My high school English teacher who was charged with Shakespeare did the same thing. He’s a professional actor and this was the day job. We got “admonished” several times for reading ahead on our own(the whole class did it at various points). However, this format makes the stories fun, interesting, and readable. It was hard to leave off at a pivotal point in the plays with the whole weekend to go, especially if the class wasn’t to be held on Monday or Friday.
I know and appreciate MacBeth, Hamlet, Midsummer Night’s Dream, and Taming of the Shrew because of this format. Now I wish that we also read King Lear.
Oh, and our memorization was one of his poems, though, not lines from the plays. Papers and exams were on both. Before starting the play each day, we read and briefly discussed his poetry.