The idea is that both the professor and students would be running TeXmacs.
As the professor gives his/her lecture in TeXmacs, notes would be incrementally transmitted to instances of TeXmacs running on the students’ computers.
This would make it easier for students to follow the lecture without having to take notes manually.
Moreover, students would be able to annotate the notes as they appear and some of their annotations could be sent back to the professor.
So as the professor is incrementally revealing/writing notes in TeXmacs, he/she would see feedback from students in real-time. For example, a formula might turn red because most students are having trouble understanding it.
And so the professor might try to better explain it.