After asking the acquaintance (a teacher), I finally got the name of the software: Master Eye. Unfortunately, it seems to have been discontinued. The successor could be this program, Mastersolution Suite. It’s probably available only in German.
I also found this program: NETOP Vision.
Both software suites provide a multitude of management functions: Check what each workstation is showing (whether they’re doing the tasks assigned or just browsing the web), blanking the screen so as not to avert attention, as well as showcasing any of the participating workstations to others.
There are probably other programs like those two. Be warned though: school software is a rather peculiar market.
I am affiliated with neither of the two companies.