Journal of Math Circles

Biographical Sketch

Dr. Nicole Sullivant (formerly Fider) is an Instructor in the School of Math, Science, and Engineering at Central New Mexico Community College. She co-coordinated the Junior division of the Tucson Math Circle (along with Dr. Durón) at the University of Arizona from Fall 2020 through Spring 2022. Her research interests include applied math in the cognitive sciences, mathematical biology, and mathematics education. As a former MAA Project NExT fellow (Silver '19), she is passionate about teaching and seeks to explore active learning methods in her university-level classes and with the Tucson Math Circle.

Dr. Christina Durón is an Assistant Professor of Mathematics in the Natural Science Division of Seaver College at Pepperdine University. She has been part of the Tucson Math Circle at the University of Arizona since 2019. Her interests include mathematics outreach, open educational resources in mathematics, and supervising undergraduate work, particularly in her area of network theory and network analysis.

Dr. Douglas T. Pfeffer is an Assistant Teaching Professor in the Department of Mathematics at the University of Tampa. He obtained his doctorate in functional analysis from the University of Florida, where he specialized in the study of Toeplitz operators associated to constrained sublagebras of the disc algebra. Still active in the field of operator theory, his research now includes the study of nomography, where he includes undergraduate students from all backgrounds. His passion for community engagement has seen him participate virtually in the Tucson Math Circle at the University of Arizona, as well as co-found the Operator Theory Talks for Early Researchers (OTTER) community. As a former MAA Project NExT fellow (Silver '19), he also enjoys providing an active, engaging classroom experience for his students.


Symmetry is a natural property that children see in their everyday lives; it also has deep mathematical connections to areas like tiling and objects like wallpaper groups. The Tucson Math Circle (TMC) presents a 7-part module on symmetry that starts with reflective symmetry and culminates in the deconstruction of wallpapers into their ‘generating tiles’. This module utilizes a scaffolded, hands-on approach to cover old and new mathematical topics with various interactive activities; all activities are made available through free web-based platforms. In this paper, we provide lesson plans for the various activities used, and discuss their online implementation with Zoom, Miro, and the TMC Widget. We touch on the benefits and disadvantages of the online environment, and provide suggestions for moving these activities to an in-person format. We also include links to files in our Google Drive, where members of the Math Circle community can download our worksheets and Miro board templates.

Description of Program

The Tucson Math Circle predominantly serves students from Tucson, Arizona. It is currently divided into two divisions: Junior (suggested for grades K-6) and Senior (suggested for grades 7-12). The website for the circle may be found here: https://www.math.arizona.edu/~ime/tmc/. The director of the Tucson Math Circle is Ibrahim Fatkullin and the email address for the math circle is: math-circle@math.arizona.edu

Symmetry_Letter.pdf (121 kB)
Author response letter

Symmetry_Red.pdf (125491 kB)
Marked up manuscript (emailed 2/5/22)