Mathematics abounds in the beauty of the seasons. Where you live, work, or travel, how do you engage with and explore the wonders of math in our natural world?

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## Mathematical Wonders and Reasons Abound in the Seasons

### Maria Franshaw

## Perspectives from Physics: Constraints on Our Curriculum

### Victor Mateas

How trigonometry is used and portrayed differently in mathematics and physics textbooks highlights potential sources for student struggle, constraints on our trigonometry curriculum, and lessons learned when looking across STEM disciplines.

## Mathematical Connections: Many Faces of the Truncated Icosahedron

### Enrique Ortiz

Examine this geometric figure in light of a set of connections among fields such as architecture, geometry, science, sports, technology, and associated uses, models, and discoveries.

## Sea of Cycles

### Paula Beardell Krieg

This article presents an example of discovering an idea through creative play. After some trial and error, I drew a wonderful image, which I later learned was a two-dimensional view of a four-dimensional shape called tesseract.

## Code of the Rings

### Wood Sophia

## Integrating Machine Learning in Secondary Geometry

### Joshua Jones

Despite the importance of artificial intelligence in our daily lives, it has yet to be integratedinto K–12 classrooms in a meaningful way. Explore a lesson in which geometry students useEuclidean distance to implement a functional machine learning algorithm in Google Sheets™.

## Supporting Probability Understanding through Area Models

### LouAnn H. Lovin

Moving beyond memorization of probability rules, the area model can be useful in making some significant ideas in probability more apparent to students. In particular, area models can help students understand when and why they multiply probabilities and when and why they add probabilities.

## Linking Factors and Multiples to Algebraic Reasoning

### George J. Roy, Jessica S. Allen, and Kelly Thacker

In this paper we illustrate how a task has the potential to provide students rich explorations in algebraic reasoning by thoughtfully connecting number concepts to corresponding conceptual underpinnings.