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Lori Burch, Erik S. Tillema, and Andrew M. Gatza

Use this approach to developing algebraic identities as a generalization of combinatorial and quantitative reasoning. Secondary school students reason about important ideas in the instructional sequence, and teachers consider newfound implications for and extensions of this generalization in secondary algebra curricula.

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Jennifer M. Suh, Sara Birkhead, Toya Frank, Courtney Baker, Terrie Galanti, and Padmanabhan Seshaiyer

This article details the design and implementation of a professional development model called Learning Trajectory-Based Lesson Study focused on issues of equity, identity, and agency. We developed the Vertical Articulation to Unpack the Learning Trajectory (VAULT) tool to orient teachers’ instructional planning toward an asset-based view of students’ mathematics competencies. We examined teachers’ use of the VAULT to plan, implement, and debrief on student strategies for one spatial reasoning task in elementary, middle, and high school classrooms. The VAULT facilitated intentional planning for a progression of anticipated strategies and equitable access to instruction. Teachers demonstrated an asset-based view of all student thinking independent of grade-level expectations.

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Valerie Faulkner, Karen Hollebrands, Emily Elrod, and Heather West

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Troy Bell, Michael Lolkus,, Jill Newton, and Craig Willey

The preparation of mathematics teacher educators (MTEs) varies widely, with little guidance regarding the essential skills and knowledge necessary to tackle the field’s looming challenges. Equitable access to, and engagement with, mathematics has surfaced as an elusive goal of mathematics education organizations. MTEs, therefore, ought to identify and engage with resources that help them comprehend and confront systemic oppression and inequities. We present the process and reflections from an examination of MTEs’ professional growth through engagement in a collaborative interrogation of critical texts outside of mathematics education. Participation in this series of structured readings and dialogue led MTEs to develop a deeper understanding of the historical movements and events that created today’s local and global status quos. Furthermore, MTEs could more readily make connections between macrocontexts of colonialism, violence, and oppression, and the micromanifestations of power and marginalization within mathematics education. Implications for future development of MTEs are discussed.

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Anna Bargagliotti, Pip Arnold, and Christine Franklin

The authors introduce the Pre-K–12 Guidelines for Assessment and Instruction in Statistics Education II (GAISE II): A Framework for Statistics and Data Science Education report.

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S. Asli Ozgun-Koca and Kelly Hagan

Growing Problem Solvers provides four original, related, classroom-ready mathematical tasks, one for each grade band. Together, these tasks illustrate the trajectory of learners’ growth as problem solvers across their years of school mathematics.

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Dionne Aminata, Deborah Peart, and Kaneka Turner

Dionne Aminata, Deborah Peart, and Kaneka Turner created #Blackwomenrockmath to connect and uplift Black women in mathematics education after recognizing the need for greater representation and support.

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Eva Thanheiser and Courtney Koestler

[The If the World Were a Village book (Smith, 2011) and activity (described in this article)] was a really good way to open one’s perspective. As an American, I tend to be a bit focused on the United States, so to see how much [or how little] of the world is actually represented in my perspective was enlightening.

Living in the United States . . . I was surprised that only 5% [of the world population] were from North America.

Long-standing and ongoing calls exist for making mathematics meaningful, relevant, and applicable outside the classroom. Major mathematics education organizations (National Council of Teachers of Mathematics [NCTM], National Council of Supervisors of Mathematics [NCSM], Association of Mathematics Teacher Educators [AMTE], TODOS: Mathematics for ALL) have called for mathematics to be seen as a tool for understanding and critiquing the world. To prepare students and teachers to do this, we must go beyond “everyday" contexts and include analysis of social justice issues into our courses. We share an activity designed to address these calls while also addressing the mathematics goals of the course. We share data showing that prospective teachers learned mathematics while also learning about their world and reframing their view of mathematics as a tool to make sense of the world.

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Anna Wan and Jessica Ivy

An activity connects the features of sinusoid curves to tangible manipulatives printed on a 3D printer.