I can provide a partial answer that might be of interest. University culture in the middle ages was highly influenced by ancient philosophies that came before it, mainly that of Greece and Rome. In both of those cases, Rome being influenced by the ancient Greeks before it, scholarly pursuits were highly tied to the field of rhetoric. You should be able to make a good case and hold a speech about a topic in order to truly be proficient in it was the idea. You would learn about subjects and facts by doing research that went into your rhetoric, but you were always "graded" by how well you could argue your case.

Therefore then middle age universities put more focus on a student's capacity as a speaker rather than their pure academic merits as we would see it today. Middle age university studies were as much about rhetoric as they were about what we today would view as actual academia, regardless of what subject you studied.

This actually continued for rather a long time. Up to the late 18th century many universities still operated that way, including Uppsala in Sweden (where I learned about this).

When I think of medieval homework, I think of 13th/14th century cathedral schools. They would practice their skill by completing "disputations." Students were given texts to read (called "lectio") and they were asked to identify the most important questions/debates surrounding this text and to present the arguments for each side.

These were formalized into what we call "quodlibetal literature," which takes it's name from the word "quodlibet" meaning essentially "whatever," because any question possible could be posed to the student and they would respond before a live audience (both of other scholars, and the community at large). There are a large amount of these quodlibetal questions extant, and they give us a lot of insight into the pedagogy and intellectual interests of the high to late Middle Ages.

And yes, these were like essays, though they were much much more formal than a contemporary university essay. They handled all kinds of questions, from theological and textual questions, to current events, so their subject matter was very broad, similar to today's college essays. But their form was very unique and these quodlibetals are not exactly thrilling reading, though taken as a whole they are fascinating (again, this is similar to today's culture of essays in universities, at least in the US which is what I'm familiar with).

Here's a good summary on disputations/quodlibets.

If you want a solid, comprehensive treatment of quodlibetal literature, check out

Schabel, Christopher. Theological Quodlibeta in the Middle Ages: The Fourteenth Century. 2 vols. Brill. 2006-2008.

To add on to this interesting question: what was a typical school day like then?

One of the standard texts is still Charles Homer Haskins The Rise of Universities (New York, 1923), despite its age. It's only about 120 pages and you can pick up a copy for a couple of bucks on amazon.

But here's a basic rundown. Cathedral schools typically only addressed basic learning – reading, writing, math, all through the primary lenses of the Bible and Roman law. Beyond this, churchmen and women were expected to pursue their own course of study as part of their religious calling. The classical educational curriculum were the seven liberal arts (lat. artes liberales). Isidore of Seville, author of the most popular dictionary in the middle ages defined “art” like this: “an art is so called because it consists of strict precepts and rules. Others say this word is derived by the Greeks from the word…‘virtue,’ as they [usually termed] knowledge.” Thus the acquisition of knowledge was also the acquisition of virtue, and virtue for most everyone in medieval Europe meant learning more about God and his creations. This was not always explicit. It could be in formal academic settings, or in more practiced professions, so even if you were a ditch digger or a barrel-maker, if you learned that skill well and pursued it to the best of your ability, there was something of God’s will to be gleaned from it.

However, nobles began recognizing the economic, diplomatic, and administrative benefits of education, and began sending their kids to be educated in increasingly larger numbers. Thus, demand for education beyond the basic seven liberal arts was needed, especially in technical fields such as civil and common law. These aspiring students began seeking out renowned or respected scholars, teachers, and writers, whether they were members of the church or not (though almost all of them were clergymen).

These teachers would profess their knowledge to their students, and were thus called professors. Eventually, these professors began to charge students to learn from them, in order to make some money to live and further their own studies, especially if they were not members of a specific religious institution. They also needed places to hold their meetings and sessions for a not always small group, so the professor might rent out an inn, or the students may pool their money and rent out the town hall on Tuesdays and Thursdays. Students often formed groups of their own to ensure fair pricing and good education. Professors also formed guilds, requiring students to have certain requirements for admission, generally obtained through examination. Professors needed a license to be in the guild, called licentia docendi, and was a teaching certification, but served as a the first kind of academic degree in the modern sense. To receive licentia docendi in Paris, students must be publicly examined by faculty on selected topics. At Bologna, students were examined before the faculty, then publicly. This is the likely origin of modern practices like the thesis and dissertation defense.

These groups were known by a particular name - universitas magistrorum et scholarium or a collegium. Let’s look at the word, university – it comes from the Latin word universitas, but more accurately universitas magistrorum et scholarium. Universitas means “whole” or “all of” like our modern cognate “universal” but in the context of this phrase it means something more like group, corporation, or community of people. The same definition applies to the word college – it comes from the Latin collegium, which also means “group, community, or society” – though it later became a technical term that we still use today, usually to indicate a specific group within a larger university group.

These communities relied primarily on standard Roman and Greek (translated into Latin) legal, philosophical, rhetorical, and theological texts. Books were commonly rented because they were expensive, and more than a few students would do pro-bono work for a manuscript producer and copy texts for free as long as the student could make an additional copy for themselves. Another method would be in the classroom, where the professor might have a text that all of the students would copy from as he dictated to the class. The students could then take notes and comment on upon that day's assigned section. These copies and notes would have been taken either on cheap, scrap parchment, or on wood boards covered in wax that could be reused as needed.

There was no real need for libraries since books could be rented, but over time, books were given to the colleges for the use of student on the spot and free of cost, and these eventually became university libraries. The oldest library catalogue at the Sorbonne from 1338 records 1,772 volumes in its collection.

Hope this helps a little. Happy reading!

In the Irish (and Scottish, we assume) bardic schools, which are arguably the Gaelic equivalent of university at the time, there were lessons on grammar and proper usage of language. The students weren't writing essays, as the materials for doing so were incredibly expensive, and in the case of the poets, you were supposed to memorize everything anyway. They did write down some of their poetry, though. The style of Gaelic panegyric remained basically identical from 1100AD-1600AD (and a little longer in Scotland), so the schooling must have been rigorous.

From Osborn Bergin's lecture/introduction to Irish Bardic Poetry:

...besides acquiring a thorough familiarity with the literature and history of the country, the student had to make a minute and careful study of the language itself. [...] There is a grammatical tract compiled or revised about the beginning of the sixteenth century. This tract [...] gives models of declension and verbal inflection with thousands of examples, rules for aspiration and eclipsis, alternative forms, forms which must never be used, and so on. The most interesting thing about it is that the compiler gives hundreds of couplets from various poets as examples to prove his statements. In this he was like a modern scientific grammarian. [...] I believe it was intended as a practical text book for use in the schools. Without something of the kind the teaching of the standard dialect could hardly have been so successful.

To answer /u/Frickinfructose about a typical school day, most of the information about what the schools were actually like come after they were all closed. There are some hints here and there in the poetry itself, though, and they echo a description of the schools published in 1722.

The schools were somewhere remote or, at the very least, quiet, so the students had the fewest distractions possible. The students lived together in windowless housing. The lack of light wasn't meant to be cruel, but rather to continue an established Gaelic tradition of the poetic arts. (They did have candles, though.) They were meant to do all their creating in a dark room, lying in bed. Other poets would talk smack about them if they composed their pieces out in the open; there are several poems where one professional poet calls out another for doing so.

They were divided up into classes by age and level of previous schooling. There, they would work on grammar or memorizing verses by previous poets. Then they would compose an original work demonstrating the skill they had learned.

From the linked memoir above:

The said Subject (either one or more as aforesaid) having been given over Night, they work'd it apart each by himself upon his own bed, the whole next Day in the Dark, till at a certain Hour in the Night, Lights being brought in, they committed it to writing. Being afterwards dress'd and come together into a large Room, where the Masters waited, each Scholar gave in his Performance, which being corrected or approv'd of (according as it requir'd) either the same or fresh subjects were given against the next Day. This Part being over, the Students went to their Meal, which was then serv'd up; and so after some time spent in Conversation and other Diversions, each retir'd to his Rest to be ready for the Business of the next Morning.

Also, they got Saturdays, festival/religious holidays, and the summer off.

Also, when you completed the work, what would the grading scale be? What would a medieval diploma look like?