.

Long before the release of the Common Core State Standards (CCSSI 2010), the Mathematical Tug-of-War was engaging students in the type of reasoning and problem solving described by the Standards for Mathematical Practice (SMP). In this updated version of a Marilyn Burns task, students use algebraic reasoning to determine the outcome of a contest…

The authors who are mathematics teacher educators, have found that classifying, composing, and transforming shapes (in particular, rotations and reflections) are areas of difficulty for adults as well as for children. However, these are also some of the most important geometric ideas. They are fundamental topics in the K-8 Geometry and Measurement…

The ideas students bring to class and their perspectives on what is happening in the classroom change constantly. Keeping track of these changes is useful for adapting lessons, nurturing student self-reflection, increasing student ownership of learning, and building a teaching practice responsive to learners' needs. In this article, the authors…

Open-ended mathematical tasks provide great opportunities for students to engage in authentic mathematical practices, such as conjecturing, generalizing, and justifying. Supporting students in open-ended tasks can be challenging. Appropriate scaffolding of a task has been linked to more opportunities for student learning and better student…

This article discusses how teaching via problem solving helps enact the Mathematics Teaching Practices and supports students' learning and development of the Standards for Mathematical Practice. This approach involves selecting and implementing mathematical tasks that serve as vehicles for meeting the learning goals for the lesson. For the lesson…