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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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## The Importance of Play in Middle School Mathematics

Using question 28 from the May Problems to Ponder in volume 114, the author and her seventh- and eighth-grade students launched into a discussion of creativity, linearity, piecewise, and recursive definitions of functions. This pattern to ponder provided rich mathematical opportunities for all students in my middle school classroom.

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## Promoting Exploration through Synthesis

The author discusses “synthesizing" teaching practice, which encourages students to explore patterns and its underlying mathematics structure through technology.

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## Leveraging Student Identities to Develop Pedagogical Fluency

Mathematics education can be positioned as fertile ground for societal change. This article deconstructs the complex work of supporting students’ positive mathematical identities by introducing pedagogical fluency to embody equitable beliefs and practices.

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## Puddle Play!

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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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## Seeing Stars: Sequences on U.S. Flag

Students analyze photographs of patterns and determine algebraic representations for the pattern growth.

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## GPS: Pattern Recognition to Explore Mathematical Structure

In this month’s Growing Problem Solvers, we aimed to help students explore patterns where they pay attention to the mathematical structures behind those patterns.

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## Conditional Reasoning Online with Mastermind

As mathematical patterns become more complex, students' conditional reasoning skills need to be nurtured so that students continue to critique, construct, and persevere in making sense of these complexities. This article describes a mathematical task designed around the online version of the game Mastermind to safely foster conditional reasoning.

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## Escape Room Math: Luna's Lines

An escape room can be a great way for students to apply and practice mathematics they have learned. This article describes the development and implementation of a mathematical escape room with important principles to incorporate in escape rooms to help students persevere in problem solving.