Publications

The Signaling Problem: Using Exploding Dots to Solve an Accessible Mystery in an Elementary-Aged Math Circle (Rodi)

ABSTRACT: Many people want to facilitate Math Circles for younger students but don’t know how. This article provides a model for how to create an engaging Math Circle for students aged 8-10 to explore different number bases and gives a detailed narrative to guide prospective instructors through the class. The narrative follows a group of eight students spending six weeks joyfully discovering underlying mathematical structure without being told what to do.  Read the article

Stop Ruining Math! Reasons and Remedies for the Maladies of Mathematics Education
(Rachel) 

ABSTRACT: Did you love math as a kid? Or was it ruined for you? Sadly, many people have had math ruined for them for various reasons. Some might say that it was because of not understanding what was going on, being bored in class, parental or societal pressure to achieve in math, not seeing a point in learning math, wrong amount of homework, grades, curriculum, physical concerns, mean teachers, or any number of things. This article delves into the many common reasons why math is ruined for so many kids, and offers solutions so that math can be enjoyable for everyone. Some of the solutions include societal shifts, some are things that math teachers can do in the classroom, some are ways parents can shift their attitudes towards math, therefore creating a healthier home culture surrounding math, and, lastly, some are ways that students can change the way they participate in math class to get the most out of it.  Read the article

(Response to Stop Ruining Math! by ALEXANDRE BOROVIK in the De Morgan Gazette: COMMENTS ON “STOP RUINING MATH! REASONS AND REMEDIES FOR THE MALADIES OF MATHEMATICS EDUCATION ”)

Introduction to the Special Issue Honoring Bob and Ellen Kaplan (Rodi, with Amanda Serenevy)

ABSTRACT: In 1994, Bob and Ellen Kaplan embarked together with other friends and colleagues on a wonderful adventure. Friends had lamented that there was a lack of high-quality math learning experiences for kids along the lines of the Math Circles offered in the former Soviet Union, so the Kaplans decided to do something about it. This special issue is dedicated to a remembrance of that adventure and its impact on the mathematical and personal development of many people. Read the article

Corresponding with the Kaplans (Rodi)

ABSTRACT: Readers of this journal have asked to hear the Kaplans’ voices: their tone, the way they were able to contextualize math questions, their generosity, and their joy. We think it’s important to share a few of these hundred-plus emails so that readers can feel that tone. Read the article

The Kaplans’ Influence on the History of Math Circles in the US: an Interview with Tatiana Shubin

ABSTRACT: Tatiana Shubin [1] was among those who pioneered Math Circles on the West Coast of the United States in the 1990s. She continues to innovate and pivot to make the Math Circle message and experience accessible to all. At the 2021 Circle on the Road conference, Tatiana Shubin presented the talk “Math Circles: A Quick Early History,” and the recording is archived on the Math Circle Network webpage [2]. In the spring of 2022, Rodi Steinig interviewed Tatiana to discuss this talk through two lenses. First, the lens of the role the Kaplans played in the broader history of Math Circles in the United States (see the article on this topic in the Notices of the AMS [3]). Second, the lens of the three aspects of the Journal of Math Circles: math, math community, and problem solving — especially mathematical engagement and habits of mind. In this article, Tatiana talks about how Bob and Ellen brought people together in community to re-frame the thinking of everyone present. Read the article

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How I Stage Mathematical Magic Tricks for Children, by Rodi
G4G16 Exchange Book, 2026

ABSTRACT: This is a short essay that gives tips on how to stage child-friendly tricks for dramatic and educational effect. (I find that it’s not enough just to know how to perform the trick.)

“The Smith Map” by Aurie Smith
(Rodi – Editor)
G4G15 Exchange Book, 2024

ABSTRACT: This map was designed by a ten-year-old Math Circle participant, Aurie Smith, in a course that studied the Four-Color Theorem, Martin Gardner, and the McGregor Map. Smith challenges people to completely color the map in four colors, to determine whether it’s possible to color it in fewer than four colors, to identify how many ways there are to color it in four colors, and to identify the regions of the map that require adding colors.
View the map and read the map creator’s statement

“Dear Mister Gardner: Apocryphal Letters from Children to Martin Gardner”
(Rodi)
G4G14 Exchange Book (2022)

ABSTRACT: In the fall of 2014, a group of six students got together for an hour per week to celebrate the Gardner Centennial. The students were all ten years old. They met in a Math Circle to explore Gardner’s life, influence, and mathematics. The mathematical goal of the course was to develop students’ mathematical thinking by seeking patterns when none are obvious and by seeking ways to crush seemingly-obvious patterns that aren’t really patterns at all. The students experienced great joy while doing so. The facilitator kept a written record of the students’ reactions, work, comments, and questions, all of which have been reorganized by the facilitator into a series of letters to Martin Gardner. The letters are paraphrased with some direct quotes interspersed, with the hope that Mister Gardner would have enjoyed reading them.

“On Noticing and Fairness” (Rodi), Playing with Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers, edited by Sue vanHattum 

EDITOR’S INTRODUCTION: “Rodi is the best observer of Math Circles I know, perhaps because of her mindfulness practice. These observational skills, along with the historical vignettes she shares with her students, enrich her circles and her writing.”
Read the article



“How to Become Invisible” by Bob Kaplan and friends (Rodi – data collection), Playing with Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers, edited by Sue vanHattum 

EDITOR’S INTRODUCTION: “This was a group effort, starting out as Rodi Steinig’s transcription of Bob Kaplans commentary as he led math circles at the 2011 Summer Institute, and then evolving with help from Maria and me and a few additions from a blog post by Joy Kogut.”
Read the article

New Books in Mathematics – (Rachel and Rodi)

KidsLab (Rodi and Rachel) #kidslabpodcast

“Mathematical Storytelling”
(Rodi – panel participant), JRMF Math Buffet

SIGMAA on Circles and the Math Circle Network

An Inquiry-Based Approach to the Handshake Problem
(Rodi), Invited Speaker; Math Circle Workshop Webinars: Thinking, Playing, Discovering; 2026

ABSTRACT: I like to tell my Math-Circle students absolutely nothing. If I want to tell them something, I use Socratic questioning to get them to say it. But no, wait, that’s not really it. I actually want to “teach with my mouth shut” in a more inquiry-based way, which can be challenging. Earlier this academic year, I started posing some graph theory questions to my 8-11 year old students. A few weeks in, outside of a graph-theory context, I presented The Handshake Problem. “Imagine that everyone in this room is invited to a party but we don’t know each other at all. We shake hands with everyone else. How many handshakes occur?” So far, students have developed four different problem-solving methods to ultimately find the answer for our class size of 13 people. I say “so far” because, months later, my students just solved it for the case of n=10. I want them to be able to generalize to any number; the students have naturally become curious about this. I also want them to discover that the solution follows the same pattern that triangular numbers do because I find that beautiful. But the students have never even heard of triangular numbers. In this talk, I’ll share both the pedagogical choices I’m making and the problem-solving strategies that my students are inventing.

FUNDAPROMAT

The Emotional Experience of Math
(Rodi), Invited Speaker, Twenty-Sixth Math Webinar In English, 2024

ABSTRACT: It’s been said that the study of mathematics is unemotional. But it’s also been said that math is the most emotional subject of all the disciplines. Let’s discuss why math evokes such strong emotions in people. We’ll play a quick game of “Never Have I Ever” to calculate our own unscientific EMEs (Emotional Mathematics Experiences) score. Then Rodi will share findings and recommendations from her own observations and experiences and from the writings of experts in human rights, emotional development, education, and mathematics instruction. The goal is to walk away with new insights and hope about how to move the needle forward in people’s K12 mathematical experiences.

JOINT MEETINGS OF MATHEMATICS

Working the Hadwiger-Nelson Problem with Young Children
(Rodi, 2027 – forthcoming) Chicago, IL

ABSTRACT: The Hadwiger-Nelson Problem is an open geometric graph-theory problem about the chromatic number of the plane. In this talk, I will share an interpretation of the problem that a group of 7-year-olds explored for six weeks: the math questions the students explored, student questions and reactions, and the evolution of their understanding of the problem.

Reimagined Use of Space in a Math Circle: from Serendipity to Intentionality
(Rodi, 2026) Washington DC

ABSTRACT: Since 2011, the Math Renaissance Math Circle has operated in six different spaces, none of which are conventional classrooms. Each space initially posed different logistical challenges: lack of board; no desks/tables; nothing to sit on; too much outside noise; physical hazards; catering events; dampness; and much more. We adapted to these challenges in ways that benefited students’ mathematical experiences and now have intentionally integrated these adaptations to enhance mathematical thinking.

Body Art and Geometry
(Rodi) 2025, Seattle WA

ABSTRACT: Over a decade ago, I teamed up with artist/acupuncturist Gina Gilbert to co-facilitate a Math Circle course called The Nexus of Sacred Geometry and Henna that combined the math of sacred geometry with the ancient art of Henna, also known as Mehndi. A temporary way of decorating the body (or other materials), Henna offers an opportunity to study geometric shapes, patterns, and symbols that have been used worldwide since ancient times. Sacred geometry is based upon the premise that certain patterns, ratios, and geometries are consistently repeated in nature. Students studied the mathematics and history underlying sacred geometries of many cultures while mixing henna, devising applicators, and learning application methods. The end goal was the creation of personal sacred geometric symbols.

In this talk, I will share some of the mathematical concepts students explored and the art they produced. Then I will discuss the impact of this cross-disciplinary course on students’ mathematical thinking and mindsets. Finally, I’ll reflect on the pedagogical decisions I made and my decade-later perspective on those choices.

Lessons Learned from the Kaplans,
(Rodi) 2025, Seattle WA

ABSTRACT: In 2011, I came to my first teacher training for Math Circles at Notre Dame with Math Circle pioneers Bob and Ellen Kaplan. I arrived with a pedagogical background of inquiry-based, student-directed, “teaching with your mouth shut” (quoting Finkel) pedagogy. I was ready to learn how to pour this philosophy into my nascent Math Circle. I reveled in the instruction and in Bob’s and Ellen’s method. In this talk, I will share my joy in “becoming invisible” (quoting the Kaplans) as a Math Circle facilitator. I will also discuss how my own pedagogy has evolved based upon my audience: my doubts, my questions, my experience, my hope, and my joy. I will share what (slight!) adjustments I have made to my philosophy of being a Kaplan purist. This experience and reflection has evolved from two Kaplan trainings, a visit to their Math Circle in Boston, a decade-long email correspondence with Bob and Ellen, and 14 years leading my own small Math Circle.

Engaging Math-Circle Topics that Have Attracted Girls 
(Rodi), virtual 2022

Sixteen Math-Circle course topics have attracted a student demographic of over 60% girls to the Math Renaissance (formerly Talking Stick) Math Circle. All sixteen of these topics, including Sacred Geometry, The Eye of Horus, Gardner, Fermat, Proofs, Compass Art, and Embodied Mathematics, will be described in this session, with the goal that session participants can recreate the activities in their own Math Circles. In addition, there will be a quick overview of the commonalities in these topics, the trends in offered topics that did not attract many girls, and the other variable that may have influenced these demographics.

MAA Minicourse: How to Run Successful Math Circles for Students and Teachers 
(Rodi was a last-minute substitute for one of the three presenters), Baltimore, MD, 2019

MATHFEST

Joyful Virtual Math Circles via Game Theory (Rodi) Philadelphia, PA, 2022

In the spring of 2022, the Math Renaissance middle-school Math Circle met virtually for eight 90-minute sessions to study Applied Mathematics. Student reaction quickly steered this course into an in-depth study of game theory and decision theory. Using 9 classic problems, students explored how math can model human behavior, some limitations of such modelling, and how we can use math to gain insight on real-world problems and, frankly, on ourselves. In this talk, I will describe these classic problems, the math involved, student reactions, our use of technology, and the joyful conversation that inspired me to offer this course in the first place.

A Hodgepodge of Non-Traditional Games (Rodi), virtual 2021

Merriam Webster’s definitions of games include the terms “rules,” “strategy,” “struggle,” “procedure,” “diversion,” and “amusement.” In Math Circles, how can we play games that are cooperative? How can we use role-playing? How can we entice reluctant students into competitive games? What games can we play with the youngest of students? What games can be used to help students focus and build frustration tolerance? How can we add complexity to classic games to facilitate deeper mathematical explorations? In this session, we’ll play “Would You Rather,” “Math Lawyer,” “Odd One Out,” “Knights and Liars with Puppets,” “The Need for Numbers,” “Mathematician Cards,” “Math Red Light Green Light,” “Mother May I Addition,” “Opposite Simon Says,” and “How Is this Math?” What do all these games have in common? Each involves strategies for success and meaningful mathematical thinking. Audience participation is encouraged but not required.

GATHERING 4 GARDNER

My Evolutionary Stages toward Becoming a Magician
(Rodi), G4G16, San Francisco, 2026

ABSTRACT: G4G has helped me overcome preconceived notions about magic and to develop appreciation for it. In this talk, I’ll explain my former buy-in to stereotypes, my three turning points, and my current evolutionary stage toward becoming a magician myself.

Bringing G4G to Children
(Rodi), G4G15, Atlanta, 2024

ABSTRACT: I brought the actual G4G14 gift bag to my Math Circle and shared the items in it with my students (ages 9-12). I’d like to tell you of their reactions and encourage you to do the same.

MATH CIRCLES ON THE ROAD CONFERENCES

What can we do for students who hate or fear math?
(Rachel) New York, NY, 2016

ABSTRACT: I posit that students who don’t like math are an underserved group in math enrichment programs. What do these kids need and how can we help them? I will share my research on the attitudes and needs of people who feel that math was ruined for them. I will delve into the reasons why so many kids hate and fear math, and why they may have faulty assumptions about math. Then the group will brainstorm ways to engage and support these students in Math Circles and in mathematical enrichment programs in general.

Using Mystery and Excitement to Draw Student into “Dry” Topics
(Rachel) New York, NY, 2016

ABSTRACT: Do you ever wonder how to draw students into topics like algebra, averages, statistics, and more? These kinds of middle school topics are often taught in a dull manner, and many students find themselves dreading learning them. However, you can stimulate intrinsic motivation by introducing excitement and mystery, thereby drawing students in.

Would you rather die in a pit of alligators or get permanently lost in space? Compelling question, right? How would you like to play a math version of the game “Would You Rather?” Guess what – you can! At the same time, you’d be learning the conceptual foundations of middle-school statistics.

In addition to playing that game, we will play “Function Machines” to introduce algebraic concepts such as variables, equations, graphing, sequences, and functions and their inverses. Leave this circle with ideas on ways to make middle school math topics more interesting, accessible, and appealing, as they were for me. I was introduced to these topics as a Math Circle student and left wanting to learn more.

Involving Students in Math Circle Leadership
(Rachel and Rodi) New York, NY, 2016

ABSTRACT: When students take on leadership roles in Math Circles, they feel more ownership and learn better. We will share the many ways in which students are more than participants in the Talking Stick Math Circle.

“Classroom Management Strategies in Elementary-Aged Math Circles”
(Rodi) New York, NY, 2016

ABSTRACT: Paper-airplane throwing, “bathroom” talk, running around, shouting: some find daunting the idea of facilitating circles for this age group for fear of such happenings. What are some best practices for managing the room, the students, and the discussion topics so that student freedom is maintained and behaviors that impinge on others’ freedom is prevented? In this session, participants will share classroom management challenges, then brainstorm both proactive and reactive solutions. Share your fears and/or experiences to discover how students can channel their playful energy into the deep mathematical thinking that young children are capable of.

“Mathematical Role Playing with Young Children”
(Rodi) New York, NY, 2016

ABSTRACT: Role playing greatly increases students’ motivation for, interest in, and ownership of a topic. In this session, “students” will play roles and use puppets in order to feel the need for numbers, and see how conceptualizing number is not only about counting. In order to feel a need for numbers, participants will dramatize scenes from pre-numeric history by improvising dialogues without using numbers. Then participants will dramatize a real-life experiment on number sense in crows. Finally, the group will act out the song The Ants Go Marching. These activities will reveal other aspects of number such as subitizing, unitizing, and exponentiating – three concepts that can get short-shrift in the classroom.

“The Accessible Mystery”
(Rodi), Mayaguez, PR, 2013

ABSTRACT: According to Bob and Ellen Kaplan, one key to a successful Math Circle is an “accessible mystery.” I will share some mathematical mysteries that my students have found quite accessible, some that turned out to be inaccessible, and the general characteristics of both. Then I will work with workshop attendees to create a new and hopefully accessible mystery to take home.

“Eight Things I Try to Remember”
(Rodi), Mayaguez, PR, 2013

“Function Machine Garden” Demonstration Math Circle
(Rodi) Mayaguez, PR, 2013

ABSTRACT: In this session, the leader will tell a dramatic story about a Creature who steals a child’s valuable treasure, then issues a mathematical challenge that the child must conquer to win the treasure back. The students will join the fictional child in an obstacle course of function machines in the Creature’s garden; each solution is a clue. In a function-machine problem, students use given input and output numbers to deduce a corresponding rule. For young children (ages 5-7), the challenge is to deduce the rules of multiple function machines. For children ages 8-10, the challenge is to deduce rules and their inverses. For middle-school students (11-13) the challenge is to deduce rules, combine them to form a compound function, and then create its inverse.

MATH CIRCLE MENTORSHIP AND PARTNERSHIP WORKSHOP

My Favorite Math Circle Moment
(Rodi), Denver, CO, 2015

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