In my college classes, I am able to use the interactive lecture style most of the time. It’s an extremely efficient way to convey information to students and I can see that students are learning based on their performance on short tasks that I assign during class. This teaching strategy works at my college because our students are highly motivated, know how to learn and behave in a lecture style class, and have excellent prior experience with mathematics.
In my RCHS classes, I have to limit my lecturing to a few minutes at most. Students don’t seem to be able to endure listening to me for more than a few minutes at least at this point, even if my lecturing is peppered with student questions and responses. (Perhaps I can slowly train them to do this?) So, to make the use of every moment in class, I am mostly asking students to do mathematics in class. My class time is usually spent like this: start class with a warm up activity, make announcements, give students instructions on a task, then let students work on the task while I walk around and help individual students. I haven’t gotten good enough to plan for closure at the end of class, but I am working on that.
I’m not sure it would be obvious to someone visiting my class that learning is happening, but I think it is. The trick is in designing the right kind of mathematical tasks that get students to learn without me telling them much. And wow, doing this well takes so much time and effort.