I don't think the school can "control your computer"
RAT = Remote Access Tool
It's called a firewall kids. They block out sites via their firewall and it doesn't allow users to go on there.
If you are talking about the wifi and shit. That's called a botnet. That monitor what sites you go on. They don't have remote access due to it.
You can't rat someone via wifi.
And If it's a school computer. They wouldn't try to get full access to monitor everyone on every computer in the school. They just track what you do on the computer so if something were to go up. They can find out who did it easier.