# Browse

### 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.

### Amber G. Candela, Melissa D. Boston, and Juli K. Dixon

We discuss how discourse actions can provide students greater access to high quality mathematics. We define discourse actions as what teachers or students say or do to elicit student contributions about a mathematical idea and generate ongoing discussion around student contributions. We provide rubrics and checklists for readers to use.

### Julie M. Amador, David Glassmeyer, and Aaron Brakoniecki

This article provides a framework for integrating professional noticing into teachers' practice as a means to support instructional decisions. An illustrative example is included based on actual use with secondary students.

### Sarah Kate Selling

To learn mathematical practices, students need opportunities to engage in them. But simply providing such opportunities may not be sufficient to support all students. Simultaneously, explicitly teaching mathematical practices could be problematic if instruction becomes prescriptive. This study investigated how teachers might make mathematical practices explicit in classroom discourse. Analyses of 26 discussions from 3 mathematics classes revealed that teachers made mathematical practices explicit primarily after students had participated in them. I present a framework of 8 types of teacher moves that made mathematical practices explicit and argue that they did so without turning practices into prescriptions or reducing students' opportunities to engage in them. This suggests a need to expand conceptions of explicitness to promote access to mathematical practices.

### Eric “Rico” Gutstein

This article provides an example of, and lessons from, teaching and learning critical mathematics in a Chicago public neighborhood high school with a social justice focus. It is based on a qualitative study of my untracked, 12th–grade mathematics class, a full–year enactment of mathematics for social and racial justice. Students were Black and Latin@ from a low–income, working–class community with a tradition of resistance. Any neighborhood student could enroll without selection criteria. The class goal was for students to cocreate a classroom in which they would learn and use collegepreparatory, conceptually based mathematics to study and understand social reality to prepare themselves to change it. Through analyzing my practice, I address possibilities and challenges of curriculum development and teaching, examine student learning, and pose questions and directions for further research and practice.

### Erin E. Baldinger, Sarah Kate Selling, and Rajeev Virmani

Leading a whole-class mathematics discussion is complex work. The teacher must attend to and respond to student thinking while continually keeping the mathematical goals of the discussion in mind. This work is especially challenging for novice teachers who are just learning to facilitate classroom talk. We present a new sortingtask instructional activity designed to support novice secondary teachers in steering a discussion toward a mathematical point while eliciting and making use of student thinking. We describe our efforts to support novice teachers through learning about, rehearsing, enacting, and reflecting on this sorting task. We document the impact of these supports for the novice teachers, and share ways that other teacher educators can take up this structure.

### Patricia F. Campbell, Masako Nishio, Toni M. Smith, Lawrence M. Clark, Darcy L. Conant, Amber H. Rust, Jill Neumayer DePiper, Toya Jones Frank, Matthew J. Griffin, and Youyoung Choi

This study of early-career teachers identified a significant relationship between upper-elementary teachers' mathematical content knowledge and their students' mathematics achievement, after controlling for student- and teacher-level characteristics. Findings provide evidence of the relevance of teacher knowledge and perceptions for teacher preparation and professional development programs.

### Katherine E. Lewis

Mathematical learning disability (MLD) research often conflates low achievement with disabilities and focuses exclusively on deficits of students with MLDs. In this study, the author adopts an alternative approach using a response-to-intervention MLD classification model to identify the resources students draw on rather than the skills they lack. Detailed diagnostic analyses of the sessions revealed that the students understood mathematical representations in atypical ways and that this directly contributed to the persistent difficulties they experienced. Implications for screening and remediation approaches are discussed.