Math Renaissance Book

Math Renaissance: Growing Math Circles, Changing Classrooms, and Creating Sustainable Math Education

(Rodi and Rachel)

Math Renaissance is for teachers and parents of children ages six and up. The authors share their insights on how math experience might be improved at home, school, and math circle. It is based upon Rodi Steinig’s experiences teaching math and leading math circles, and Rachel Steinig’s experiences as a school student and homeschooler.

In alternating chapters, Rodi tells stories about her math circle and exactly what happens there, while Rachel discusses why so many kids hate math, documents the ways math is taught in the classroom – and ways that can be improved. We hope that the book will help to uplift humanity by shifting math education toward inquiry, discovery, conceptual understanding, and lasting joy to mathematics.

The book gives voice to many students, parents, teachers, and administrators. It is a grassroots effort to make people aware of problems in math education, in hopes that you find new approaches that can be implemented in your home or classroom. We invite you to take from this book anything that might help you: validation of your feelings, math circles know-how, acknowledgment of your struggles, techniques for making the best of a hard situation, or classroom investigations of specific mathematical concepts.

We’ve learned that everybody can access the beauty and joy in mathematics. Parents, teachers, and mathematicians all have a vision of math being taught in a way that’s collaborative, profound, and accessible to everybody, a Math Renaissance if you will. In our book we hope to repair damaged relationships with math and enhance good ones.

Advance Praise

“Rachel’s is the voice of the silent majority of school students; it sounds authentic. This authenticity is the most important quality of her writing.”
– Alexandre Borovik, Professor of Pure Mathematics, University of Manchester

“Thought-provoking and entertaining. It opens up so many more possibilities for all of us experienced with traditional math instruction.”
– Paige Menton, parent and classroom teacher

“Empowering and eye-opening. It is exciting to think about math in this way! Rodi challenges assumptions about how math is taught and learned. Anyone who cares about math learning will find this book worthy of a good, hard, re-think session. Besides turning traditional math education on its head, Rodi also writes with a personal, humble and enjoyable voice, making it fun to read.”
– Melissa Church, parent and classroom teacher

“The truth can’t ring louder about the struggles of students. Everything that Rachel is saying is totally relatable, simply everything. Not only are her suggestions smart, her writing sneaks in small funny moments. She offers realistic situations that can be used in the classroom.”
– Amina Fong, high school student

Journal Articles

Honoring Robert and Ellen Kaplan (Rodi)

Rodi is serving as Co-Guest Editor for this Special Issue of the Journal of Math Circles.

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

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


Anthology Contributions

“The Smith Map” by Aurie Smith
(Rodi – Editor)

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”
G4G14 Exchange Book (Forthcoming, Spring or Summer 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

Panel Discussions

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



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


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.


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.


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

For the Princeton Review


  • Contributing Author to SAT/ACT Review/Reflect/Rank Process Activities
  • Contributing Author to SAT Course Manual, Version 6.0
  • Contributing Author to Cracking the GRE, 2014 Edition (Random House)
  • Contributing Author to Cracking the NTE, First Edition
  • Contributing Author to 11 Practice Tests for the SAT and ACT, First Edition (Random House)