How to do exercises for online course on ext mon?

I have an external monitor connected to iPad where my online course is running. When I want to do an exercise, I pull up Notability, but there is a problem. If I pull up Notability on the main screen, it drops into this goofy mode that is difficult to use, mangling the resolution on the external monitor and removing my course from the screen. I effectively cannot take notes. If I open Notability on the external monitor, I cannot take notes on it nor on the iPad display.

How do people take notes and perform homework exercises using an external display?