Then he brightened and explained how the blue light on top of police cars worked.
My daughter moved to senior school and a wirier, more troubled-looking policeman appeared. "No doubt about it," he told the girls, "you are going to get mugged and you might get assaulted." He taught them how to hand over a mobile phone without provocation. He advised them to carry money in order to give it away because, occasionally, frustrated mugger equals murderer.
The lesson was to stay alert, avoid conspicuous gaiety and never catch a stranger's eye. There are still areas of Britain where doors are left unlocked and people stop for a chat in the streets, but cities have a distinct Children of Men undertone to them.
A few weeks ago, my daughter was visited again, this time by self-defence instructors. When asked about the legal limits to fighting back, they said:
"Better be tried by 12 than carried by six." They also said: "Let him have your property. Don't let him have you." Should my daughter be groped on the underground, she now knows to lift the man's arm high in the air and say:
"Look at this dirty old man." If she is sexually assaulted in the street, she has some nifty karate moves ready. There is no training to protect her against guns and knives.
Still, she comes home confident after self-defence lessons. Her older brother looks at her with admiration and unease. He has already been mugged with dreary regularity. Boys between 13 and 17 are the most frequent victims of street crime and see phone theft as a tax on leaving the house.
Each time it happens, their pride is catastrophically hurt and the police have to impress on them that resistance is foolish.
Meanwhile, the savviness and swagger of the sanction-free modern mugger is growing. Recently, my son saw two older boys on bikes watching him from the corner of the road. Experience taught him to run. The boys' experience taught them that liberal, middle-class boys are cannon fodder. One shouted:
"Why are you running away? Are you being racist?" Sure enough, my son returned, mortified. As he was assuring the boys that he abhorred racism, one of them hit him to the ground and demanded coins and phone.
So how should schools portray the world to their pupils? The educational ethos tends to be optimistic about human nature. It is positive about teams and communities and citizenship. I certainly prefer this teaching to one that says "fear your neighbour". Schools represent sanctuary, but they should not be a parallel universe. Whether it is local crime or global terrorism, the threat must not be dismissed nor exaggerated. Politicians have a duty to children of school age not to distort crime statistics or terrorist threats.
What do politicians - and teachers - want children to think the world is like? At the moment, the picture they have is pretty confused.