The factors that will influence the choice of times and dates to meet vary so widely from one math circle to the next that it would be impractical to attempt to include them all. Each organizer will need to make allowances for room and speaker availability (don't compete with the Tuesday afternoon colloquium), local traditions and holidays (Wednesday night is out in the Bible Belt), traffic patterns (nobody would make it to campus on time before 6:30 on weekdays), and a myriad of other factors. However, there are still several general principles that can be applied in a range of settings.
For starters, the age of the students attending the circle makes a difference: middle school students can squeeze a late afternoon time slot into their weekday schedules more easily than high schoolers, who have a greater number of demands placed on their after-school time. Both age groups can usually manage an early evening meeting time, although this may again be asking more of high school students given their typically larger homework load. It goes without saying that Friday night is not desirable, but Monday night works better than one would at first expect. Gathering on a weekend allows students from a wider geographic area to attend. Thus Saturday morning or Sunday afternoon have proven to be a viable alternative for many groups like the Boston Math Circle. (The official title of the latter group is simply "The Math Circle," but the modifier "Boston" will be inserted from here on to avoid confusion.)
A weekend time is especially well-suited for larger groups such as the San Diego Math Circle. The intended mode of transport will also play an important role in determining a meeting time. The San Francisco Math Circle provides programs for both teachers and students; since these teachers drive their students to and from the circle a late afternoon time is essentially the only option available. A math circle targeting an urban population that would travel via public transportation might also be better off in the afternoon, when service is more frequent. On the other hand, parents are the primary chauffeurs to the San Jose and Stanford Math Circles, which meet on Wednesday evenings and Sunday afternoons, respectively. To some extent, families will organize their schedules around a math circle they strongly wish to attend; often the best plan is to pick a feasible time and stick with it for a year, knowing that it is impossible to please everyone.
Most organizers make very similar choices with respect to meeting dates. It makes sense to slate the initial meeting a week or two after Labor Day; by this time students have begun to establish a weekly routine but have not yet become too busy to consider a new activity. This time frame also gives coordinators the chance to advertise the circle. Universities on a quarter system may opt for an October start, but should probably begin as early as their academic schedule permits in light of the previous considerations. There is time for a couple of meetings after Thanksgiving, although attendance usually dwindles. Following winter break the default would be to continue meeting until final exams begin to loom for either those attending the circle or those hosting it, which typically occurs in late April or early May. However, there may be good reason to draw the year to a close slightly earlier, such as difficulty in finding enough good speakers to support a full year’s worth of meetings, or simply a desire to avoid an
overly ambitious schedule the first year. In early April the Stanford Math Circle segues into practice sessions for the American Regions Math League (ARML) team, which take place at the same time and location.
Coordinators of most existing math circles favor weekly meetings, for good reason. There is much to be gained from holding a regular math circle - the event becomes part of a weekly routine and it is possible to establish a sense of continuity. A student who misses one biweekly meeting (even if for a good reason!) goes three weeks without attending the math circle, at which point she decides that she can live without it. The exception to this rule occurs, for example, when a middle school circle gathering every other week is associated with a companion high school circle meeting more regularly, so that students have a fall-back option during the off weeks. But in general it is preferable to shorten the year in favor of regular meetings rather than to thin out a schedule with biweekly math circles.
Lastly, almost all math circle coordinators make the same choice with regard to the length and format of a meeting. While an hour is sufficient for presenting significant mathematics in a lecture format, it is barely enough time to allow students to make substantial headway in exploring a new topic for themselves and to actually work on problems in the process. On the other hand, two hours begins to approach the limit of a group's attention span, even with a short break in the middle. Besides, it would be asking a lot of a family to devote more time than this to any single activity. Therefore most sessions last from an hour and a half to two hours in duration. Announcements, mathematical tidbits, or speaker introductions usually occupy the first five to ten minutes while those caught in traffic arrive. The presentation for the day follows; the style of delivery should be so interactive that there is no need to reserve time for questions at the end. Instead, save a few minutes for snacks, or provide a ten minute break in the middle of longer sessions.
Next: Filling the Schedule: Finding Speakers