After the teacher's unnecessarily flashy demonstration, all the students, under his direction, went out into the school yard so that they could get down to the business of what the course was all about, which was improving their control of their skills.
The courtyard, like many other fields at the academy, consisted of a large grassy field with the occasional tree popping up from time to time, giving the entire school more than enough space for all of its students.
As for why they had not headed to the training center, it was because the center was for specialized training, with conditions such as qi inhibition and so on being present, things that were not necessary for an introductory class.