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## Early Algebra: Expressing Covariation and Correspondence

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## Hook and Hold

Set sail to explore powerful ways to use anchor charts in mathematics teaching and learning.

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## Untangling Geometric Ideas

This geometry lesson uses the work of abstract artist Wassily Kandinsky as a springboard and is intended to promote the conceptual understanding of mathematics through problem solving, group cooperation, mathematical negotiations, and dialogue.

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## Connecting the Threads of Area and Perimeter

See how sixth-grade students design and create quilt squares for this geometry project.

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## Improving Preservice Secondary Mathematics Teachers' Capability With Generic Example Proofs

Preservice mathematics teachers are entrusted with developing their future students' interest in and ability to do mathematics effectively. Various policy documents place an importance on being able to reason about and prove mathematical claims. However, it is not enough for these preservice teachers, and their future students, to have a narrow focus on only one type of proof (demonstration proof), as opposed to other forms of proof, such as generic example proofs or pictorial proofs. This article examines the effectiveness of a course on reasoning and proving on preservice teachers' awareness of and abilities to recognize and construct generic example proofs. The findings support assertions that such a course can and does change preservice teachers' capability with generic example proofs.

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## The Mathematics of Tiling

People who lay tile for a living use mathematics every day to decide how much tile, grout, and other supplies are required to complete each job. Measurement and geometry are an integral part of designing tile patterns. Collections of short activities focus on a monthly theme that includes four activities each for grade bands K–2, 3–4, and 5–6 and aims for an inquiry or problem-solving orientation.

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## Using Constructed Knowledge to Multiply Fractions

Observe fourth graders' thinking in action as they connect the multiplication of whole numbers to arrays.

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## Helping Young Children See Math in Play

Capitalize on opportunities for mathematical concepts to emerge in common preschool contexts, such as doll corners and block centers.

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## The Functionator 3000: Transforming Numbers and Children

Be inspired by a formerly timid third grader who now confidently conveys a new understanding of numbers, patterns, and their relationships as functions.

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## Developing Addition Strategies: Preservice Teachers' Learning From Standards-Based Curriculum Materials

Despite the prevalence of mathematics curriculum materials in elementary classrooms, most current mathematics methods texts provide little or no support for preservice teachers (PSTs) learning to use curriculum materials. To meet this need, we have designed and studied several modules intended to provide PSTs with opportunities to learn about and from the use of curriculum materials. This article describes our research related to 1 of these modules–Addition Starter Sentences. Our results examine the nature of PSTs' developing content knowledge and pedagogical content knowledge, evidenced through their interactions with and reflections on Standards-based curriculum materials. We conclude with implications for mathematics teacher education research and practice.