This runs counter to much of the advice given to teachers today. We are told that our classes should be filled with the sound of conversation. Work should be done in groups, not alone. Ideas should be tossed about, criticized and then refined.
Now, I don't doubt that a bit of this is good. (When it's done, it must have direction and that must be provided by the teacher. Students, if left on their own, will often allow themselves to put the work of the day aside and simply socialize.) But more than a bit is not good at all. To learn mathematics, one must be able to think. One must have the time, and the quiet, in which to step through a sequence of ideas. The continual chatter of others makes this difficult if not impossible.
Thus as I said I plan to clamp down. I plan to enforce silence.
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