In the past, jazz musicians such as Miles Davis have had negative experiences of ‘straight’ academies and conservatories, and these institutions have been negative towards jazz. This may represent a conflict between creativity and recreativity. But as a teacher of jazz at the Guildhall School of Music the author is finding that this conflict disappears when students from jazz and classical backgrounds learn to improvise by the same approach. This approach works upwards from the harmonic basis of jazz, which in fact is the same as that of classical music. As, at the outset, both jazz and classical students often seem to lack a precise concept of underlying harmonic form, the author concludes that more needs to be done with harmony at an earlier stage in music education, and that jazz may be the best context in which for this to happen.