This paper seeks to integrate a scholarship of ritual with a scholarship of improvisation and relate the intersection thereof with mathematics teaching and learning and with mathematics education research. Drawing on their experiences as classroom teachers, as practicing improvisers, and as current education researchers, the authors draw from scholarship about ritual, improvisation, and related concepts from sociocultural and mathematics education literature. They propose ways that mathematics teachers and mathematics education researchers might find ritual and improvisation to be illuminating concepts for their work.