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## Discourse Actions to Promote Student Access

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.

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## Envelope Curves Unify Sinusoidal Graphing

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.

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## Giving Birth to Inferential Reasoning

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.

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## Practices for Mathematics and Science Integration

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.

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## Then: Surprisingly Impactful Past Mathematics Education Events

In celebration of NCTM's 100th birthday I'm very pleased to have this opportunity to share this retrospective on two early career events that had a big impact on mathematics education nationally and internationally, and turned out to be surprisingly instrumental in my own professional development.

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## Quick Blocks: Developing Spatial Sense

This article shares the importance of giving K-12 students opportunities to develop spatial sense. We explain how we designed Quick Blocks as an activity to engage our students in both spatial reasoning and number sense. Several examples of students thinking are shared as well as a classroom dialogue.

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## Reveal Limitations through Fraction Division Problem Posing

Students notoriously struggle with division of fractions in 5 key areas. Hear what those 5 areas are and how recommendations address the limitations.

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## Conceptualizing Mathematics Using Narratives and Art

To support mathematical investigations, use this framework to guide students in constructing art-based and technology-based literature.

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## Beyond the Write Answer: Mathematical Connections

Allowing students to write in mathematics class can promote critical thinking, illustrate an awareness of mathematical connections, and result in clear communication as they share ideas comfortably with peers.

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## For Whom the Tolls Charge

### when will I ever use this

Calculating tolls based on miles traveled provides the real-life tie-in to this activity involving rates.