Three deliberate teaching practices can help students strengthen multiple connections to a unifying concept.

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### F. Paul Wonsavage

Three approaches to the Doughnut task highlight how representing functions in multiple ways can support student understanding in interpreting key features of functions within a context.

### José N. Contreras

### Megan H. Wickstrom

Preservice elementary teachers (PSTs) often enter their teacher preparation programs with procedural and underdeveloped understandings of area measurement and its applications. This is problematic given that area and the area model are used throughout K–Grade 12 to develop flexibility in students’ mathematical understanding and to provide them with a visual interpretation of numerical ideas. This study describes an intervention aimed at bolstering PSTs’ understanding of area and area units with respect to measurement and number and operations. Following the intervention, results indicate that PSTs had both an improved ability to solve area tiling tasks as well as increased flexibility in the strategies they implemented. The results indicate that PSTs, similar to elementary students, develop a conceptual understanding of area from the use of tangible tools and are able to leverage visualizations to make sense of multiplicative structure across different strategies.

### Nicole Garcia, Meghan Shaughnessy, and D’Anna Pynes

Representing and recording student thinking in public spaces during mathematics discussions is challenging work. We share principles for recording student thinking in the moment and share an activity for improving your recording practice.

### Emiliano Gómez, Risa A. Wolfson, and Introduction by: Trena L. Wilkerson

When implementing this task, you see multiple effective teaching practices at play (

### Michael Daiga and Shannon Driskell

The two provided activities are geared for students in middle school to facilitate and deepen their understanding of the arithmetic mean. Through these activities, students analyze visual representations and use a special type of statistical thinking called transnumerative thinking.

### Nina G. Bailey, Demet Yalman Ozen, Jennifer N. Lovett, Allison W. McCulloch, and Charity Cayton

Three different technological activities to explore parameters of quadratic functions each has its own pros and cons.

### Thomas Edwards, S. Asli Özgün-Koca, and Kenneth Chelst

A quadratic equation was the basis for activities involving both concrete and technological representations.

### Christine Taylor and Jean S. Lee

We implemented a STEM task that highlights the engineering cycle and engages students in productive struggle. Students problem solved in productive ways and saw tangible benefits of revising their work to achieve mathematical goals.