This is part of a sequence of posts developing a new project for Bridge to Enter Advanced Mathematics called BEAM 6. BEAM 6 will be a non-residential, four-week summer program for underserved 6th grade students in New York City. You can find the other posts about its design here.
How can we possibly make everything fit?
Seriously, we have a highly ambitious curriculum planned and we must also fit a vibrant social schedule. The community formed at BEAM 6 will carry students through their future studies if we get this right; it will provide a beacon that tells them that they can have good friends and be serious about math at the same time. It will also encourage them to continue on to BEAM 7, and we want them to come! What schedule will let us accomplish these goals?
BEAM 6 will run six days per week. Five days will be class days, which will mix both classes and activities. The sixth day will be a field trip or activity of some kind to further build community and friendships.
We need to fit in as much time during the week as possible, but we have a serious limitation: rush hour! Students will be brought to the program by our undergraduate counselors, who will meet them at subway stations near their homes. However, navigating the subway during rush hour with a bunch of 11-year-olds is not a great plan.
We can’t avoid rush hour completely without terribly shortening our day, but we can avoid the worst of it. If we start at 8:15am, then the farther students will be boarding the subway at 7:15am, which is not too bad, and by avoiding an “on the hour” start we also avoid peak times. Then if we end at 3:40pm, we can get on the subway before the afternoon commute.
That’s our day: 8:15am-3:40pm. I’m not crazy about how that schedule makes us feel like a normal school, but we have few other options.
I debated for a while which day should be our sixth day. BEAM 7 runs on a Tuesday-Saturday academic schedule (adopted from Canada/USA Mathcamp), with field trips on Sunday and Monday. The advantage of Monday trips is that you can visit when places are almost entirely empty. However, such a schedule might cause significant confusion among students and families, and the subway has unpredictable problems on weekends that could interfere with students’ on-time arrivals. So, in another compromise, classes will run Monday-Friday, with activities on Saturday. We might reconsider this in future years when we have more capacity to deal with any unexpected challenges an unusual schedule causes.
We have five courses planned: Logical Reasoning, Applied Math, Math Foundations, Math Team Strategies, and Exploring Math. We cannot possibly offer all four in the same day. With lunch, two activities, and study hall, we simply run out of hours. (Study hall is very important to me, because it gives students time to reflect on their work and instills study habits.)
The first decision I made was that “Exploring Math” can naturally be simply “Afternoon Math Circle”. The last thing in the day, it’s a fun piece of math, different every day, taught by different people. We can also use the time for guest speakers talking about how they use math in their work. Regardless, this will be in the final block, 2:40pm-3:40pm.
For the rest of the courses… well, let’s consider two different options.
Plan #1: Two two-week sessions
The four other courses naturally break up into two groups of two, so we can have 2 two-week sessions. Students would focus on one pair of courses during each two-week session.
Applied Math with Math Foundations. I paired these because Applied Math will likely be the most intrinsically exciting course, and Math Foundations the least exciting. Applied Math needs as much time as it can get: if students are to become independent in programming, then they need to do lots of programming. Hence, while Applied Math can expect to give 1-1.5 hours of homework per day (depending on the day – see below), Math Foundations should give no more than 15-30 minutes per day. Math Foundations is not designed to drill students in procedures, but rather to encourage creative solutions to problems, so it is all right to give less homework.
Logical Reasoning with Math Team Strategies. Math Team Strategies would get the bulk of the homework time, because we want students to become acclimated to using online resources such as Alcumus and the Art of Problem Solving forums. These classes are both in the middle in terms of intrinsic excitement, so they pair well together. Additionally, by putting Math Foundations and Math Team Strategies in different sessions, we know that students are always getting something related to math they’ve learned in school.
Plan #2: Odd/Even Days
There is another way to divide the courses. Instead of two groups of two, they could alternate days. One day is Applied Math and Math Foundations courses; the next day is Logical Reasoning and Math Team Strategies. In this plan, all courses run the full four weeks, but every-other-day.
Pros, Cons, and Choosing a Schedule
With Plan #1 (2 two-week sessions), it is easier to find faculty (who can now teach for just two weeks) and students can focus on specific topics as they go along. Moreover, by studying the same thing each day, teachers don’t have to spend as much time reviewing at the start of class.
On the other hand, with Plan #2 (alternating days), students get more practice balancing competing demands on their time with homework assignments. Moreover, their ultimate recall is stronger because they spend a longer time actively engaged with each topic. Finally, it makes things more uniform. For example, suppose that in Plan #1, someone is teaching Math Team Strategies. For the first two weeks, their students are new to the program and haven’t taken our Math Foundations course yet, so they will struggle. But when the course is repeated for different students in the latter two weeks, all of those students have had Math Foundations. If we use Plan #2, this goes away.
After talking with my colleagues, we settled on Plan #2. We feel that it is a better educational experience for the students. While finding faculty may be harder, it is worth it for a stronger program.
At BEAM 7, the courses provide no homework. Students do all their work in class, with attention from the instructor. This allows for a fast-paced, highly-interactive environment. However, there are disadvantages as well. It doesn’t train students to budget their own time and develop independent work skills. Moreover, it doesn’t fit well with part-time faculty for a day program. At BEAM 6, we’ll have shorter classes and time for students to do work.
My first draft of the schedule came out like this:
12:20pm-1:30pm: Study Hall
2:40pm-3:40pm: Afternoon Math Circle
Lunch can be short, because we will almost certainly get catered boxed lunches that students can grab and eat. Since it is right after activity, it still provides a good break from their classes. If we had just one more hour, I could fit two hours of class/study hall/whatever between lunch and activity, but with avoiding rush hour we just don’t have that time.
However, after reflecting on this schedule, I want more time for study hall. Especially for the programming course, there just isn’t much time for student independent work. Currently students would have a total of 20 hours of work on programming (10 with the instructor and 10 in study hall); more time would be a huge asset. Moreover, having 20 Afternoon Math Circle sessions, while delightful, is not really necessary. Hence, on some days we can replace Afternoon Math Circle with a second Study Hall time. In the end, I decided that Monday, Tuesday, and Friday will have Math Circle (good way to end the week!), while Wednesday and Thursday will have extra Study Hall, allowing students to work on projects or longer assignments later in the week when they are in the thick of things.
This is all very complicated. Now we have odd/even days determine which of the four long-running classes are happening, while days of the week determine if Math Circle is happening. I think these are all the right decisions, but we will need clear messaging to make it work and make sure that students feel comfortable with their schedule.
There are, of course, a whole wealth of other details. For example, at what point do students select their courses? Should they do so on the first day of the program (which eats up class time), or in some earlier orientation? Right now, my plan is to schedule an orientation for students and families before the first day to talk about the program and how it will work, and to include course selection there. Unfortunately, some students will miss that event, and we will have to give them another time for course selection.
We must also schedule Saturday trips. We are thinking about movies, or a trip to the Bronx Zoo, or similar events. These will each have their own schedule based on what we are doing.
We may also want some sort of closing ceremonies with parents. Again that will require separate scheduling. Most likely, we will go for Friday night after the program is done, and provide some sort of food.
Finally, we must have training/setup and wrap-up/take-down with staff. I am planning the Friday before the program for the former (full-day for counselors, half-day for faculty) and the Saturday after the program for the latter.
I’m sure there are other details that we will think of as we go along.
Things fit. They don’t fit as much as I want; the day feels too short to me, making it hard to really bond with everyone as much and get as involved in the classes. I am worried that we won’t be able to instill in students the habits we want them to have for their educations. But this is an iterative development process. We will run a great program, and then make it even better for next year.
Despite any shortcomings in our available time, this will be a tremendous experience for students. It will open up so many educational pathways. Seeing a concrete schedule really gets me excited for the summer!