With an increased focus on using social discourse to enhance students' mathematical thinking and reasoning (NCTM 2014, Staples and King 2017), teachers are looking for discussion strategies that encourage middlelevel students to make sense of mathematical concepts. However, structuring these valuable discussions is complex. Teachers must carefully…

In education, "dialogue protocols," or "protocols," are structured guidelines that were developed to promote meaningful and efficient communication and learning. They are "vehicles for building the skills--and culture-- necessary for collaborative work. The authors share protocols that were found to transform practices…

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.

In April 2018, the National Council of Teachers of Mathematics (NCTM) released "Catalyzing Change in High School Mathematics: Initiating Critical Conversations," a long-needed and well-articulated position for transforming the core purposes, structures, instructional practices, essential mathematics concepts, and organization of high…

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…

The article uses vignettes to illustrate a small group of of grade 5 students who worked on different types of temperature problems (Wessman-Enzinger and Tobias 2015). The Common Core State Standards for Mathematics (CCSSM) recommends including contexts, such as temperature, paired with the introduction to integers in grade 6 and integer…

As middle school teachers, the authors want their students to develop voice and agency because they want them to be able to make productive decisions about how to approach mathematics, communicate mathematics, and use mathematics to interpret and transform the world in which they live. They use this article to present two vignettes that examine…

How can a cognitively demanding real-world task such as the Seven Billion People problem promote productive struggle "and" help shape students' mathematical dispositions? Driving home from school one evening, Jaclyn Murawska heard a commentator on the radio announce three statements: (1) experts had determined that the world population…

Research suggests that embodying mathematical concepts through movement supports improvements in students' spatial fluency, communication, collaboration, critical thinking, and problem-solving skills (Alibali and Nathan 2012; Cone and Cone 2011; Sarama and Clements 2009). This article describes a dance-based strategy that middle school mathematics…

Middle-grades teachers and students can have different perspectives on the value of discussing students' mathematical mistakes, despite various classroom evidence that such discussions can help foster strong conceptual understanding. Some teachers consider student mistakes to be an opportunity to correct errors in individual student thinking.…

A framework using contexts, language, and representations can support middle school students' justifications. This article introduces classroom tasks and student work to provide a vision of framework implementation in classroom settings. Although the students in this article are future elementary and middle school teachers, the framework tasks and…

As a group of middle school mathematics teachers and teacher educators, the authors have focused their attention on using innovative practices coupled with high cognitive demand tasks to engage students, pique their interest in mathematics, and promote conceptual understanding. This article explores their three-act task design. In act 1, students…

The phrase "interdimensional relationships" may conjure images of UFOs, alien beings, wormholes, and even mystical powers. These notions of interdimensionality were not out of bounds in the middle school learners' experiences described in this article. However, these notions do not entirely capture the mathematical relationships…

In their ongoing professional development project, the authors had an opportunity to work with a group of teachers who were particularly insightful. These teachers shared written reflections about their thinking, prior experiences, and changing self-awareness of their mathematics practice. In one session, teachers were provided the…

The Common Core's Standards for Mathematical Practice encourage teachers to develop their students' ability to reason abstractly and quantitatively by helping students make sense of quantities and their relationships within problem situations. The seventh-grade content standards include objectives pertaining to developing linear equations in…