Much of the focus in my school is on team teaching. It is effective to pace lessons with other teachers who are teaching the same material. As a result, most of my students take the exact same test over the same material the very same day that students with other teachers are doing the same thing. Lectures typically occur the same day, and a student could move from one section to another without much loss of time.
I believe that asynchronous learning amongst all sections of, say, academic geometry could occur using a Google Doc as a sort of running journal. Here's how it would work:
1) I would create and format a document in Word that would resemble a journal entry book.
2) I would then upload that document onto my Google Drive and share it with all of my students.
3) Students would be encouraged (and given some sort of grade or bonus) to write about their experiences within the classroom each day. They would be encouraged to speak particularly about topics or aspects that they did not understand or exercises they did not enjoy or receive any benefit. They could leave their initials as their calling card.
4) I would also share the document with other academic geometry teachers who could, in turn, share it with their own students.
5) As the year progressed, the journal would be an excellent way to constantly and informally assess the learning within the student body and make adjustments to the curriculum and manner of instruction. The document would also serve to capture the progression of learning and provide a record of areas to address for the coming years. The more input the students yielded to it, the more fruitful it would be.
Hope this makes sense. Good luck in the classroom!