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Construct It! Introducing Integers with Floats and Anchors

Christy Pettis and Aran Glancy

Use the Floats and Anchors context as well as physical and digital materials to help students understand integer addition and subtraction.

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Beware of “Gaps” in Students’ Fraction Conceptions

Patrick L. Sullivan, Joann E. Barnett, and Kurt Killion

Many students have a dominant part-whole conception of fractions. We examine why this is problematic and explore strategies to move students beyond this limitation.

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Building Algebraic Procedures From Concepts: Like Terms

Leah M. Frazee and Adam R. Scharfenberger

This task sequence for adding and subtracting like terms—grounded in the concepts of equivalence and algebra as generalized arithmetic—helps students see connections between concepts and procedures in algebra.

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

Gülseren Karagöz Akar, Merve Saraç, and Mervenur Belin

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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Building Coherence and Progression on Sound Frameworks

Travis Lemon and Scott Hendrickson

A robust framework can support teachers and their students’ learning.

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Using Series to Construct Pythagorean Triples

Darien DeWolf and Balakrishnan Viswanathan

This article provides a series-focused approach to computing Pythagorean triples.

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

Joel Amidon, Anne Marie Marshall, and Rebecca E. Smith

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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Teaching Is a Journey: What Did I Really Mean?

Karla Bandemer

This department provides a space for current and past PK-12 teachers of mathematics to connect with other teachers of mathematics through their stories that lend personal and professional support.

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“Reflections on High-Quality Math Instruction”

Blake E. Peterson, Douglas L. Corey, Benjamin M. Lewis, Jared Bukarau, and Introduction by: Wendy Cleaves

From the Archives highlights articles from NCTM’s legacy journals, previously discussed by the MTLT Journal Club.

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GPS: Iterating and Partitioning

Daniel K. Siebert and Monica G. McCleod

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.