The Common Core State Standards for Mathematical Practice asks students to look for and make use of structure. Hence, mathematics teacher educators need to prepare teachers to support students’ structural reasoning. In this article, we present tasks and rubrics designed and validated to characterize teachers’ structural reasoning for the purposes of professional development. Initially, tasks were designed and improved using interviews and small pilot studies. Next, we gave written structure tasks to over 600 teachers in two countries and developed and validated rubrics to categorize responses. Our work contributes to the preparation and support of mathematics teachers as they develop their own structural reasoning and their ability to help students develop structural reasoning.

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## Characterizing Secondary Teachers’ Structural Reasoning

### Stacy Musgrave, Cameron Byerley, Neil Hatfield, Surani Joshua, and Hyunkyoung Yoon

## Experience First, Formalize Later

### Sarah Stecher, Luke Wilcox, and Lindsey Gallas

The EFFL model empowers students to build strong conceptual understanding of mathematics through carefully designed, equity-minded activities that disrupt the traditional lecture-based classroom.

## Math-Inspired Artwork

### Alessandra King, Sophia Ouanes, and Claire Doh

Students and teachers enjoy exploring the boundaries between mathematics and art.

## Technology and Median Income Data: Opening Doors

### Gail Burrill, Joan Funderburk, Becky Byer, and Rachael Gorsuch

Classroom stories show how using technology to investigate the wage gap provided opportunities to develop students’ identities and agency and enabled a classroom culture of sharing and risk-taking.

## Enacting Co-Craft Questions Using Flexible Teaching Platforms

### T. Royce Olarte and Sarah A. Roberts

Teachers can implement a mathematics language routine within in-person/hybrid and remote instructional contexts.

## Rethinking Wait Time: What Can 3 Seconds Do?

### Kathryn Early, K. Elizabeth Hammonds, Brea Ratliff, Mariya Rosenhammer, and W. Gary Martin

A high-leverage strategy first discussed more than 50 years ago, wait time has many benefits for both teachers and students yet is not used to its full potential. See how it can enhance your students’ mathematical discourse.

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Variations on a Theme of Fibonacci^{
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### Sheldon P. Gordon and Michael B. Burns

We introduce variations on the Fibonacci sequence such as the sequences where each term is the sum of the previous three terms, the difference of the previous two, or the product of the previous two. We consider the issue of the ratio of the successive terms in ways that reinforce key behavioral concepts of polynomials.

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S^{3}D: Small-Group, Student-to-Student Discourse

### Sarah Quebec Fuentes

Learn about strategies and tools to examine and improve your practice with respect to fostering equitable small-group, student-to-student discourse.

## Exploring Geometry with Origami One-Cut-Heart

### Lauren R. Holden, Yi-Yin (Winnie) Ko, Devon W. Maxwell, Connor A. Goodwin, Cheng-Hsien Lee, Jennifer E. Runge, and Elizabeth B. Beeman

One-Straight-Cut-Heart activities can help teachers support students’ engagement with geometry and can deepen students’ geometric reasoning.

## Using School Mathematics to Develop Students’ Data Literacy Skills

### Joshua David Jones

To be literate in a society where the information shared online is often exploited, learners should be exposed to multiple aspects of contemporary predictive modeling. Explore a lesson in which students learned an algorithm used in practice to automate the process of making recommendations.