Of course, headteachers continually deal with situations like this. Creative heads often use them to advantage, to restructure the school's staffing, to provide opportunities for junior staff, to save money.
But the fact is that half-termly deadlines for resignation pose unwarranted difficulties for even the most creative of heads. A resignation in October or February effectively means that the post cannot be filled for a term-and-a-half on anything like a satisfactory basis - the deadline for other, currently employed, teachers to resign has already passed. A resignation just before a summer half-term effectively means that a post can be filled only by a newly qualified teacher.
It is difficult to see why schools are still operating like this. When local education authorities managed staffing budgets, the imposition of three deadlines for teacher resignations perhaps made sense: it gave them the opportunity to manage staff deployment across the authority and, if necessary, to respond to short-term difficulties. In an age of devolved budgets, the requirement makes no sense.
It ma once have made sense for teachers to begin at a new school only at the beginning of a new term. But it is difficult to make a strong case for that now and if, as seems likely, some schools are operating four or five-term years, then term dates will become more variable than ever across the country.
A simple change in teachers' conditions would ameliorate the difficulty: if they were simply required to give six weeks' notice any time in the school year, then schools would face a smaller hiatus.
It would mean that teachers would be able to leave post in mid-term, but it would also mean that schools could decide to make appointments to fill posts much more quickly. Heads would gain much greater flexibility. Teachers would be able to move on much more quickly, rather than working out what can be up to three months' notice. Pupils too would gain, because their heads would be able to fill posts with high-quality staff more quickly.
These advantages are not outweighed by the spurious neatness of filling a post with effect from the first day of a new term. A simple, liberalising change in contractual conditions would help everyone.
Of course, none of this will be of any comfort to my daughter, disappointed not to see the year out with her much-loved teacher, but it would give the school the chance to choose a replacement it would like much more quickly.
Chris Husbands is professor of education at Warwick University