In an article in today's New Statesman, the Home Secretary suggests adults should not be afraid to tell off youngsters when they misbehave.
He said that it was important to set children clear standards and that everyone had a "mutual responsibility for the maintenance of order.
"Somewhere along the line we as a society started to feel that what other people's children got up to in pubic was none of our business - it was a job solely for their parents or teachers or police officers," he writes.
"Today how many of us, seeing a group of 11 or 12-year-olds vandalising a phone box or picking on a younger child, would actually intervene? Yet if we do not, who will?"
Mr Straw said that he wanted the public to realise that everyone had a role to play in confronting "the low-level disorder and disrespect" that leads on to more serious crime.
"If we want to live our lives free from crime, we must recognise that we all have a responsibility to help reduce it," he says.
"A `walk on by' society betrays the interests of young people. If we ignore young people when they are causing trouble, we start to ignore them when they are in danger.
"We all have an interest in children growing up into responsible members of the community. That can only happen if we support parents in setting clear standards of how they should treat others."