There we observed that changing the claim from "this country's teachers" to "many of this country’s teachers" would account for the exceptions, teachers who did not fit the generalization.
I like that it points out, here and above, phrases good to be used for exceptions. This is because in the past while writing I have felt like I'm being too wordy, vague, or that my statement just isn't true when I change the claim. If I wrote something like "some teachers" or "most LGBT people" I felt like I wasn't writing the most efficiently.