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## Construct It! Introducing Integers with Floats and Anchors

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

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

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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## Teaching Is a Journey: The Frog in the Well

Three authors from different cultural and linguistic backgrounds, who discovered that their understanding of math and education have been limited by their cultural views, collaborate to become better educators.

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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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## Filling Vases and Making Tanks

Two classic hands-on tasks address conceptual understanding of functions. The tasks center student discourse and rough draft mathematics as students grapple with the relationship between input and output.

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## Building Coherence and Progression on Sound Frameworks

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

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## Experience First, Formalize Later

The EFFL model empowers students to build strong conceptual understanding of mathematics through carefully designed, equity-minded activities that disrupt the traditional lecture-based classroom.

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## Using Series to Construct Pythagorean Triples

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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.