Less is definitely more. In the first summer of the Crimson Summer Academy (2004) we attempted to explore two different (but related) topics in our Quantitative Reasoning (QR) course for rising sophomores: Visual Representations of Data and Models of Voting. This was a four-week program, where QR met for 5 hours per week. Needless to say, this wasn’t enough time, but we foolishly decided to fix the problem by tweaking the schedule rather than cutting down on the breadth. Furthermore, in 2005 we now had the second half of the course to teach: six weeks for rising sophomores. In six weeks we could do three topics, right? So we started with Cryptology, and then followed it with a pair of intertwined topics: Probability and Game Theory, wrapped up into a double topic called Risks and Benefits. With a small increase of 20 minutes per week, there still was insufficient time.
So we learned our lesson. We decided to go for more depth and less breadth in 2006. Aiming to focus on interdisciplinary applications of math that didn’t duplicate what the students were learning in their regular schools, we cut out Visual Representations of Data and Probability. We also renamed the Game Theory unit to Conflict and Cooperation. These changes were definitely successful: the summer was less frantic, and there was time to concentrate on applications in depth. The only downside was that some students perceived the two-summer course as less mathematical, since it contained very little material that was familiar from their regular math courses. (The irony is that the most traditionally mathematical activities, such as using systems of linear equations to solve mixed-strategy game theory problems, were the least successful.)