There are a couple of ways to defragment a HDD without a defragmenting tool. One would be to reformat the drive. If it is the boot drive, reinstall the OS after the reformat. In the situation of a professional teacher who starts anew every year anyway, this is a good idea for the reason of defragging as well as normal bitrot. Just not probably all that necessary.
Another method is to simply remove all data, and then move it back. This accomplishes less, but it is less invasive.
Neither of these techniques nor others is probably all that necessary. If you feel like your car performs better after you clean the windshield, then superstitious behavior may also have the effect of making you think the Macs perform better after defragging. My thought is, probably not noticeably so. It may be that this behavior is driven by experience with Windows. If so, that is mostly irrelevant, as Macs may seem similar, but under the hood are a full paradigm shift from Windows. It may be time to jettison behavior built on experience from a previous and quite different universe.
Windows is a different story. Everyone tells us not to defrag our Avid NewsCutter editor platforms (all 14 of which use ISIS shared storage for media and do not store media files locally). But the experience proves differently; once we defrag performance noticeably improves, to the point where we have a defrag routine scheduled task that now runs every day before shutdown, on each platform.
I have learned that this may be due to virtual memory fragmentation. If you can run the page file on a separate HDD, and if you can make that file 4.5 times the size of installed RAM, and especially if you make the minimum and max size for the page file the same so it does not grow and drop back dynamically, it will handle virtually (no pun) any task without unnecessary paging slowdowns, and won't defragment at all. But I have had neither the luxury of those conditions nor the ability to figure out how to do that on Mac OS quite yet.
There are really two things going on in defragging: consolidating fragmented files, and consolidating fragmented free space. Consolidating files does have the very minor effects of taking access time mostly out of the equation (I have seen Windows files that have 3000 or more fragments each, and on a relatively empty HDD, but never on a Mac), and of not needing a listing in the extents tree file, which means if the extents tree file gets corrupted it wont cause part of the file to be lost. Both of those advantages are exceptionally minor.
Consolidating free space keeps some file fragmentation from happening, but that is only a problem if the drive had tons of small files on it and many are still there when you begin writing comparatively larger files to that drive. If the files are always large (video files) it probably does not help very much. It sounds like consolidating free space is really the only advantage of defragging that this teacher could benefit from, since all of the video files are removed regularly (and if they are, that sort of consolidates the free space automatically).
If you have multiple HDDs but not large ones, it is still easy to manage fragmentation by reserving the boot drive for OS and apps and putting media files on the other drive. That way just wipe the media drive, and the video files will not fragment the boot drive.
Bottom line, I think he/she might be overthinking this, or at least overvaluing the benefits of a defrag. If there is down time the teacher needs to fill between semesters, vaya con Dios, but otherwise I would ignore the issue until problems potentially stemming from fragmentation appear.
Mr. Me is basically correct, but that does not mean that HFS+ drives do not get fragmented, they do, but not likely to the extent that NTFS or FAT partitions do under normal use. Its not so much a Q of whether fragmentation happens as it is a Q of whether that is problematic or not. Mostly, its not, and in a case where the files are normally all removed regularly anyway, probably even less so.
Linux HDD protocols are rumored to not fragment at all, but I would want to see the proof. And of course OS X being unix is much closer than x86 to Linux (which may mean absolutely nothing).