Licenses are always downwards compatible. This holds true for EDU as well.
Meaning, a license for 24 can also unlock version 23, 22, 21, etc....
But of course this is one way. License for version 22 won't unlock 23, 24, 25....etc.
You get the idea.
It is not an issue of compatibility but access. EDU versions have serial numbers that expire yearly and IIRC if you skip one year then even if you are a student then you will not get access to that version and even if you do, since that version is more than a year old, then the serial for 23 would not be valid.
If you are a student there is no reason to be working in an older version. All my current students are using 25 at this time.