There was a time, perhaps at the turn of the century, when classroom teachers were observed in their teaching with a focus on the moment by moment attention of their pupils. Full attention was even considered to be an indicator of maximum learning. It was as if by appearing to attend equated with learning. A pupil’s gaze out of the window meant that the pupil wasn’t learning.
In feed back on their teaching teachers would be informed about the degree of their pupils’ attentiveness, and often in precise quantitative terms. While this particular reign of terror may not have been common, it is an example of the way in which what has come to be labelled pupil engagement became a marker of successful teaching and viewed as being co-extential with learning. Musical engagement equals musical learning.
It would seem that engagement has become a quick and easy label through which all kinds classroom activity can be justified, and a good selling point for particular methods and materials – ‘This or that will engage your pupils.’ – presented as an end in itself.
The promise of engagement erases … well … disengagement, a lack of engagement, dispirited pupils, pupil alienation.
My purpose here is not to bury the idea of engagement but to clarify what it might mean. And I must confess the origins of my own interest in the idea.
Somewhen in the 1990s Csikszentmihalyi’s flow theory attracted my attention. I engaged with it. Flow theory offered some understanding of how we are when deeply involved in an activity, and music seemed to be a good example, so involved in fact that we lose all sense of time, distractions are excluded and self-consciousness disappears. One attractive element here was that engagement could be linked to intrinsic motivation, often thought to be some ultimate goal of education. 
In the case of flow I was thinking of engagement on a micro here and now time scale, that state of being where we are … well … deeply engaged in the music. But then I came across the term engagement being used on a macro time scale referring to pupils musically engaged over the period of a year meaning that during that time they were learning to play an instrument. These pupils may or may not have experienced flow. The term engagement here meant a commitment over time.
Unfortunately, research into the idea of engagement has failed to yield much in the way of clarification, except that there are three kinds of engagement: behavioural, emotional and cognitive.  This doesn’t seem to take us very far and begs the question, what engagement is for?
‘Engagement for what’ would seem to be a reasonable question. Is it sufficient to view engagement simply as a matter of pupil motivation, as getting involved, committed? The implication is that once engaged, then you are off rather like a motorist engaging a gear and releasing the clutch.
This would make sense if your view of music education is that of a teacher stimulating their pupils to make music and being the facilitator of musical learning as a sufficient end in itself. However, if your view of the teacher is of somebody who places substantive matters before pupils, musically worthwhile ones, then engagement would be seen as emanating from the pupil themselves in the act of understanding something significant.
So, are your pupils musically engaged? What is it that is engaging them? What are they coming to know and understand?
 Csikszentmihalyi, M. (1991) Flow: The psychology of optimal experience. Harper Perennial.
 See Frederiks, J. A., Blumenfeld, P. C. and Parks, A. H. (2004) School Engagement: Potential of the Concept. State of the Evidence. Review of Educational Research, 74. 1, pp. 59-101.