The relationship between the independent school Head and the Board is enormously complex and full of seeming paradoxes. For instance, the Board is the Head's employer, but the Head is often the Board's teacher. Heads are wise to seize teaching moments as they arise, wiser still to keep an active, on-going syllabus of operational topics to include in trustee orientation, retreats and Head's reports at full Board meetings.
Here's a quick take on what that syllabus should include:
How we hire people
How we evaluate and compensate people
How we work on curriculum and pedagogy
How we work on diversity and inclusion
How we assess/communicate kids' growth
How we help kids/parents in the secondary school/college process
How our athletic and other extracurricular programs reflect our mission
To be clear, these are "windows" as opposed to "doors" conversations. The Head should make it clear that the effort is to keep the Board informed about important operational practices so that they can be confident about the Head's leadership and knowledgeable ambassadors for the school--rather than to seek input. It's also important for the Head to include reflection on the dynamic edges of any of these practices--what's new, what you're working on--lest you unwittingly give the impression that they are monolithic, immutable. The Head should boot up the Board Chair so that he/she can head off any conversation contributions that might lead the Board into the operational weeds.
Because the Board's membership evolves year after year, Heads must remind themselves to put these "lessons" on a regular cycle. Longer-serving Heads know the experience, somewhere around year 7, when you look out across the Board room and realize that not a single trustee was present when you were hired. And here is another reason for the Head to observe these teaching duties: the Head as political capital builder with the Board, the leader who's on top of things, who's "got it" and making the school even stronger.