National Association of Math Circles Wiki

The concept of a math circle supported purely by the desire to enjoy math for its own sake has a certain appeal. This dream can be realized, as evidenced by the San Jose Math Circle, which thrived on a strictly volunteer basis for years. However, money spent on a modest year-end party, prizes for exceptional students, and books for the lending library does add up over the years. And while generous organizers can easily pay for these items out of pocket, a math circle is very much a joint enterprise between an institution and a community, so it is also appropriate for both sectors to contribute financially to the effort.

Therefore the San Jose Math Circle recently began to accept donations to help cover expenses. Regardless of who foots the bill, any coordinator would agree that there are costs associated with running a math circle in the manner they envision.

The precise amount of money that should be allocated and the corresponding source of this funding varies more dramatically from one math circle to the next than practically any other single attribute. But the planning process should always begin in the same way; namely, by creating a budget. The bottom line can range from a few dollars, to several thousand dollars, up to amounts exceeding one hundred grand. These budgets might cover occasional snacks, or supply honoraria for regular speakers and cover travel and lodging for several out of town visitors, or underwrite a large scale operation which provides stipends for teachers who receive college course credit for attending a teachers' math circle course while their students explore related topics in a nearby classroom. Developing a budget is an illuminating process that helps to shape and focus the vision for a math circle. It is a document to which a coordinator will return time and again as practical decisions are made in the planning of the circle.

The following list gives a sampling of the different categories that could constitute a math circle budget, along with considerations that will influence the relative amounts dedicated to each. The headings shown below are by no means comprehensive, but will at least provide general guidelines regarding some of the more common expenses. The last several paragraphs apply primarily to larger scale math circles that will reach out to teachers as well as students or that will be seeking philanthropic support.

**Director compensation.** This item may be omitted all together, come to a few thousand dollars, or equal the equivalent compensation for one university level class, on the order of \$20,000. Coordinators should choose an annual amount that allows them to sustain the activity over several years and, if possible, enough to free them of other responsibilities so that they can devote adequate time to the needs of the circle. For example, the coordinator of the Utah Math Circle is given release time in the form of one less course per year in order to devote attention to math circle administration. Coordinators tend to love their circles passionately, but are also subject to burnout. Adequate compensation permits them to invest sufficient time and energy in the circle while staying fresh and enthusiastic. Some organizers have started their circles with no compensation and then paid themselves in later years when resources were more plentiful. Even if an organizer feels strongly about donating their time, the budget should still accommodate incidental costs that inevitably accrue, such as manipulatives, overhead slides, or babysitting costs.

**Speaker compensation.** Some circles don't compensate their speakers, others offer them from \$100 to \$200 per visit. The expectation for compensation usually rises with the number of times the speaker will come. While many excellent speakers are happy to volunteer their time to lead math circle sessions, it is certainly good etiquette to show appreciation by some means - and an honorarium is one of the best. Speakers may have to pay for babysitting, transportation, or parking on top of giving of their time. It is also the case that speakers who know they are being paid for their efforts will spend more time polishing their presentation, are more willing to put together an effective problem set, and will think twice about canceling an engagement if a conflict arises. As worthwhile as math circles are, it can be difficult for speakers to justify going the extra mile if they feel under appreciated.

**Recruitment. ** Getting the word out to students and teachers might involve nothing more than a few well-directed email messages, perhaps with an announcement attached as a PDF file. For only a few dollars one can print simple flyers for posting at local schools. (With teachers' and administrators' blessings, of course.) With an amount in the range of \$2,000 a coordinator could mail glossy color brochures directly to all residences within strategic postal codes. Finally, around \$7,500 will retain the services of a consultant to interact with the local school district, unions, teachers, principals, and administration.

**Snacks.** As noted previously, it would be great to recruit a parent to coordinate volunteers who bring snacks each week. Remember to allow for a gift for the snack marshal, and also plan on food expenses for any social events that take place throughout the year. The Washington University Math Circle convinced a nearby pizza vendor to sponsor their circle and deliver a couple of pies towards the end of each meeting! However, if the organizer will be purchasing snacks each week, budget for it here.

**Books and Prizes. ** If the math circle features a lending library then budget a modest amount to replace lost books and buy more copies of popular titles. Some coordinators might also wish to purchase an entire set of books to use as a supplement to their circles over the course of the year. Awarding small prizes, such as mathematical puzzles, for attendance or problem of the week solutions is another way to enliven a math circle and encourage participation at the same time. Some math circles host math olympiads and offer more substantial prizes for top scorers.

**Supplies. ** There are any number of additional expenses that might crop up during the year. This line item might cover videotaping, Zome tools, or ingredients for a soap bubble demonstration, to name just a few of the possibilities.

**Visitors. ** Inviting mathematicians from further afield to present guest presentations can add an element of excitement and anticipation to any math circle schedule. As mentioned previously, this speaker could also give a colloquium talk during the trip. Figure on approximately \$600 for travel, accommodations, and meals for each visitor. This amount might also be partially covered by the departmental colloquium budget.

**Space rental. ** The vast majority of math circles use space donated by universities. Coordinators from outside the academic environment who seek the support of a math department in providing speakers should also request their cooperation in securing a space for holding the circle. If one must pay rent though, this is the time to budget for it.

**Insurance.** Some locations require liability insurance to protect the owners of the site from liability claims. Experience shows that insurance is rarely required - when mandatory it can usually be purchased for about $500 per year.

**Teacher compensation.** Some circles that target "unenriched" kids, notably the San Francisco Math Circle, offer a stipend to teachers who bring students to take part in the math circle. This is a very expensive proposition, but one of interest to some funders. Teachers are also encouraged to come through the promise of free continuing education units which they receive by way of their participation in a simultaneous session tailored for educators. The San Francisco circle compensates teachers at the rate of \$100 per weekly event, and pays on the order of \$150 for each teacher for continuing education tuition. This line item for the San Francisco Math Circle exceeds \$30,000 but has been critical to its success.

**Administrative overhead. ** It is never too early to take into consideration who will be managing math circle funds. An organizer applying for philanthropic support will want to work with a non-profit organization eligible to receive a gift or grant. (Assuming that the circle is not already a registered non-profit organization as set forth in IRS section 501(c)3.) The host institution, Mathematical Sciences Research Institute, or other local organization could serve as a fiscal agent. Ask them about administrative overhead - this is usually charged as a percentage of the grant.

**Assessment.** Those applying for philanthropic support will no doubt be stating objectives to achieve with the donors funds. Be careful committing to these objectives so that they motivate the donor, are realistically achieved, and can be measured without interference to the program. In one recent math circle grant, in a fit of enthusiasm to please the prospective funder, the application promised pre- and post-testing of the students, and projected significant improvement. No doubt there was improvement, but most students would have fled this friendly program at the prospect of tests. Fortunately, the promise was renegotiated with the funder.

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