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## Characterizing Secondary Teachers’ Structural Reasoning

The Common Core State Standards for Mathematical Practice asks students to look for and make use of structure. Hence, mathematics teacher educators need to prepare teachers to support students’ structural reasoning. In this article, we present tasks and rubrics designed and validated to characterize teachers’ structural reasoning for the purposes of professional development. Initially, tasks were designed and improved using interviews and small pilot studies. Next, we gave written structure tasks to over 600 teachers in two countries and developed and validated rubrics to categorize responses. Our work contributes to the preparation and support of mathematics teachers as they develop their own structural reasoning and their ability to help students develop structural reasoning.

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## Designing for Sensemaking of Research: The Mathematics District Leader Research Group

In this article, I share a design-based research intervention meant to help mathematics district leaders build their capacity to engage with research quality. I present my design (i.e., principles, key features, and intervention structure) and elaborate on how the features of the design allowed for mathematics district leaders’ sensemaking of educational research quality, especially regarding the process for collecting data and research implications. I conclude with recommendations for mathematics teacher educators on how they might adapt my design to their contexts.

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## Exploring Prospective Teachers’ Development of the Cartesian Form of Complex Numbers

In this study, we investigated prospective secondary mathematics teachers’ development of a meaning for the Cartesian form of complex numbers by examining the roots of quadratic equations through quantitative reasoning. Data included transcripts of the two sessions of classroom teaching experiments prospective teachers participated in, written artifacts from these teaching sessions, and their answers to pre-and-post written assessment questions. Results point toward prospective teachers’ improved meanings regarding the definition of complex numbers and the algebraic and geometrical meanings of the Cartesian form of complex numbers. Implications for mathematics teacher education include providing specific tasks and strategies for strengthening the knowledge of prospective and in-service teachers.

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## Are We Preparing Agents of Change or Instruments of Inequity? Teaching Toward Antiracist Mathematics Teacher Education

The authors began this work with the understandings that (a) there is no “neutral” when it comes to the teaching of mathematics, and (b) mathematics teacher educators need to do something to help produce teachers of mathematics that develop students’ relationships with mathematics and push against the inequities that exist both within and outside of the classrooms in which they will teach. In response, the authors created, deployed, and studied a learning module in an attempt to enact antiracist mathematics teacher education. The learning module activities, the findings about the learning from the prospective teachers who engaged in the module, and messages for mathematics teacher educators who want to engage in this work are shared.

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## Dilemmas and Design Principles in Planning for Justice-Oriented Community-Based Mathematical Modeling Lessons

This article details the development of design principles to support teachers in planning for a Community-Based Mathematical Modeling task with a focus on social justice in the elementary grades. By reflecting on the dilemmas we encountered in the design and enactment of the tasks, we developed five design principles that allowed us to address issues of social justice as well as attend to powerful mathematical ideas to bring awareness and take action around a local problem. Through our article, we hope to share with mathematics teacher educators design principles to help plan for tasks with pre- and in-service teachers that prioritize connecting mathematics to social issues and empower both teachers and students to take action to make a positive impact in the community.

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## “Rahul is a Math Nerd” and “Mia Can Be a Drama Queen”: How Mixed-Reality Simulations Can Perpetuate Racist and Sexist Stereotypes

This article focuses on using simulations of practice in teacher education. We studied preservice teachers’ engagement with a popular simulations platform, which creates mixed-reality simulations of five digital avatars controlled by a single live interactor. Because simulations are only an approximation of real practice, our overarching goal was to understand how mathematical stereotypes might arise in simulated spaces. We used Discourse analysis to classify the stereotypes present and the EQUIP observation tool to understand how PTs made participation opportunities available. We found that the simulations might have perpetuated overtly racist and sexist stereotypes and that negatively stereotyped students were afforded lower-quality opportunities to participate. We discuss how to mitigate potential harm caused and offer guidance for redesigning more equitable and antiracist simulations. Our goal is to raise critical questions for our field around the use of simulations of practice.

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## When Only White Students Talk: EQUIP-ing Prospective Teachers to Notice Inequitable Participation

We introduce a teacher learning practice called EQUIP-ing, which aims to foster sociopolitical noticing by leveraging EQUIP, an equity-oriented classroom observation tool. We detail our iterations of EQUIP-ing to a field-based Number Talk experience in a secondary mathematics methods course with 25 White prospective teachers (PTs). We offer empirical accounts of how EQUIP-ing empowered PTs to connect their teaching practices with racialized and gendered patterns of student participation; as a result, PTs began to reconsider taken-for-granted practices. However, we also found that PTs demonstrated potentially detrimental ways of attributing marginalizing patterns to minoritized students without actionable plans to redress the inequity. We conclude by inviting mathematics teacher educators to apply EQUIP-ing while emphasizing purposeful support for asset-based noticing.

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