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I can't help but smile at this. I've working in schools and have seen teachers use this name/checkmark system. Though none would send the child to the principal on third strike (does that not just scream I can't discipline so I'll send you to someone who can?).
I just giggle the way your son interpreted this as 2 freebies. The teacher is thinking that having his name on the board will bring fear and shame to the children and that no child will let their name go on the board and there's you son happily ensuring it is there every day with a checkmark.
Completely different viewpoints. heehee. Clearly the teacher completely missed out on fully explaining her expectations for the children. She also clearly missed out on understanding the children's understanding and motivations!
To the OP...I would meet with the teacher and ask very specific questions about who/what/when/where all the incidences are taking place. I would guess your child is lost in a swarm of children and merely doesn't understand what is expected of him. Even the best of children start acting out when they just don't know what to do with themselves. Moving from 1 in 5 (whether with mom or not) can be overwhelming if they end up with a classroom that isn't run with very, very clear expectations and directions.