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

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### Corey Webel and Sheunghyun Yeo

In this article, we share results from a field experience model in which junior-year methods classes were held in an elementary school and preservice teachers (PSTs) worked with a single student (a “Math Buddy") on mathematics for 30 minutes per day. We focus on the development of PSTs’ skills for exploring children’s thinking and the structures and tools that we used to support this development. Data sources include screencast recordings of interactions with Math Buddies and written reflections completed by PSTs. Although the responsiveness of interactions varied across individuals and interactions, in general, PSTs showed improvements in exploring children’s thinking. We share implications of these findings for similar field experience models and for practice-based approaches to teacher education generally.

### Min Wang, Candace Walkington, and Koshi Dhingra

An example of an after-school club activity gives educators some tools and suggestions to implement such an approach in their schools.

### Kathryn Lavin Brave, Mary McMullen, and Cecile Martin

The application of exact terminology benefits students when forming and supporting mathematical arguments virtually.

### Crystal Kalinec-Craig, Emily P. Bonner, and Traci Kelley

This article describes an innovation in an elementary mathematics education course called SEE Math (Support and Enrichment Experiences in Mathematics), which aims to support teacher candidates (TCs) as they learn to teach mathematics through problem solving while promoting equity during multiple experiences with a child. During this 8-week program, TCs craft and implement tasks that promote problem solving in the context of a case study of a child’s thinking while collecting and analyzing student data to support future instructional decisions. The program culminates in a mock parent–teacher conference. Data samples show how SEE Math offers TCs an opportunity to focus on the nuances of children’s strengths rather than traditional measures of achievement and skill.

### Esther M. H. Billings and Barbara A. Swartz

### Cory A. Bennett and Mick J. Morgan

Chalk Talks, a silent discussion protocol, can be used to begin developing cocreated norms. The insights gained shaped the support provided by both the teacher and students throughout the year.

### Karl W. Kosko

Use Cuisenaire™ Rods to emphasize the column-and-row structure in arrays for meaningful multiplication.

### Amanda L. Cullen, Carrie A. Lawton, Crystal S. Patterson, and Craig J. Cullen

In this lesson, third graders were asked how many degrees is a full rotation around a circle. After we gave students time and space to disagree, to make and test conjectures, and to explore, they reasoned about angle as turn and determined a full rotation is 360 degrees.