Discipline is "the key education issue" for most parents asked about recent government initiatives in England.
People believed discipline had worsened in recent years
Mori organised eight 90-minute discussion groups in London and Manchester, on behalf of the Department for Education and Skills.
Parents tended to be satisfied with their children's schools and thought standards had risen - in part due to greater investment.
But they felt they did not have meaningful choice of school places.
They did not like what were perceived to be "American" words such as "academies".
Government proposals to tackle indiscipline were favoured but there was a debate about the extent to which parents could be held responsible, especially for their children's attendance.
The term "off-site provision" was misconstrued by many.
"Some believe it refers to a youth club style arrangement for delinquent children and others to a boot camp," Mori said.
"The latter is preferred in order to drive up standards of discipline."
A spokesman for the Department for Education and Skills said: "Real progress had been made in tackling serious bad behaviour in schools."
Behaviour in most schools was good for most of the time.
Mori's report said many participants were of the opinion that it had declined over the past few years - with more reports of attacks on teachers and other pupils.
Teachers were also believed to have fewer rights to enforce order.
Access to good secondary schools was another big issue - though parents did not necessarily want more choice if it meant having to become "experts" to make the right decisions.
They did not see why poor children should have free transport - they wanted the offer extended to all children, but also felt those arriving on "the poor bus" would be stigmatised.
Many disliked businesses backing schools.
"It prompts concern as to why businesses would want to do this" - with a feeling that they "would wish to get something out of this arrangement" or "make a profit out of schools".
They also were confused over what sort of parents might want to set up their own schools.
While turning round failing schools was a priority area, people felt the new one-year deadline was "far too short".
On personalised education, parents welcomed more one-on-one tuition but had concerns about how it would be implemented - and did not favour the involvement of teaching assistants.
There was however great support for head teachers and teachers "both of whom are held in the highest regard", the report said.