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.

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### Katherine Baker, Naomi A. Jessup, Victoria R. Jacobs, Susan B. Empson, and Joan Case

### 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.

### Erell Germia and Nicole Panorkou

We present a Scratch task we designed and implemented for teaching and learning coordinates in a dynamic and engaging way. We use the 5Es framework to describe the students' interactions with the task and offer suggestions of how other teachers may adopt it to successfully implement Scratch tasks.

### John K. Lannin, Delinda van Garderen, and Jessica Kamuru

This manuscript discusses two important ideas for developing student foundational understanding of the number line: (a) student views of the number sequence, and (b) recognizing units on the number line. Various student strategies and activities are included.

### Debasmita Basu, Nicole Panorkou, Michelle Zhu, Pankaj Lal, and Bharath K. Samanthula

We provide an example from our integrated math and science curriculum where students explore the mathematical relationships underlying various science phenomena. We present the tasks we designed for exploring the covariation relationships that underlie the concept of gravity and discuss the generalizations students made as they interacted with those tasks.

### Jonathan N. Thomas and David M. Dueber

Through the use of rich examples, we examine the non-verbal ways in which teachers and students may communicate with one another. We will explore how gesture may be used to clarify and enrich interactions in the mathematics classroom.

Have you ever noticed a gap between research and practice? How can research effect change in the classroom? The Connecting Research to Teaching department of Mathematics Teacher (MT) invites classroom teachers to explore research findings in relation to their practice. MT also invites education researchers to demonstrate how results from their studies shape classroom practice. Findings from collaborative action research projects are also encouraged. Evidence of connections from research to practice commonly includes student work and brief transcripts from interviews or classroom videos.

The Editorial Panel of Mathematics Teaching in the Middle School is seeking submissions for a department titled Informing Practice. The articles written for this section should entice and invite classroom teachers to learn about aspects of research that are closely related to their classroom practice.

### Peter Kloosterman and Tracey L. J. Warren

*Computer Aided Assessment of Mathematics* focuses on assessment in college mathematics courses with a special focus on computer-based assessment as a means of providing partial credit and immediate feedback on student work. Written by Chris Sangwin, a senior lecturer in mathematics at the University of Birmingham in the United Kingdom, the book is an important resource for mathematicians or software developers interested in understanding the promise and the pitfalls of using computers to assess student work in college courses. Each chapter of the book addresses a different issue so readers have the option of reading most of them out of order or selecting the chapters that are most valuable to them. Thus, in addition to describing Sangwin's perspectives on teaching and assessing mathematics, this review is designed to help readers decide which chapters in the book will be useful to them.

### 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.