San Jose Math Circle
Involving Students in the Beauty and Power of Mathematics
By Molly A. Walker
The San Jose Math Circle (SJMC) in Northern California is one of the nation’s oldest math circles, with its beginnings in 1998. Prior to the pandemic, the math circle offered two parallel weekly meetings for middle (seventh and eighth grade) and high school (ninth through 12th grade) students. About 60 youth gathered in a classroom at San José State University on Friday evenings for 2 hours to tackle difficult, original and always fun mathematical problems. In September 2020, the circle moved to online instruction, running a single group of about 40 students in grades 7 through 11.
In addition to hosting weekly meetings, SJMC is also a co-sponsor of Bay Area Mathematical Adventures (BAMA), a series of public lectures featuring renowned mathematicians, which “circlers” are encouraged to attend. The circle is also part of the annual Bay Area Mathematical Olympiad, typically held the last Wednesday in February at Bay Area schools.
Origins and Leadership
How did SJMC get its start? In 1998, co-founders Tatiana Shubin and Tom Davis attended a talk by Zvezdelina Stankova, founder of the Berkeley Math Circle, who discussed math circles in Soviet bloc countries, and how she wanted to start similar math programs and a math contest in the San Francisco Bay Area.
While Tatiana is credited with doing most of the early work to get the math circle going, the backing and enthusiasm for the program offered by many individuals and two math institutes — the American Institute of Mathematics (AIM) in San Jose and the Mathematical Sciences Research Institute (MSRI) in Berkeley — were crucial. Other early SJMC co-founders and co-directors were Brian Conrey, director of AIM; David Hayes, San José State math professor, now retired; and Raghu Subramanian, founder and CEO of startup Nonadoo, then a recent PhD in electrical engineering. Longtime SJMC leaders also include Joshua Zucker, a veteran instructor with the Art of Problem Solving, along with Alon Amit, vice president at Intuit. Tom Freeman, retired computer software professional, served as an SJMC director for 10 years before moving to Arizona; he continues to help out with the math circle long-distance.
“The best part for me is working with the kids,” says SJMC co-founder Tom Davis. “There are always a few who are a lot smarter than I am, but I have the advantage of 50 more years of mathematics work, so we’re evenly matched. When I lead a session, I am totally engaged, and after an evening session, I am sometimes so energized that I have a hard time sleeping. I often attend sessions by other leaders and that gives me ideas for my own future sessions, and I learn some cool math.”
“Kids are naturally inquisitive and curious,” says SJMC co-founder Tatiana Shubin, who recently retired as a math professor at San José State University. “They are not satisfied with an approach often taken in their school math classes: ‘Here’s an algorithm, just memorize it and apply it to crunch numbers.’ True, algorithms are useful, but mathematics is so much more than that. At SJMC we want to involve students in the real beauty and power of mathematics through hands-on investigation and challenging yet deeply satisfying problems. We also believe that it is extremely important for students to meet their like-minded peers and to exchange ideas with them and with professional mathematicians.”
“Tatiana Shubin invites a variety of mathematicians to lead the sessions, each with a particular passion and teaching approach. I consider these differences and diversity of topics one of the best parts of the math circle,” says Aida Rivera, SJMC parent and administrator.
Tom Davis describes what it was like in the early days. “At first it was hard just getting students to attend. Nobody knew what a math circle was,” he recalls. “After just a couple of years, however, it became easier, with the siblings or classmates of attendees showing up. Sometimes local teachers would recommend the circles to their students.”
Joshua Zucker is equally enthusiastic about his math circles work. “Students get excited and discover new things — sometimes even new things for me! Last year at San Jose we explored what happens if you take all the ways of writing a list of numbers that have a certain total, say 7, and organize them based on how many 1s are used. For instance, with no 1s, you have 7, 5+2, 2+5, 4+3, 3+4, 3+2+2, 2+3+2, 2+2+3. If you use some 1s you get a lot more possibilities for a while, but not so many options with five or seven of them (and no possibilities with exactly six 1s!). We discovered a bunch of patterns that I had never seen before as we dug more deeply into this, and eventually found reasons why those patterns occurred.”
Joshua says the hardest part of any instruction is what to do with the students who seem disengaged. “You wonder if they are just confused, and with some help will get back to a problem. Or are they just not interested in the topic? Or maybe they don’t want to be there and are only sitting in the room because their parents are forcing them to come? How much should I slow down (and risk being boring for some of the students) to try to get these people back on track?
“Sometimes when they’re not very confident about what’s going on, it’s a challenge to get the students to take risks — to speak up or try to answer a question or offer an idea,” he adds. “On the other hand, one of the big successes sometimes is getting them to be more comfortable with the feeling of not knowing what’s going on. That’s a lot of what life as a mathematician is!”
Student Success Stories
Parent and math circle administrator Aida Rivera’s three children have all benefited from SJMC. “When Tatiana met my son Sebastián Urdaneta in 2015, she invited him to join SJMC,” says Aida.
Now a student at Foothill College in California, Sebastián joined SJMC in seventh grade and found the experience a revelation. “I encountered a new side of math I had not seen before. I was in awe at how the professors would introduce a seemingly simple topic and expand it into something deep,” says Sebastián. “I was able to explore many topics with people who really knew the material and were very happy to share their know-how with us.”
After going through SJMC’s middle school and high school programs, Sebastián decided he wanted to remain part of SJMC and now contributes to the math circle community as an assistant. “It is pretty neat to see the spark of curiosity that I had in me in the faces of the younger students!” he says.
Another involved parent who is also a math teacher is Iulia Rusu. Born in Eastern Europe, Iulia was familiar with the math circle model. When she learned about SJMC, she encouraged her daughter Inimai Subramanian to apply.
Last summer, Iulia and Inimai had the opportunity to attend the Alliance of Indigenous Math Circles (AIMC) Math Camp at Navajo Prep in Farmington, New Mexico, with Tatiana Shubin, who in addition to co-founding the SJMC is a co-founder and co-director of the AIMC. As a junior mentor, Inimai worked alongside university professors to help Native American students solve challenging math problems and also ran a table station with complex puzzles at the local Julia Robinson Mathematics Festival. She led one of the camp’s cultural activities by performing and teaching hand gestures and footwork from ancient Indian classical dance to students and staff. Every evening after dinner, she helped the students program sphero bots to autonomously move within the tracks they had taped on the gym floor.
“Being a mentor for the math camp taught me not only how I can help others, but also how to engage with different students in a considerate and tactful way,” says Inimai. “Coming from a wide variety of tribes, the students were quite rooted in their respective cultures and found it hard to be comfortable around an outsider. At first, it was difficult to connect with them. Once we started discussing mathematical concepts, their inhibitions quickly vanished; they became more open and eager to describe their ideas on how to solve the assigned problems. That is when I realized that mathematics is the universal language of all cultures, and that it has the power to bring sets of completely different people together.”
The experience of Timothy Ngotiaoco is also instructive. Now a graduate student at MIT studying the representation theory of Lie groups, he did math research during his gap year with SJSU mathematician Daniel Goldston, whom he met at the circle. Timothy joined SJMC as a sixth or seventh grader in 2009 and was involved through 2015. Because he had been homeschooled for three years, it was especially important to him to have found a place to learn math and peers to learn it with. He was the captain of the SJMC Math Wrangle team and served as a junior mentor at Baa Hózhó Math Camp in Arizona.
According to Timothy, “The math wrangle was amazing because we needed to present proofs and solutions to more theoretical problems. It’s a fantastic way to improve one’s mathematical ability, since you need to learn to prove things rigorously. My favorite part is the rebuttal process, where the opposing team can point out flaws in your proof and propose fixes, or perhaps even a better solution. Now that I’m a graduate student, I value being able to do things like this, since I often need to question the theorems I read or prove, and make sure the proofs I have are correct.
“I was certainly blessed to have a mother willing to drive me everywhere and bring me to so many math programs. I was also fortunate to live in the Bay Area, where there are so many math programs offered. I didn’t realize until I came to MIT how rare this is. Many math students I’ve met had never heard of math competitions or math circles. Those of us who did have these experiences are often better prepared for math subjects, simply because we have seen more math, and by that I don’t mean taking advanced courses like abstract algebra, multivariable calculus, linear algebra. I didn’t do much of that in high school.”
“Being part of a math community like SJMC is the sort of environment that many mathematically curious and math-loving kids are looking for,” observes Aida Rivera. “Yet they typically don’t find this within their schools. SJMC is an environment where what is being presented is new and challenging, and that’s completely okay. It’s where persevering brings you amazing ‘Aha!’ moments that will long be remembered and will serve as inspiration to tackle more uncharted territory.”
Favorite Math Circle Problems from SJMC LeadersFrom Joshua Zucker: What are ways of organizing all the lists of positive integers with a total of 7, and what do you discover with each different way you can organize them?From Tom Davis: Suppose you start with one pile of 10 coins. To make a move, you pick an existing pile that has more than one coin in it and divide it (not necessarily evenly) into two piles, so your first move might be to split the pile of 10 into piles of 6 and 4. Whatever those numbers are, your “score” is increased by the product of those numbers, so for the example above, your score would increase by 6x4=24. (If your first move had split the pile to make two piles of 5, you would have added 5x5=25 to your score instead of 24.) As you make moves, the piles get smaller and smaller, and finally you will have ten piles with 1 coin in each. What is the largest possible total score you can get? What is the smallest total score you can get?
About the Author
Molly A. Walker is a business communication consultant and writer living in Oakland, California. She is on twitter @mwalkercom.
