Can You Build It? is an engaging Improve It! task that asks children to construct 3D shapes based on 2D depictions. Students' initial 3D creations often need revision, and as they build and re-build, they develop spatial relationships. This task was implemented in a first-grade class, connected to composing 3D geometric shapes to address the…

The authors wondered if there was a way to support their reluctant Grades 4, 5, and 6 students in contributing their starting points and strategies and advancing their collective knowledge. They wanted to ensure that the students had the space to develop and take ownership of the strategies they produced through a visual representation of ideas…

The authors developed an instructional nudges as part of a larger research project. These instructional nudges are designed to be small but powerful changes to teachers' existing practices. Some instructional nudges focus on modifying tasks used in classrooms. In this article, the authors share Rate and Review. The goal of Rate and Review is to…

Even though there is a great temptation as teachers to share what is known, many are aware of an idea called "rules that expire" (RTE) and have realized the importance of avoiding them. There is evidence that students need to understand mathematical concepts and that merely presenting rules to carry out in a procedural and disconnected…

In this article, the authors provide some insight into how teachers can potentially facilitate among students' representations and activities on mathematical tasks: between or among -- (1) student representations and the context; (2) multiple forms of student representations; and (3) processes in student representations. The authors use the…

Students at the elementary level should have opportunities to critique the world through mathematics and to see themselves as capable doers of mathematics. The lesson described in this article prompted students to consider how to use mathematics to organize an emergency evacuation. In this article, the authors show how small changes to a task…

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…

There is a substantial amount of literature focusing on the importance of culturally relevant teaching that emphasizes connecting the school's curriculum with the culture of students. This approach can be accomplished through the concept of ethnomathematics. Ethnomathematics studies how cultural groups practice and use math in daily activities…

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…

This article describes how to build a classroom community by building representations and visualizations of data related to students' names. The goal of this task was to allow students to get to know each other's identities better by collecting and analyzing data about their names and exploring the connection between names and identities. The task…

Students often look to the standard algorithm, which requires rewriting the task, regrouping tens to create enough ones to subtract, and other opportunities to make errors. However, when the authors apply structural thinking, the resultant strategy is an efficient and elegant shortcut and even brings a positive connotation to the word…

Culturally rich stories may not explicitly refer to mathematical content. Consequently, teachers may overlook the potential for using content-invisible literature as a resource for mathematical investigations. Reflecting on the key elements of the what from the What-How-Who structure builds teachers' capacity to develop paramount tasks from…

Mathematical modeling involves using mathematics to represent, analyze, and make predictions or decisions about real- world situations. Garfunkel and Montgomery (2016) elaborate on six components of the mathematical modeling process, including identifying the problem, making assumptions and identifying variables, doing the math, analyzing and…