As all veteran math circle coordinators can relate, recruiting a sufficient number of good speakers to lead the circles is the greatest challenge they face from year to year. Their selection is crucial, for the person presenting the mathematics will determine whether the participants eagerly explore or gradually disengage from the day’s topic. Suffice it to say that the job calls for an understanding of interesting, accessible mathematical topics that are not part of the standard secondary curriculum; knowledge held by individuals who typically pursue careers in academia, software engineering, national security, or other fields requiring specialized math skills. On the other hand, this knowledge could be squandered if it is not presented in a creative, engaging, interactive manner; much as a favorite middle or high school math teacher would have done. Paul Zeitz, the director of the San Francisco Math Circle, has this cautionary advice to offer:
Don’t assume that knowing cool math will immediately translate into an exciting, compelling mathematical experience for secondary school students! It is harder to break with the lecture style of presentation than most people realize, and delivery makes a difference.
This being said, there are a few guidelines that will help ensure a solid lineup of speakers for any math circle. To begin, start looking around early—the best people are usually the busiest. Look for people that fall into at least one of the categories mentioned above, then provide resources to give support in the other category. For example, college or university faculty members often have interesting topics at their fingertips. However, they are accustomed to lecturing to advanced students and may not have as much experience conducting an interactive, open-ended exploration at the secondary school level. Sending out a friendly “what to expect” letter a week or two in advance, which includes a description of the style and content employed at a typical math circle meeting, will go a long way towards bridging the gap and will probably be much appreciated. (A sample email message is contained in the appendices.) It is also a good idea to ask speakers to prepare a handout ahead of time with a variety of problems related to the presentation. This will help keep students occupied and engaged during the session, and will also provide a gauge of the difficulty level of the topic, in case adjustments need to be made given the background of the audience. Above all, speakers unfamiliar with the math circle philosophy will benefit from seeing one in action, so invite new instructors to visit the circle a week or two in advance of their debut. This practice can become standard protocol: at the Utah Math Circle all first-time speakers are required to attend a math circle before leading a session.
Professors are certainly not the only ones with the requisite mathematical background. Graduate students, high school teachers, and a wide variety of professionals can all make excellent candidates for leading math circles. One of the most popular presentations at the Stanford Math Circle last year was given by a local private school. In theory undergraduates and middle math circle school teachers could also be included in this list, but these two groups might be uncomfortable at the helm. Undergraduates may be too close in age to their audience, and will probably lack speaking experience. Middle school teachers would be more effective than they might suspect, but may not consider themselves sufficiently advanced in math to feel comfortable leading a mathematical enrichment activity.
Regardless of where one looks, the universally accepted method for tracking down math experts can be summarized as: keep an ear to the ground and persistently ask around. It makes sense to start with local colleges or universities, but look further afield also. Keep in mind that the most important qualities for a speaker to possess are a dynamic, engaging presentation style, a love for and general competency in mathematics, and some familiarity with the target age group. If there is money available to support a guest’s travel and accommodations, consider inviting a more well-known mathematician to speak at the circle session. Anticipating such a visit can provide focus and generate enthusiasm among regular math circle participants. It might work well to arrange for this guest to also give a department colloquium; the trip becomes twice as worthwhile for the speaker and other funds may become available for covering the visit. Naturally the director of the circle should speak frequently as well, without letting the responsibility of preparing for sessions turn into an unwelcome burden.
Most individuals who enjoy mathematics will already have their own list of favorite problems which they would delight in discussing. However, some potential speakers may be unsure as to which topics would be best to present since they do not have regular contact with pre-college students or may not have a working knowledge of mathematics outside the standard secondary curriculum that is both accessible and well-suited for exploration. Look no further—the chapter on leading a math circle includes a long list of possible topics along with suggestions on how to present them. Furthermore, the second part of this handbook contains a variety of ready-made math circle sessions that can be used directly or adapted for a particular audience. And while substantial mathematical content should constitute the staple of any math circle diet, there is certainly latitude for incorporating related subjects into the schedule. Thus students might enjoy learning about mathematics as it is applied to computer graphics, or sailboat design, or survey data analysis, for example.
Finally, there is the question of how often individuals will visit a particular math circle. Should a speaker come just once? This approach places less of a burden on the speaker and ensures a greater variety of topics during the year. However, this practice also makes it more challenging to fill up a schedule and gives the math circle a bit of a guest lecture series flavor. (There are ways to counteract this effect, described in the section on retaining students.) Should a speaker come twice in a row? Fewer people may be willing to commit to two appearances, but the advantages gained include an increased sense of continuity between meetings, the ability for a speaker to build on material from the previous week, and a far easier time slating enough presentations for the year. The majority of math circle coordinators attempt to book speakers for at least a couple of visits, particularly those who are known to be effective. At the other end of the spectrum, some directors arrange for instructors to conduct an entire block of math circles lasting a month or more in length. This approach allows students to become very familiar with the speaker, promotes regular attendance, and permits a more thorough treatment of a subject by the instructor. It also calls for a different model of math circle, in which speakers are paid for their time through the support of outside funding. The math circle might also choose to charge tuition to help guarantee the regular presence of excellent instructors; this issue will be addressed in more detail in an upcoming section on funding.
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