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S. Asli Özgün-Koca, Jennifer M. Lewis, and Thomas Edwards

Mathematical knowledge for teaching is a complex web of knowledge domains. In this article, we share findings from an 18-month professional development project that aimed to improve middle school mathematics teachers’ mathematical knowledge for teaching (MKT) of proportional reasoning by focusing on the critical analysis of mathematical tasks and student work. Although multiple studies have shown that professional development can contribute to teachers’ MKT globally, little is known about how this knowledge grows and how specific domains of MKT can be targeted through professional development. Findings in this study show how professional development positively influenced participants’ knowledge of content and teaching and knowledge of content and students, two domains of MKT, through teachers’ twinned analyses of tasks and student work in proportional reasoning.

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Kelly Hagan and Cheng-Yao Lin

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

The Mathematics Teacher Educator journal is co-sponsored by the National Council of Teachers of Mathematics and the Association of Mathematics Teacher Educators. In June, both organizations released statements that call for mathematics teachers and mathematics teacher educators (MTEs) to “engage in anti-racist and trauma-informed education in our daily practices as processes of learning and adjustments” () and to “actively work to be anti-racist in our acts of teaching, research, and service” (). This editorial highlights equity-related interventions and tools that can be implemented by MTEs. We reiterate statements made by NCTM and AMTE, describe key features of interventions and tools, and share equity-related resources published in the journal for MTEs to use with teachers.

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Robert Q. Berry III, Basil M. Conway IV, Brian R. Lawler, and John W. Staley

Ear to the Ground features voices from various corners of the mathematics education world.

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Jennifer L. Ruef and Ana M. Torres

Students learn new ways of being good at mathematics by overcoming the fear of being wrong and embracing the challenge and wonder of proposing, refining, and coming to a consensus on mathematical arguments.

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Katelyn A. Devine

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Steve Ingrassia and Molly Rawding

Problems to Ponder provides 28 varied, classroom-ready mathematics problems that collectively span PK–12, arranged in order of grade level. Answers to the problems are available online. Individuals are encouraged to submit a problem or a collection of problems directly to mtlt@nctm.org. If published, authors of problems will be acknowledged.

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Sandra Madden

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Cathery Yeh, Trisha Sugita, and Paulo Tan

We challenge traditional models of individual differentiation and share design principles that broaden competence and participation for all students, including those with disabilities.

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Matthew P. Campbell, Erin E. Baldinger, and Foster Graif

Approximations of practice provide opportunities for teacher candidates (TCs) to engage in the work of teaching in situations of reduced complexity. A problem of practice for teacher educators relates to how to represent student voice in approximations to engage TCs with interactive practices in meaningful ways. In this article, we share an analysis of our use of “planted errors” in coached rehearsals with secondary mathematics TCs focused on the practice of responding to errors in whole-class discussion. We highlight how different iterations of the planted errors affect the authenticity of how student voice was represented in the rehearsals and the resulting opportunities for TC learning. We offer design considerations for coached rehearsals and other approximations of practice.