Years ago, a child went to school and their attendance was checked-off in a paper ledger, morning session and post-lunchtime. Signed by the teacher, these were sent to the school office for keeping. The system was fairly infallible and could be read by anyone with physical access - it was essential these books were brought outside during fire-drills as a quick and accurate way to establish that little Johnny wasn't hiding in under a desk somewhere - and that Mr. Lucas wasn't still in the loo having a crafty smoke!
Fast-forward too many years and I had to attend a kindergarten yesterday for work. Access to the site was via a carded entry system with a camera, as was the entrance footpath from the parking area and another one at the main entrance door. These serve both for visitor-control AND staff check-in. The children's attendance is logged by staff in a class-based system so, in the event of a fire-drill, someone has to grab some kind of portable IT to conduct a roll-call (one assumes they've planned for a real fire taking out the systems; I wouldn't bank on them having pre-printed paper copies to hand).
However: without the IT systems, not only is the school 'blind' to which children they legally have in their care, the back-end finance and HR system won't know know which teachers made it in that day, nor will the system be able to generate the required reports on teachers' attainment (they're performance-measured as much as the kids these days). While the former problems can probably be dealt with by a combination of pen and paper for the children and calling HR to confirm that Mr. Lucas did, in fact, make it in today, there's no fallback for the performance monitoring because that only really started once schools had the tech. to monitor and record it; there's no pre-existing paper system they can restart.
And all that before Mr. Lucas has even walked into his room and told the kids to settle down. In short, a modern school without its IT could probably still teach kids - but they would struggle to know which kids, which teacher and what the lesson-plan was - and the longer IT remains FUBAR, the harder it'd be to conduct meaningful staff performance reviews...and they heavily influence future salary decisions.