Those who know my background may be surprised that I am arguing "no". I am a qualified teacher, and when I was a college principal I taught every week. As a leader it is important to command the respect of the teachers, and having done the job can certainly help with that. So a few years ago, I would certainly have argued "yes".
So what has changed? Schools and colleges have increasingly become independent, free-standing bodies and their leadership teams are now more diverse. Such teams include not just teachers, but specialists in areas such as finance, estates and personnel. Together, they understand their school or college.
Why should someone who has spent a career working in education and served for 10 years as a deputy be debarred from applying for the top job simply because he or she started off as a bursar?
Since incorporation (when they were removed from local council control), colleges have moved further down this road than schools, and several non-teacher principals have been appointed. Not all have been signally successful, but then neither have all the former teacher principals. On the whole, their colleges have gone on much as before, just as schools have.
I remember when I first introduced non-teacher senior leaders into a college more than 10 years ago, some of the teaching staff suddenly discovered their Department for Education numbers. This may have been a form of restrictive practice, trying to reduce the competition for high-status posts - though I am sure that is not a conscious calculation by most of those who take the other side of this argument.
More dangerous is the tendency of some teachers to look down on their support-staff colleagues. This was certainly the case with some of my teacher colleagues 10 years ago - despite liberal, even left-wing, views they unconsciously thought of support staff as making less of a contribution, and were bemused that some of them might aspire to senior posts. In an increasingly diverse workforce, such ideas need to be laid to rest.
The focus of schools and colleges must always be teaching and learning - helping students to achieve and to become successful adults. So the person at the top, regardless of professional background, must be held accountable first and foremost for this.
I am not saying that leaders can be parachuted in from business. Certain elements in Westminster apparently believe that the private sector is somehow better at leadership than the public. There is no evidence for that. My experience working in both sectors is that there is a similar mix of good, bad and indifferent leaders. And when people who don't know a business or its culture are dropped into top jobs, the results are often poor - we certainly do not want to be put in the position of parts of the health service.
However, the days of the "hero head" are gone (if they were ever here).
Schools and colleges are too complex for one person to master. To be successful a head must show leadership, and must also be part of a multi-disciplinary leadership team. The top job remains a very demanding one requiring energy, dedication, empathy, intelligence, and a raft of particular skills. Not many people have what it takes.
Only a small (and dwindling) proportion of teachers and even of leadership teams aspires to it. Nor are these qualities limited to teachers. Of course, whoever in the team is in charge of teaching and learning must understand it well, and that person should be a qualified and experienced teacher. Normally, so will the head or principal. But they needn't necessarily be so - we should be prepared to at least consider the unthinkable.
Martin Ward is deputy general secretary of the Association of School and College Leaders, previously the Secondary Heads Association.