Is it really possible that here in the 21st century - when only on the fringes of Ukip is the desirability of gender equality anything other than received wisdom - the teaching profession suffers from a public-esteem problem because it is dominated by women?
The answer, unfortunately, appears to be a resounding yes.
Is it really possible that the profession is paid less than others because it has three women for every man?
The question should be preposterous, yet the answer again seems to be in the affirmative.
If we accept both these propositions, as most sensible observers do, we end up at the question of why. Why is this still the case?
The issue is explored in this week's feature, and it is striking how long it has been going on. Since the creation of school boards in the 19th century - the first step towards a free, state-run education system - teaching in this country has been both female-dominated and badly paid.
For nearly a century and a half, it has been characterised as the profession of choice for educated yet family-minded women who accept that theirs will likely be their household's second income. Teaching has also been characterised as one of the "caring professions". And, as seen in nursing, social work and elsewhere, this status seems to go hand in hand with lower pay.
But which comes first? Are these professions perceived as "caring" because they are female-dominated, or is it the other way round? Chicken or egg, it's a financial cross that millions of committed teachers, nurses and social workers have borne for generations.
This is so exasperating that I would like to set it aside and move on, but I can't resist pointing out how strange the reverse sounds: "Because lawyers and bankers care less - the soulless bastards - they are paid more."
And what of the childcare argument? Is there an unspoken social contract between women who choose to enter teacher training and the powers that be stating that although the pay packet may be light, the working conditions will be well-suited to rearing school-age children? It is, of course, true that despite huge strides forward in the past few decades, even in the most progressive households it is the woman who does the majority of the childcare.
This is an issue so gargantuan that it would take more than these few column inches to truly get to grips with it.
Whatever the reason for its existence, this idea of "caring" teachers doing a job that suits family life is currently being stress-tested, possibly to destruction, for two reasons.
First, the absurd workload of most full-time teachers means it is no longer so easy to fit Little Jemima and Little Jonny around the job. Second, the data-driven, results-obsessed culture of the present school system is not, according to many, conducive to "caring".
As one female teacher told me earlier this week: "Most schools these days feel more like the New York Stock Exchange once the first bell goes."
There could be an upside to this, of course: if the working life of the average classroom teacher increasingly resembles that of the average Wall Street trader, perhaps the salary will follow suit.
And pigs might fly.