So, as readers of Tremontaine know, Rafe Fenton wants to found a new school. I have a few thoughts:
With visitors from Chartil, perhaps arrangements could be made for guest lecturers from that land, bringing their knowledge of the sciences and the arts. When the ambassador is available, perhaps Rafe might talk with him.
I have no idea what Joshua's specialty is. I think he could probably teach basics and organization, and these need to be taught by someone good, but I'm sure there's something else he'd rather teach. And, in the matter of practicalities, someone needs to be doing the books for this school. This isn't a job for Joshua, but perhaps he knows how to find the right person -- or perhaps Rafe's father does.
I've been thinking about how Micah might teach. I think she would have some success if she tried to explain how she played cards. Certainly, students would have more inspiration with a clear example of the practicality of mathematical knowledge!
Maybe a walkthrough of a game, perhaps in an appropriate tavern setting with beer and tomato pie, possibly with Tim and the rest of Rafe's circle, with editorial comments about how Tim is obviously bluffing, and really shouldn't, and why it's obvious Tim is bluffing -- that could be educational, especially for Tim.