An online activity provides instructional strategies that can help students engage in mathematical modeling and autonomous learning.

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## Digital Learning Routes: An Example of Mathematical Modeling

### Salomé Martínez, Flavio Guiñez, and Darío González

## Construct It! Progressively Precise: Three Levels of Geometric Constructions

### Carmen Petrick Smith

This article shares an activity scaffolding the construction of the circumcenter of a triangle, culminating with a Triangle-Ball Championship game.

## Characterizing Secondary Teachers’ Structural Reasoning

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

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.

## The Do Nothing Machine

### Keith Dreiling

The Trammel of Archimedes traces an ellipse as the machine’s lever is rotated. Specific measurements of the machine are used to compare the machine’s actions on GeoGebra with the graph of the ellipse and an ellipse formed by the string method.

## 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.

## Using Series to Construct Pythagorean Triples

### Darien DeWolf and Balakrishnan Viswanathan

This article provides a series-focused approach to computing Pythagorean triples.

## Algebraic Thinking in the Context of Spatial Visualization

### Arsalan Wares and David Custer

This pattern-related problem, appropriate for high school students, involves spatial visualization, promotes geometric and algebraic thinking, and relies on a no-cost computer software program.

## The Exponent Maze: An Opening for Creativity

### Kira Rivera and David Peabody

When students create their own exponent mazes, their creativity and problem-solving abilities flourish.

## Math-Inspired Artwork

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

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

## Conceiving Phase Shift as Time Travel

### Jeffrey Connelly and Pablo Garcia

Two teachers use homemade pendulums for their students to explore phase shift in sine curves. The use of Desmos’s Activity Builder enabled students to become mathematical explorers and supported their sense of mathematical agency.