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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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## 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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