This paper presents the collective reflection of a temporary community of inquiry (COI) created during an international workshop at the 20th biennial ICPIC conference--“Philosophy In And Beyond the Classroom: P4wc Across Cultural, Social, and Political Differences”-- and the suggestions emerging from that event. The workshop, entitled “Pedagojazz—improvising and inquiring, community interplay”, was conducted via Zoom, but participants were both online and present in person. The topic focused on the pedagojazz perspective, and the short activities proposed were aimed at (...) involving the (temporary) COI in a collective discussion about how it would be possible to transform a community of inquiry into an inquiring-jazzing community. Three premises were introduced as common background on which to develop our reflections: the pedagojazz perspective; the connection between pedagojazz idioms and the different roles of the facilitator in P4wC; and the idea that jazz, and collective improvisation in particular, can inform COI development. The principles and practices of pedagojazz and collective improvisation are presented in detail here. During the workshop, Zoom chat and the Wooclap site were used to involve all participants and to gather their contributions and suggestions. A word cloud and three tables were produced and are presented here. Interesting themes, questions and perspectives emerged that can help us reflect in a more complex way on the education of P4wC facilitators across cultural, social and political differences. (shrink)