My Roles as the Instructor
The University of Michigan has a long history of formatting intro-level math courses, such as Calculus I and Calculus II, in the spirit of Inquiry Based Learning (IBL). A class of ~20 students form groups of 4 to 5. In an 80-minute class meeting, the instructor gives an interactive lecture which involves asking the students to test ideas or compute examples in groups in the middle of a lecture so that the students are learning actively. More details can be found here.
As an instructor for Calculus I and II, I roughly spend 40~50 minutes lecturing and 30~40 minutes facilitating group work.Â
As a teaching assistant for Calculus III, I lead lab sessions each week. The labs involve guiding the students to use MATLAB and Desmos to experiment on ideas they learned in class, holding (IBL-based) lectures on extended materials, and holding review sessions before exams.