Most parents want schools to encourage values such as honesty and fairness in pupils, a survey suggests.
Some 87% say schools should play a wider role than just delivering academic results.
More than 1,000 parents were questioned by Populus for the University of Birmingham's Jubilee Centre for Character and Values.
"Many schools do not know how to teach character", said Prof James Arthur, the centre's director.
"They might have a statement of values, but too often they are bland paragraphs that have little impact on what goes on in the classroom."
Deputy director Tom Harrison added: "We are not saying academic skills are not important - it's just got out of kilter."
"Clever children are great, but they also need be able to turn up on time and be honest, self-disciplined and respectful in the workplace," Mr Harrison told BBC News.
Some 84% of the parents polled said it was part of the role of a teacher to encourage good morals and values in students - while 81% agreed schools should set out the core values they aimed to instil in students.
An overwhelming 95% said it was possible to teach a child values and shape their character in a positive way at school through lessons, team-building exercises or voluntary work.
Only 5% said children would pick up these traits from their peers and experiences at school.
Some 13% said schools should focus on delivering academic results rather than shaping character.
Of this group, most said their child learned good values at home and about a third said it was not the government's role to guide a child's life.
Among parents who agreed schools should do more than deliver exam results, most said schools had become too exam focused, while more than three quarters said it was important to instil good values in the next generation.
Mr Harrison said the survey showed parents' support for more focus on character development in schools.
He added subjects such as religious education and citizenship could analyse desirable character traits but sometimes other approaches were needed in order to instil good morals.
Russell Hobby, general secretary of National Association of Head Teachers, said: "Teachers and heads overwhelmingly support teaching values as well.
"They know that it supports academic achievement and employability.
"Academic skills are vital but you also need the character to use your knowledge well. Resilience, curiosity, courtesy, initiative - they matter.
"I think people will be surprised by how much is actually going on in schools, but we must be careful not to crowd out character building with too many assessments or a narrow vision of the curriculum.
"Sport, adventure, volunteering, performing arts and cultural visits can all contribute, as can the study of great literature and history."
The Jubilee Centre opened in 2012 with the stated aim of contributing through multi-disciplinary research "to the renewal of character and values in Britain through research and development activities".