In the early Middle Ages the methods of teaching the novitiate monks were relatively static and drew heavily from Classical precedents.

However to really delve into the educational practices of the early Medieval Church, we need to look to Late Antiquity for guidance. The Church after all inherited the classical approach to education from the late Roman world, it did not invent a wholly new approach to education wholesale, but rather modified and adjusted its Classical heritage to suit the new environment.

So what did Late Roman education look like? In short not necessarily similar to what we are used to. Schooling in the late Empire was limited to the upper crusts of society. It was connections and patronage that got "students" admitted to the prestigious academies in the empire. Cities such as Athens and Alexandria were centers for the elite of the Roman world to send their sons to be educated. Once they arrived the students would live their lives as a general nuisance to anyone and everyone around them.

Students were stereotyped as violent, drunkards, rapists, and in short generally out of control. Their courses may have prompted this out of control behavior as their manner of learning was often harsh. Lectures and memorization were the name of the game. Students would memorize large amounts of literature, philosophical works, mathematical algorithms (and the line between those last two was not clear). The classical corpus emphasized works such from figures such as Homer and Plato, that were suppmemented by other philosophers, mathematicians, religious figures, and historical works. Those other works would change over time and in different locations. Other elements that were emphasized were rhetoric, grammar, astronomy (and astrology), and logic.

The education of elite Romans was something of a cross between a modern univeristy lecture, fraternity hazing, and country club that was built off of connections, adherence to a, quasiflexible, canon of texts, and memorization over critical thinking skills.

How did Medieval education differ? In short, it took a similar approach, filtered it through monastic discipline, and replaced many of the works of philosophy with Christian writings.

Christian education has a contentious history during the empire, and the suitability of Christians to work with and teach classical texts was not always clear cut. For example Julian the Apostate tried to prevent Christian teachers from teaching works like The Iliad to limited success. And this is important because Church figures such as St. Augustine stressed the importance of education for Christians in matters beyond the religious. Some early church fathers, such as Tertullian, argued that Christians had no reason to work with classical literature or philosophy, but other figures such as St. Augustine won out, and texts as diverse as Caesar, Galen, Cicero, Arrian, and more became mainstays of Church education. Some for their philosophical/educational merit, this is how writers like Pliny the Elder survived, or as a useful tool to teach Rhetoric, Grammar, Logic, and so on, this is how Caesar and Cicero made it into the Middle Ages.

Combine this work with the scriptures of the Christian faith, especially for monks the Psalms, Gospels, and epistles of Paul, and you have the basis for the corpus of medieval learning.

Now the actual methods by which many students learned their Latin, rhetoric, history, astronomy, and such, would have been recognizable to the Romans. Strict adherence to memorization and recitation were still the name of the game, only this was compounded by the natur of monastic life. In Late Antiquity many teachers were of mich lower social status than their pupils, but in medieval monastic communities strict deference to the masters was expected, and enforced at the tip of a rod.

The confines of monasteries were supposed to be centers of strict discipline and this was borne out in more than just religious observance. Messing up Latin in rhetoric/grammar instruction was grounds for a savage beating if the monk Ælfric's Colloquy is to be believed (a document from Anglo-Saxon England that was used in monastic instruction). Students were expected to learn Latin (as well as sign language) quickly and through the tried and true methods of memorization and recitation.

It was only later in the Middle Ages, as education broke outside the confines of monastic communities that curriculum changed, but the means by which students learned remained the same, in some cases up through to the modern world.

A related item to this question is the 11th century Benedictine monk Guido of Arezzo. He wrote about and taught music, music theory, and music pedagogy which were important within monastic tradition. His main work, the Micrologus explains tenets of music theory like intervals and how to tune them using a stringed instrument. The whole thing is short enough to be considered a handbook and is definitely oriented toward pedagogy. Another of his works hits on similar points and is actually a rhyming poem to make it easier for students to remember, I believe it is called the Prologus.
Guido is also considered to be a pioneer in what is today called solfege. (Do, re, me, fa, so, etc.) The general idea being that these techniques make it easier and faster to learn the vocal music so many monks were performing. Scholars generally agree that it did not come from Guido, but there is also a Medieval music learning system called the Guidonian Hand where singers anchor pitches mentally to fingers, joints, etc which is also a loose precursor to modern vocal instruction techniques.

I believe Guido never made “head monk” but his work does show clear evidence of a pedagogical line of thinking in monastic tradition.