Disclaimer: my only experience with the American school system has been as a student. I also don't have any examples or statistics to back up my proposals. Reader beware.

Currently most schools I know of teach in quarter or semester format, with multiple subjects being taught at the same time. While this theoretically reduces compartmentalization of subjects, I've found that in practice most teachers don't bother to tie in their subjects with the others that the students learn at the same time. Additionally, the prevailing attitude seems to be (at least among the teachers I studied under) that their subject is the most important. This is understandable, since they are being paid to teach that subject, but when multiple teachers hold that view semesters tend to get laborious.

A monthly approach would see students focusing on just one subject at a time for the majority of the day, for that month. Testing would occur at the end of the month, followed by a considerable break (5-day weekend or something similar). Then, next month, classes would rotate and students would begin a new subject. At the end of the year (or perhaps biannually), all subjects that the student had pursued in that time period would be tested using exams that had been designed by the teacher in advance.

I recognize that there are several drawbacks to this system, such as holidays, teacher fatigue, class separation, and registration and scheduling difficulties. However, it seems to me that requiring students to focus on a single subject at a time may produce better outcomes, encourage cooperation, and lead to a deeper understanding of that subject. Again, I can't back any of this stuff up with statistics or examples, it's just a thing in my head that I think would be neat.