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## Enacting Co-Craft Questions Using Flexible Teaching Platforms

Teachers can implement a mathematics language routine within in-person/hybrid and remote instructional contexts.

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## Point-Line Ellipses and Hyperbolas

The author alters the definitions of ellipses and hyperbolas by using a line and a point not on the line as the foci, instead of two points. He develops the resulting prototypical diagrams from both synthetic and analytic perspectives, as well as making use of technology.

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## Rethinking Wait Time: What Can 3 Seconds Do?

A high-leverage strategy first discussed more than 50 years ago, wait time has many benefits for both teachers and students yet is not used to its full potential. See how it can enhance your students’ mathematical discourse.

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## Using Judicious Telling to Strengthen Literacy in Mathematics

Language is a conduit for communicating and understanding mathematical ideas. This article explores how we can use judicious telling to attend to students’ written and spoken literacy in mathematics.

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## Variations on a Theme of Fibonacci 1

We introduce variations on the Fibonacci sequence such as the sequences where each term is the sum of the previous three terms, the difference of the previous two, or the product of the previous two. We consider the issue of the ratio of the successive terms in ways that reinforce key behavioral concepts of polynomials.

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## The Case for High School Math Pathways

The standard high school math curriculum is not meeting the needs of the majority of high school students and that serious consideration of rigorous alternatives is a solution whose time has come.

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## Delving Deeper: What Else Comes after 1 + 2 = 3?

The simplest of prekindergarten equations, 1 + 2 = 3, is the basis for an investigation involving much of high school mathematics, including triangular numbers, arithmetic sequences, and algebraic proofs.

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## Perspectives from Physics: Constraints on Our Curriculum

How trigonometry is used and portrayed differently in mathematics and physics textbooks highlights potential sources for student struggle, constraints on our trigonometry curriculum, and lessons learned when looking across STEM disciplines.

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## Access, Power, Identity, and Healing in Mathematics

Co-teachers in a ninth-grade algebra 1 class offered instruction that integrates mathematical learning with social and emotional learning during hybrid (online and face-to-face) class meetings, promoting healing and positive identity development among students.

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## S3D: Small-Group, Student-to-Student Discourse

Learn about strategies and tools to examine and improve your practice with respect to fostering equitable small-group, student-to-student discourse.