My children both attend Montessori schools, so I understand the importance of the calm quiet class environment.
My observation-based photographic approach ensures minimum disruption to the children's routine.
I usually arrive before the class starts, so that I can greet the children as they arrive, and learn their names.
During class, I will not interrupt the children and ask them to 'look up & smile'. Instead, I will quietly observe them concentrating on their jobs, or engage with their teachers and peers.
If any children become overly interested in what I'm doing, I usually tell them that my job is to photograph children who are working, then gently steer them back to their jobs.
During outdoor playtime, I will run around and engage with the children to get those natural candid happy cheeky smiley photos that parents love.