They keep learning at as fast a pace the teachers can reasonably manage. Math, reading and writing, flying lessons, navigation, etiquette and procedures. People in the sleepy little village they fly over sometimes are happy to wave up at the little witches flying around above them! Apparently a bunch of the students' families live there, too.
Occasionally the school is visited by Important People in fancy clothes - the adults all bustle around and make lots of fuss about how well the young witches are learning, but the visitors aren't very interested in actually meeting students, apparently.
Once four weeks have passed, it's about time for the special magic classes to begin. They have been scrambling to find appropriate teachers. The class for their special magic can't really be held in groups, except for a few pairs or trios with similar powers. There are three witches who can shoot lightning with differences in control level and kind, two who can shoot fire (with subtle differences there, too), three with generalized telekinesis (same deal), two who can do geases, two who can fly really really fast, two who can make ice all around them, two with magic for aiming with weapons. Everyone else is unique enough not to benefit from groupwork.
One day, her math teacher keeps her after class for a minute. "We think we've found someone who would be good at helping you learn to use your special! Miss Jacqueline Blucher. She also has a metal-related special and comes well-recommended. However, she wants to teach you for whole days at a time, because she is rather busy and travelling here and back to Karlsland takes a while. You'd miss your usual classes for those days and have to catch up on what we covered later. We could find someone with a more convenient schedule but who might not be as good at teaching you how to use it if you'd rather not miss whole days at a time though."