Good to see someone developing that again. Now, complaints.
First, obviously you haven't implemented the kinds of choices that made the original fairly interesting. No rules, no clubs, no re-play mechanics. You also haven't differentiated the teachers or even subjects in any meaningful way. But you knew that already, I see.
In that case, on to the core mechanics... they seem pretty solid as far as they go. Not really many ways to screw up, but I'm sure adding rules and clubs will help with that. Also it seems like a pretty linear movement from 30-30-30-30 to 100-100-100-100, with a few minor exceptions in the upward direction. That doesn't seem to have an obvious fix, but something like allowing skills to decay once they pass a certain threshold (even allowing progress past 100 and just decaying back toward 100) might help.
Finally, interface. I have to say that it's already better then the original, or at least less confusing, but I have two major complaints on this front.
1.) Non-standard use of windows. My stats bar floats off to the side with no header bar or way to manipulate it. The same with the pop-up "teacher" window. Properly, the stats bar should be a part of the main window and the "teacher" window should be a proper pop-up dialog, one the blocks access to the main window but that has the standard "manipulation" bar at the top.
2.) The "teacher" window isn't very clear when first used. There should be some visually obvious sign of how to assign a subject to a teacher.... if nothing else, putting "click on a subject then a teacher to assign classes" hint somewhere on the page.
Now on to the "constructive" part - two content suggestions:
First, teacher specialization. The original had a pretty boring and static variety... just giving each teach a bonus to exactly one subject set at game design. Better would be to split a teacher's stats into three parts - "general" skill, "area" skill, and "class" skill. "General" skill is just their generic skill as a teacher, "area" skill is specific to a group of classes (academic, artistic, physical?), and "class" skill applies only to the class it was earned in. This could probably be simplified to "general" and "class", but either way it ought to be hidden from the user except for the change in numbers when they change classes.
It should be obvious that someone who was an expert at teaching algebra wouldn't automatically be an expert at teaching history. Also that some qualities of a teacher might pay off no matter what the subject. Slightly less obvious may be that there are some skills you learn teaching algebra that would transfer to english, but not to gym. An example might be discipline - maybe in algebra and english you'd assign extra homework, but in gym you'd make them run a lap.
Experience earned just teaching should be split between all the categories, but experience earned in special events might not be (for example, sending all your teachers to a seminar probably means it's generic rather then particular to their discipline). There should be a cap for generic experience below the cap for total experience.
Secondly, the "which do you want to focus on" dialog could use a little help. I'd suggest either making the two attributes you're choosing from bold (up top where the numbers are), or including the stat in the choice ("Loyalty(30) Teaching(35)").
I'll be interested to see the final product.