As previously stated, there normally are not more than five students enrolled in the school at a time. And even then, enrolled is a hard word to put in there. People sensitive to the arcane, or people that just found out they could use magic, or children from well known magic families, are all invited in here.
the lessons are normally held after they're done with their regular school or jobs, or on the weekends if that works better for the students. Besides the owner of the boxing club, a few members of the circle of magic frequent the school, and if students are enrolled, some of them act as their teachers. Sometimes, when very special students with a special purview enroll in the school, those student can have a single Solo-Teacher, with a more flexible schedule if need be.
What is a purview and how does that affect the teaching?
A purview is very simple the root of a mages power. It can be the source of their power, or the tools they need. What a purview is, and how a mage uses it, is bound to their understanding of it. A mage with the purview of electricity is either able to command thunder or is immune to being shocked. Or they can control everything that runs on electricity. How an individual interprets their purview and flow of Mana, and how sensitive they react to it, is absolutely up to them.
With the abundance of possible use cases for magic, it is hard to fit that in any sort of teaching guidelines. And rather than teaching new mages one correct way of using magic, the teachers at the academy prefer a more hands-on experience. Showing them examples within their own purview, and testing the students creativity and knowledge.
But alas, the most important part in using magic, is controlling one's Mana. The flow of magic energy in the body itself is the power house of every magic, and understanding and controlling that battery, is the first step to every lesson.
How do you actually finish a school with no actual curriculum?
One of the finer prints of the academy is, that no one ever really finishes learning and studying. Since our creativity and knowledge can grow and meanings shift, the purview of a mage can change form as well. That is why it is hard to actively teach spells or something like that.
That's why the one common rule is the teaching about Mana control. If a student is able to control their Mana, the teacher(s) start developing the individual brilliance of the student. Depending on the students general affection to the arcane, or innate talent, the overall study time varies a lot.
Rule of thumb is, as soon as a teacher is convinced, that their student(s) have a general understanding of their purview and the way magic works, they prepare a practical exam. It is individual for every single student, made to highlight their strengths, while also testing their weak spots. It is dangerous, to a certain degree, but never life threatening. And to finish school, and get a certificate from the academy, as well as a traditional invitation letter to "La Troupe d'Elégance", the Circle of Magic in Heldencoast.
But even after finishing the exam and becoming a part of the magic circle, the academy is open for everyone, and one of the favorite hang-out spots for mages all throughout the city.