Ear to the Ground features voices from several corners of the mathematics education world.

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### Mollie Siegel, Cathy Sinnen, and Penny Smits

### Lybrya Kebreab, Sarah B. Bush, and Christa Jackson

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.

### Erin Smith

Teachers’ positioning can affect multilingual learners’ participation, identity, and mathematical success. Learn what positioning is and how to productively position multilingual learners in your classroom.

### Amanda K. Riske, Catherine E. Cullicott, Amanda Mohammad Mirzaei, Amanda Jansen, and James Middleton

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.

### Katherine Baker, Naomi A. Jessup, Victoria R. Jacobs, Susan B. Empson, and Joan Case

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.

### LouAnn H. Lovin

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.

### Tracy E. Dobie and Miriam Gamoran Sherin

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.

### Dr. Zandra de Araujo, Ms. Deborah Hanuscin, and Ms. Samuel Otten

In this paper we discuss different ways teachers can integrate science and mathematics into their curriculum. In particular, we focus on science and mathematics integration via the disciplinary practices.

### Susan Baker Empson, Victoria R. Jacobs, Naomi A. Jessup, Ms. Amy Hewitt, D'Anna Pynes, and Gladys Krause

The complexity of understanding unit fractions is often underappreciated in instruction. We introduce a continuum of children's understanding of unit fractions to explore this complexity and to help teachers make sense of children's strategies and recognize milestones in the development of unit-fraction understanding. Suggestions for developing this understanding are provided.