ArM5 p.164 state that the limit on teaching is "The teacher's score in the Art or Ability" Is that no extra points beyond the score. If you are learning Magic Theory from a magus with a score of 7, could you get more than 140 XP? Or could you get 179 (one short of Magic Theory 8)?
I agree. A Teacher can only take to his or her own score, not up to a single point below the next score. The score in an ability is an abstraction, the real measure of knowledge or skill is the amount of exp. In practice the character with 7 is as good as the one with 7(39).
But in essence you shoudl be able to reach the same amount of exp as your Teacher. But for the sake of simplicity I'd only look at the score.
I've always thought you should be able to get to your teacher's number of xp, but most storyguides I've played with would stop at 140xp to try and stop people from minimaxing "I'm studying up to my teacher's xp, then spending a season in practice so I go to the next level".
I think that it should be the teacher's xp. At higher levels this can be significant.
Imagine a teacher who had level 9 + 38 xp in an ability. Thirty eight xp might take 4 or more seasons to gather, it seems implausible that the teacher would have learned nothing that he or could relate to the student that would increase the students understanding during this year of learning.
So you propose a house rule, which AFAICS wouldn't break anything. But you need to agree upon it with your troupe in time.
Note also, that by the paragraph from ArM5, which contains the quote above, a teacher with Magic Theory 7 (plus 0 xp) with a Teaching Source Quality of 15 can bring a student with Magic Theory 6 (plus 34 xp) to Magic Theory 7 (plus 14 xp) in one season by teaching.
That's only true if you assume that the xp come "in a lump". If you do, a Teacher who knows Magic Theory at a score of 3(0) and generates a Teaching Source Quality of 25 can bring a student in two seasons from a score of 0 to a score of 4(0), one full point higher than his own. Also, if you do assume that xp come "in a lump", the same reasoning should apply to Summae (which a student "may continue to study... as long as his score in the Art or Ability that it concerns is lower than the level of the text"), and many Roots of the Arts should probably be Level 1-3 Summae, rather than Level 5-6 ones.
I've never seen anyone else read the rules that way, though.
Let's read it again:
So every single season, teaching is done "in a lump" - as is e. g. also practice, training, learning from books or from raw vis. ArM5 p.165 Distractions resolves, what happens if several activities occur during the same season.
The tricky thing is, how to read the TEACHING GAIN LIMIT: Does it limit just the student's score reached in that season, or also the student's experience points gained in it? This is not written out: but as the limit is spelled in terms of the score, the simple, natural reading is applying it to the score.
It might be simple and natural to you; but no one else I know opts for an interpretation that allows the student to potentially exceed the score of the teacher by the end of the season, just because he was below it at the beginning. And even worse: it allows a Level 1 Summa to teach an Art to Level 5 or 6. So, I'm not saying you are wrong: I'm just saying you are alone.
The issue is settled in errata.
So my note here renders the contents of the paragraph on Teaching at ArM5 p.165 correctly, but does not take into account the errataed explanation of Limits on ArM5 p.163.
If errata on one page affect the reading of text on another in such a way, it is hard to keep track of them.
keep in mind as well that according to artes and academe up to 1/2 the points from a teaching source may be "diverted" into teaching or Latin (which is presumably the language for the lessons), or if the class is in Latin then they may be diverted towards artes liberales. In any case the point is if you would go over you can shunt the extra education points somewhere else, unless those abilities are also maxed out compared to the teacher.
Provided, that the academic learning in question is administered at an appropriate institution (A&A p.79 box has the list), or the teacher - likely at least an A&A p.91 Magister in Artibus - follows its established education methods.
I would allow the student to surpass the master. It's more interesting.
Puissant (Art/Ability) allows for exactly this, since the ranks granted by Puissant are considered 'on top' of the norm.