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…

How might teachers transform routine tasks into non-routine ones? The purpose of this article is to address this question. The article opens with a discussion of why non-routine problems require creative and original thought. Specifically, I discuss how non-routine problems require students to confront uncertainty and how uncertainty can serve as…

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…

Complex Instruction is a multifaceted instructional model designed to provide highly challenging learning opportunities for students in heterogeneous classrooms. The model provides a rationale for and philosophy of creating equity of access to excellent curriculum and instruction for a broad range of learners, guidance for preparing students for…

Mathematical conventions -- which account for the choices of mathematics community regarding definitions of concepts, their names and symbols -- are the focus of this paper. We introduce the task of unpacking, that is, offering plausible explanations and arguments for the choice of conventions. Using responses of four prospective teachers to the…

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…

The English as a foreign language classroom is a plurilingual setting par excellence since it involves at least two languages. However, plurilingual practices such as code-switching and translation have been consistently discouraged in formal learning contexts, based on the belief that keeping languages compartmentalized helps learning, and…

Matrices occupy an awkward spot in a typical algebra 2 textbook: sandwiched between solving linear systems and solving quadratics. Even teachers who do not base their course timeline and pacing on the class textbook may find a disconnect between how matrices are taught (procedurally) and how other topics are taught (conceptually or with real-world…

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…

A challenge for teachers is to incorporate the Standards for Mathematical Practice (CCSSI 2010) throughout their teaching of mathematics so that the Common Core Standards do not revert back to a purely content-driven curriculum. One way to achieve this is through the use of mathematically rich, investigative tasks. These tasks encourage students…

Twenty-first century literacy requires students to analyze and create images for communication across and within academic disciplines. Thus, literacy teachers are now responsible for supporting students as they engage with visual texts. We must carefully and intentionally choose images for teaching practice and consider the reader, instructional…

It is a truism to say that intelligence and happiness depend almost exclusively on what we choose to pay attention to. However, this is much easier said than done. The individual and collective attention of teachers is often drawn in many different directions. Paying attention to what is truly important is becoming more and more…

As someone who values collaboration with her students, supports students' ownership of their own learning, and looks for opportunities to increase their critical learning skills, Ce Rosenow finds many benefits to using task-specific rubrics that evolve from class discussion. She explains that this process is ideal for honors students because of…

Engaging students in meaningful applications of their knowledge is a key aspect of both addressing the standards and providing greater access. Not only do the standards emphasize the importance of meaningful engagement in real-world tasks, but evidence shows that engagement is strongly related to student performance on assessment tasks, especially…

In this article, the authors provide an overview of engineering and the engineering design process, and describe the steps they took to develop a fifth grade-level, standards-based engineering design task titled "Getting the Dirt on Decomposition." Their main goal was to focus more on modeling the discrete steps they took to create and…