Ms Williams questioned whether parents were distrusted
Parents who spend quality time with their children should be rewarded through the benefits system, head teachers' leaders have said.
Punitive steps like fining parents for truanting children rarely worked, National Association of Head Teachers president Clarissa Williams argued.
She also quizzed the logic of insisting young mothers go out to work.
But the children's minister Beverley Hughes said: "Government doesn't raise children, parents do."
A more creative approach was needed, Ms Williams told NAHT members in Liverpool.
Ms Williams said at her association's annual conference that she had twice written to the prime minister questioning the rationale behind "a punitive approach to ineffectual parenting".
'Listen With Mother'
She asked: "Why do we feel the need to send children into an educational environment at the age of two?
"Are parents so distrusted that we want to separate them from their children at the earliest opportunity?"
She said "real communication" took place at mealtimes around the table, "without the TV and the video games".
She recalled the "good old days" when mums sat in at schools while their children enjoyed the stories of Listen With Mother on BBC radio.
Her association heard stories of "little ones" in early years centres who were not able to sit still because they were so over-stimulated "or just plain tired because they did not get put to bed early enough," she said.
Ms Williams called for a benefit system which provided incentives for good parents.
"What I would like to see is a benefits system that would reward parents for engaging with schools - that could be linked in some way to the benefits they get," she said.
HAVE YOUR SAY
Good parenting should never be rewarded: it should be required by the law
Bob, Hamilton Canada
Perhaps parents who spent time reading to their children, going to school parents evenings or helping out in their school, could get higher payments, she suggested.
She acknowledged it was a complex area and that there would always be some parents that would be hard to reach, but that did not mean it should not be tried.
"We all know what good parenting is, and in fact unless we actually show that and reward that in ways that people see the rewards, which - let's be honest - financial rewards are quite important.
"In the long term it will be less expensive in a society, than one which is forever paying out when things go wrong," she added.
Head teachers were reluctant to instigate "parenting orders" as they did little to improve home-school relationships, she added.
Children's Minister Beverley Hughes responding by saying: "Government doesn't raise children, parents do.
"Our job is to give parents as many choices as possible, so they can make their own decisions on what is best for their family and their children.
"We have extended maternity leave and introduced paid paternity leave for the first time ever.
"We also give every child 12.5 hours of free high quality early years education a week, which research shows has a lasting positive effect on a child's education and life chances."