Estelle Morris reckons it "sends a message", but the trouble is it sends so many that it is hard to disentangle them.
The first, most obvious, message is from the Education Secretary to the nation's parents. It goes: "Come on then, if you think you're hard enough, make my day! Next thing, we're going to get you in the arrow-pattern pyjamas and matching ball and chain for taking your kids to Torremolinos in termtime, see if we don't! And shut up about the cost - we know it costs more to put a woman in prison than it would to arrange a home tutor for troubled girls, but this is pour encourager les autres, OK?".
But there are other potential messages. One is from the magistrates to the Government: "You passed this rubbish law two years ago, and it's time someone demonstrated the actual result. Single mother, bit of a sad sack, chuck her in jail, what good will it do? On the other hand, we're not that mean, so we made sure there's a 25-year-old sister on hand to look after these kids. Suppose there hadn't been, huh?"
Then there is the gender-specific message to single mothers: "Listen up! So these girls' fathers are out of the frame. That may well have a bearing on this, but we cannot be bothered to track the idle bastards down and make them share the blame, so we will lock up their only half-decent parent instead. Your fault for being so soft, woman.
"Should have put them into care years ago, then they could have bunked off school as much as they liked, or gone on the streets like all those other girls we pretend to look after."
The messages from the family are equally odd. The big sister says: "She used to get them dressed and send them - it isn't her fault that they came home again."
The girls say that their mother had been low since their Nan died and they did not want to leave her. Which is quite sweet, I suppose, but we are talking about two years. Which sends a message that this community is not very good at supporting families which have fallen into drifting, purposeless depression.
But the really unnerving message, which I devoutly hope has got through to Estelle Morris, is that these girls plainly saw no point whatsoever in being at school. Kids, however kind to Mum, tend to do what they want after a while. School, for the Amos girls, was not it.
School was somewhere they were told to go. It was not, in their view, a dynamic centre of life, a community of friends and mentors, a stepping-stone to achievement, freedom and security. It was irrelevant.
Why was it irrelevant? Because their mother had five children by three men, the earliest in her teens, and the elder sister is also a youngish mother? Were the girls siding with Professor Tooley (of "the mis-education of women" theory) by preparing for nothing but motherhood? Or were they just bored? It can happen even in a good school.
So I browsed the school in question's OFSTED report to look for clues.
It has a dynamic head, is improving and oversubscribed, but inspectors in 2000 found key stage 3 teaching faulty, communication with parents poor, and punctuality and attendance not impressive. But on the whole it is no different from hundreds of others. Not anarchic, not a sink, a normal school.
But it did not grab these girls. Not at all. They only went because they had to. Exams cannot have mattered in their scheme of things, nor what lies beyond. No play, no project, no concert, no match, no promised fulfilment of a common effort drew them through the school gates. They got dressed, set out, then thought "what the hell!" and headed back home to Mum.
Their sister says they have "grown up" during these events and will go to school now: but still the message niggles. They may go physically, but in spirit? How can they be made to want to go?
I sense cynical jeers from staffrooms and authoritarian barks from the educational right-wing. But still I worry. The Social Exclusion Unit produced a report called Truancy and School Exclusion in 1998, and proposed "tackling disaffection with more imaginative approaches to the curriculum". I do not see much evidence of that.
And I do not see, either, much joy in a system where great swathes of the pupils are only in class because their parents will be locked up if they are not. There is a message in there. Someone decode it.