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## From Notes to Strings

Four teachers and a teacher educator move from guided notes to strings in a series of problems that support students in increased engagement, reasoning, sense making, and problem solving.

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## Puddle Play!

For the Love of 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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## Seeing Algebraic Structure: The Rubik's Cube

Few high school students associate mathematics with playfulness. In this paper, we offer a series of lessons focused on the underlying algebraic structures of the Rubik's Cube. The Rubik's Cube offers students an interesting space to enjoy the playful side of mathematics, while appreciating mathematics otherwise lost in routine experiences.

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## Connecting Research to Teaching: Evaluating and Writing Dynamic Geometry Tasks

The advent of dynamic geometry software has changed the way students draw, construct, and measure by using virtual tools instead of or along with physical tools. Use of technology in general and of dynamic geometry in particular has gained traction in mathematics education, as evidenced in the Common Core State Standards for Mathematics (CCSSI 2010).

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## Open-ended Questions and the Process Standards

Educating students—for life, not for tests—implies incorporating open-ended questions in your teaching to develop higher-order thinking.

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## For ELLs: Vocabulary beyond the Definitions

A classroom teacher discusses ambiguities in mathematics vocabulary and strategies for ELL students in building understanding.

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## Counterexamples as Starting Points for Reasoning and Sense Making

Asked to “fix” a false conjecture, students combine their reasoning and observations about absolute value inequalities, signed numbers, and distance to write true mathematical statements.

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## Sorting Out Ideas about Function

A card-sorting task can help students extend their understanding of functions and functional relationships.

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## Connecting Research to Teaching: Classroom Collaboration: Moving beyond Helping

Do you use group work in your mathematics class? What does it look like? What do you expect your students to do when they work together? Have you ever wondered what your students think they are supposed to do?