Years of failed attempts to engage my mathematics teacher students in exploration and co-creation led me to radically change my teaching approach. Inspired by literature that uses the jazz improv metaphor for teaching, I derived three tenets based on principles from jazz improv. First, I would bring no more than a single problem-solving task to class. No lectures were prepared. Second, I would not do any mathematics myself throughout the entire semester. Third, I would only mention a theory if we encountered a situation described by that theory. Here, I describe the rationale behind these tenets and the unfolding of the first tenet-led semester. I embraced improvisation as the new norm, stopped preparing traditional lectures, and started preparing myself. While being the facilitator of co-creative mathematical explorations, I was on the constant lookout for experiences that could serve as starting points for curriculum-relevant theoretical discussions and discussions about teacher actions. Drawing on the students' engagement, their feedback, and the final examinations, it seems they gained important insights from this experiment. Most importantly, I felt the joy of participating in the joint mathematical explorations, and I believe the students experienced the same. [The page range (p. 8-12) on the URL: is incorrect. The correct page is p. 8-13.]