Although teaching would seem to be exclusively coupled to each country's economic and technological development, it can also be associated with social transformation, provided that it promotes social innovation: in other words, new ways of conceiving society. This leads us to ask how music teachers are being trained in terms of innovation, a concept that plays a decisive role in our current knowledge-based society and economy. This article seeks to obtain an overview of the goals and structures associated with the concept of innovation as featured in the Master's Degree for secondary-school music teaching in Spain. We analyzed the Spanish legislation and the Master's Degree programs of 26 Spanish universities. Our results evidence a lack of consensus regarding which objectives should be pursued and which innovative practices should be prioritized. We nevertheless note a tendency to view innovation merely as an exercise designed to help teachers and students adapt to existing school reality by proposing activities and projects in the area of digital technology, along with examples of "good practices". We conclude that educational innovation needs to make fundamental progress, not only in terms of its presuppositions, but also in its actions, which should lead to the development of critical, creative attitudes that can foster true social transformation.