I work for a school that has the ability to view the screen content of any of their computers or iPads at any time. Makes sense. Occasionally though I do banking or buy something online. If I am logged on to an https or encrypted site, would those show on the surveillance screen? Or would the content be stored on their server to be possible to be constructed later? Hate to think of account numbers or that 3 digit security number on the back, usernames or passwords being visible.

ThanksIf they're using a screen viewing program such as NetOp or RealVNC (our school has used both in the past), then they have the ability to read anything on the screen at any time, as HTTPS only secures the WEB communication (and if they have a filter in place things get complicated.) This doesn't necessarily mean they log SCREENSHOTS, but they could watch your screen while you ENTER the information. As for STORING on the server, that's somewhat doubtful. With the amount of internet traffic schools generate, they probably only log addresses requests are sent to, but not the contents of the transmissions.

TL;DR: anything is possible, but it is somewhat unlikely for this to be an issue for you. All the same, I wouldn't trust the security of a school internet connection and I would try to do it somewhere else (at HOME if possible.)