The term "orchestration", has been used to describe the teacher's role in activity settings incorporating interactive technologies. This musical analogy suggests pre-planned manipulation of events to generate "performance" leading to learning. However, in two recent projects we have observed how effective teaching and learning is often based on serendipity and improvisation--characteristics more often associated with jazz. This paper explores how a jazz analogy can be useful when analysing classrooms in which serendipitous events were exploited and performances were improvised. [For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]