We all have the philosophy at Vivo Strings that our job as teachers to keep students engaged by meeting them where they are currently. Ideally, we would love to work on really serious classical music in the order that we have found works the best with every single student. However, when you get down to teaching real students sometimes those methods do not engage every student. We firmly believe that taking these "detours" from our regular music to topics and styles that students want to explore makes us better teachers and students better musicians.
Often these detours end up solidifying an important concept more strongly into a student's musical vocabulary. For example, a student might discover that the pop music they want to play is more difficult than they realized and they desire to come back to more fundamentals so that they can play the pop music more successfully. Or a young student might need to move around rather than sit still at piano. I have been encountering this with a young piano student over the past several months. I got a large floor piano (Like the one in "Big"!) a few months ago for us to use in lessons. Today, we actually played all the way through two whole pieces (which is a huge accomplishment for this student!).
Kathryn, Brittany and I talk often about the desire make music fun for students but with the end goal being to teach every single one of our students mastery of their instrument. It is important for us to always have the end goal in the sight but at the same time have the flexibility to take detours along the way to keep students engaged.