Nope, that's not a feature of Windows. Never has been, probably never will be. If you had this functionality before, odds are it was via some third party program, not Windows itself, so it's not that Microsoft simple did away with it.
The one and only possibility that comes to mind, and it may well have some nasty unintended consequences, is to set the user profile's desktop directory as read-only. I don't know if that would stop kids from moving icons around, but it would likely prevent name changes and deleting of icons.
But another possibility is to look at it from the perspective that since you're in the profession of education, think of this as a kind of independent study for the kids. They are experimenting with things, figuring out what works, what doesn't, etc. What kind of a teacher would you be if you stood in the way of any kind of learning?
I have read a number of different posts on this and none of them fit the bill. I have Kinder through 8th grade students using Windows XP Pro desktops. They continually change the icon names, delete icons or move them around the desk top. Windows 98 had a way to lock down the desktop from changes like this. However those machines are now gone and I guess Microsoft has very little concern for technology in education as such they removed that option. Does anyone have a solution that does not require rebooting. I would rather not have to reboot 6 times a day.

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