The Asked & Answered department shares excerpts from discussion threads on the online MyNCTM community. In this issue, featured threads highlight responses to members' questions related to mathematical depth in preschool, spiral review in the upper elementary grades, ideas for differentiation in middle school, and projects for high school algebra.

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### 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.

### Christopher Harrow and Nurfatimah Merchant

Transferring fundamental concepts across contexts is difficult, even when deep similarities exist. This article leverages Desmos-enhanced visualizations to unify conceptual understanding of the behavior of sinusoidal function graphs through envelope curve analogies across Cartesian and polar coordinate systems.

### Ryan Seth Jones, Zhigang Jia and Joel Bezaire

Too often, statistical inference and probability are treated in schools like they are unrelated. In this paper, we describe how we supported students to learn about the role of probability in making inferences with variable data by building models of real world events and using them to simulate repeated samples.

### Kelly Hagan and Cheng-Yao Lin

April 2020's GPS department provides tasks for each grade band that invite students to reason with age-appropriate number theoretic concepts.

### Sandra M. Linder and Amanda Bennett

This article presents examples of how early childhood educators (prek-2nd grade) might use their daily read alouds as a vehicle for increasing mathematical talk and mathematical connections for their students.

### Chris Luzniak

Debate and discussions have often been staples of humanities classrooms. However, as Elham Kazemi states “everything we know about student learning and classroom practice tells us that classroom conversations are crucial to mathematics learning.” Let's explore ways to incorporate short debates into everyday math lessons.

### 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.

### Zachary A. Stepp

“It's a YouTube World” (Schaffhauser, 2017), and educators are using digital tools to enhance student learning now more than ever before. The research question scholars need to explore is “what makes an effective instructional video?”.