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## Productive Struggle in Action

Productive struggle is an essential part of mathematics instruction that promotes learning with deep understanding. A video scenario is used to provide a glimpse of productive struggle in action and to showcase its characteristics for both students and teachers. Suggestions for supporting productive struggle are provided.

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## Supporting Probability Understanding through Area Models

Moving beyond memorization of probability rules, the area model can be useful in making some significant ideas in probability more apparent to students. In particular, area models can help students understand when and why they multiply probabilities and when and why they add probabilities.

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## What's in a Name? Language Use as a Mirror into Your Teaching Practice

Language is key to how we understand and describe mathematics teaching and learning. Learning new terms can help us reflect on our practice and grow as teachers, yet may require us to be intentional about where and how we look for opportunities to expand our lexicons.

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## Engaging Latino Families as Mathematicians

We share our experiences and those of culturally diverse families who participated in math workshops. We tie our experiences with the importance of family engagement, in particular, viewing families as a resource to be tapped into. We do so, in hopes that other school personnel take on a similar venture.

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## Creating Joy in PK–Grade 2 Mathematics Classrooms

Children experience joy in well-designed mathematics classrooms. This article describes five research-based practices for bringing joy into PreK-Grade 2 math lessons.

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## GPS: From Folding to Dynamic Geometry Environments

In this month's Growing Problem Solvers, we focused on supporting students' understanding of congruence and similarity through rigid motions and transformations. Initial understandings of congruence and similarity begin in first grade as students work with shapes in different perspectives and orientations and reflect on similarities and differences.

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## Problems to Ponder

Problems to Ponder provides 28 varied, classroom-ready mathematics problems that span grades PK-12, arranged in order of grade band. Links to the problem answers are available in this department.

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## Quick Blocks: Developing Spatial Sense

This article shares the importance of giving K-12 students opportunities to develop spatial sense. We explain how we designed Quick Blocks as an activity to engage our students in both spatial reasoning and number sense. Several examples of students thinking are shared as well as a classroom dialogue.

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## A STEAM Exploration of Tiny Homes

The incorporation of the “M” in STEAM must extend beyond simply a tool to address science and engineering standards (Authors, 2016; NCSM/NCTM, 2018). We present a mathematics- rich STEAM inquiry in which elementary students engaged in solving the issue of homelessness for one family in need.

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## English Learners' Participation in Mathematical Discussion: Shifting Positionings and Dynamic Identities

This study investigated discursive positioning moves that facilitated Latino/a English learners' (ELs) opportunities to take on agentive problem-solving roles in group mathematical discussion. A focus on mechanisms that support students' agentive participation is consistent with our view that recurrent experiences participating and being positioned in particular ways contribute to identity development. Findings suggest several ways that discursive positioning facilitated ELs' agentive participation, including via: (a) explicit statements that validated ELs' reasoning, (b) invitations to share, justify, or clarify thinking that positioned ELs as competent problem solvers, and (c) inviting peers to respond to an EL's idea in ways that positioned the idea as important and/or mathematically justified.