University of Arizona
Institute for Mathematics and Education

Report on MSRI Math Circles Study Trip to Russia

David Savitt

I have a dual interest in MSRI's effort to promote and organize Math Circles in the United States. For the past ten years I have mentored high school students at Canada/USA Mathcamp, a five-week national summer program for mathematically talented high school students. I began working as an instructor at Mathcamp the summer before I started graduate school; I am now Deputy Director of Mathcamp, and a faculty member at the University of Arizona. This year, Bill McCallum, also at the University of Arizona, has founded an institute for collaborative research involving mathematicians and mathematics educators (the Institute for Mathematics and Education, or IM&E for short). In this startup year, I am assisting Prof. McCallum as an assistant director of IM&E, helping to shape the mission, scope, and structure of the Institute. It is in these two capacities, as a partner in both Mathcamp and IM&E, that I applied to participate in the MSRI Math Circles in Russia trip.

The Institute for Mathematics and Education is a natural venue to host a Math Circle; once our meeting space has been renovated, we intend to initiate the Southern Arizona Math Circle. Although I have worked with young students at Mathcamp for many years, before the Russia trip my experience with Math Circles had been somewhat limited, especially relative to some of the other participants. (I attended the 2004 MSRI Math Circles and Math Olympiads workshop, and a number of years ago I led a session at the Boston Math Circle.) I was therefore ecstatic to have the chance to participate in Math Circles in their more-or-less native setting. I look forward to making use of the institutional knowledge contained in Sam Vandervelde's "Circle in a Box" at the Southern Arizona Math Circle, but there is no substitute for the kind of direct experience we obtained on the trip.

I noted with great interest a lesson that appears to have been well-learned in Russia: that Math Circles are an effective way of inducing an interest in mathematics education among community leaders—when their children start attending the Math Circle! I hope this will prove to be a natural way of informing Tucson's community leaders about the IM&E, and involving them in it.

I hope that the opportunity to forge connections with MSRI—one of the national mathematics institutes whose professionalism and stature the IM&E can only hope to approach—will prove to be just as valuable as the connections made in Russia. IM&E would be pleased to partner with MSRI on projects where the participation of a second institute might be valuable. We will have a well-appointed meeting space, and can host conferences and workshops on occasions when MSRI's other scientific activities do not permit the scheduling of Math Circle-related workshops. (Or, in case the usual cadre of participants is interested in a change of venue from time to time!) As an example, one of the key missions of IM&E is the study and promotion of effective teacher preparation. It would fit well with this mission for IM&E to host a workshop focusing on teacher involvement in Math Circles: how to attract teachers to attend the Circles with their students, how best to design activities and materials that would involve teachers, etc.

IM&E may also support and/or host short- and long-term research projects, and we would be glad to receive proposals for projects related to Math Circles (such as longitudinal studies of the effects of Math Circles on their participants).

Switching from wearing my "IM&E hat" to my "Mathcamp hat", I was struck by the philosophical similarities between Mathcamp and Moscow High School 57. We have often overheard our campers wishing that there could exist a year-round Mathcamp; School 57 is by far the closest approximation that I have ever seen. Both institutions first and foremost strive to assemble a community of like-minded students, united by their interest in mathematics, and to imbue this community with a sense of freedom and flexibility.

For such a program to succeed, the students certainly must be chosen carefully, and it may not be surprising that the similarities between Mathcamp and Moscow High School 57 begin with our respective entrance tests. The teachers at School 57 design their entrance questions to test how their applicants think, not what they happen already to know; we at Mathcamp strive to do the same. (As an example, we both avoid asking geometry questions whose solutions depend on knowing just the right theorem.) We both have elaborate entrance procedures, to assess the motivation and perseverance of our applicants, in particular to screen out students who are being pushed by their parents but are not actually interested in mathematics. We both look beyond raw exam scores, searching for students whose solutions show the right temperament for our programs.

During our visit I worked with several students at School 57, and I found them similar in attitude to most Mathcamp students—eager to absorb mathematics, thrilled to be among peers—and similar in level to the stronger end of the range of Mathcamp students.

I was pleased to learn from Sossinsky about the Dubna summer camp. I asked our new contacts in Russia to encourage some of their students to apply to Mathcamp (I stressed to them that we do have full scholarships available, for which foreign students are eligible), and reciprocally I hope that some adventurous Mathcamp alumni might consider applying to the Dubna camp.

[Update, November 21, 2007: The renovation of IM&E's meeting space is well under way, and we plan to launch the Southern Arizona Math Circle in 2008. We have obtained modest funds for student recruitment from the MAA's Tensor-SUMMA program. Following the ARCC workshop in June 2007, the IM&E has founded a Teacher's Circle that meets once a month. The first meeting of was in September 2007. For more information on the Teacher's Circle, see its website:]