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## Visualizing Mathematics Through Knitting

The author uses mathematical concepts to inform her knitting. Her knitting also helps her to experience mathematical concepts in new ways.

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## Three Ways to Enhance Tasks for Multilingual Learners

Enacting these considerations supports integrated thinking about how to attend to both mathematics content and language development.

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## Weaving the Rainbow (Odd I)

This piece is a rumination on flow, pattern, and edges/transitions, focusing on polynomials of odd degree and overlaying/underlaying the flow of the graphical structure with a rainbow to suggest the central importance of queer visibility in mathematics.

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## Student Engagement with the “Into Math Graph" Tool

We introduce the Into Math Graph tool, which students use to graph how “into" mathematics they are over time. Using this tool can help teachers foster conversations with students and design experiences that focus on engagement from the student’s perspective.

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## “Counting” on Quantitative Reasoning for Algebra

Use this approach to developing algebraic identities as a generalization of combinatorial and quantitative reasoning. Secondary school students reason about important ideas in the instructional sequence, and teachers consider newfound implications for and extensions of this generalization in secondary algebra curricula.

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## Reasoning and Sense Making in High School Mathematics with Two Ways

This article illustrates ways to extend Two Ways into high school mathematics content and advantages of doing so.

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## GPS: Popsicle Place Value and Polynomials

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.

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## NCTM Leadership Then and Now

How has NCTM leadership shaped the evolution of teaching and learning mathematics? What are your expectations for NCTM leadership?

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## With Reason: A Portrait of Sophia Kovalevsky (1850–1891)

Sophia Kovalevsky's story

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## Modeling a Bouncing Ball with Exponential Functions and Infinite Series

We modify a traditional bouncing ball activity for introducing exponential functions by modeling the time between bounces instead of the bounce heights. As a consequence, we can also model the total time of bouncing using an infinite geometric series.