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At an opportune moment, pause to reflect on what aspect of coordinating a math circle is most appealing. Whether this be a love of teaching, a desire to reach underserved kids, or an interest in bringing students to campus, it is important for coordinators to identify the elements of the math circle that they find to be the most motivating and inspiring and then ensure that these elements remain at the center of their involvement with the math circle. Circumstances inevitably change, and it is surprising how easily coordinators can find themselves spending the majority of their time dealing with tasks (typically administrative in nature) which are draining rather than energizing. When this situation develops it is crucial to recall the original source of inspiration for taking charge of the math circle and find ways to regain this role.

For example, a person who enjoys presenting sophisticated topics to a tight knit, internally motivated group of students will face a challenge when the circle becomes more popular and attracts the attention of parents who bring kids for the sake of improving their math skills. Rather than becoming resigned to watering down material for this new, wider audience, the coordinator must dream up creative means for pursuing their original vision while simultaneously being diplomatic. One possible solution would be to arrange for a “fun group” and a “serious group,” although not in so many words. (They could be dubbed the “Pythagoras” and “Archimedes” groups, for example.) The former group could make soap bubbles with Zome tools, learn basic counting techniques, and meet for a shorter length of time. The latter group, on the other hand, would be expected to complete a challenging weekly problem set, actively take part in a discussion of these problems, and tackle topics such as inversion or generating functions. To avoid doubling administrative duties, oversight of the fun group could be completely delegated to the parents.

Another coordinator might take pride in the fifty minutes worth of math games that are run each meeting for the kids. Although this sort of activity requires some advance preparation in terms of assembling and photocopying questions, it is easily justified by the level of enthusiasm and active participation it produces in the students. This person would be dismayed, therefore, if the size of the group doubled or tripled so that preparing for the math games became an unwelcome weekly burden. Rather than discontinuing the games or despairing at what has now become a chore, this coordinator might look for solutions such as raising funds via the parents to pay a team of graduate students to run the games. Another alternative might be to arrange for the more advanced students

to host the games every other week for the rest of the group.

As a final example, consider a coordinator who initiates a circle at his university to serve kids who are interested in math but who have not had much exposure to extra-curricular topics. This person would be understandably distressed if the math circle caught on among nearby private schools so that kids with a much broader mathematical background began to dominate the discussions and scare off the target audience. One practical solution would be to change location in such a way that the event simply becomes much more accessible to the target audience. If feasible, the original circle could continue for all interested students under the leadership of another person, while the founding coordinator could establish a second circle at the new site.

All of these illustrations are meant to suggest that a little healthy self-interest on the part of the coordinator is good for the life of the circle and will help to ensure that it can weather the inevitable changes in circumstances that will arise. There are certainly other factors which also contribute to the longevity of a math circle, such as a tight-knit leadership team, supportive parents, or stable funding. But a math circle is often initiated through the vision of one or two people, and to persist (at least in its original incarnation) it is important that these individuals are able to keep sight of their original motivation as the math circle develops over the years. In other words, math circles endure when directors continue to find the challenge of organizing them year after year to be stimulating and rewarding.

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