Any further significant gains in attainment will probably only come from schools that talk about their values and communicate them to their parents and community.
Gordon Jeyes, director of children's services in Stirling, said that school effectiveness strategies had probably reached their peak. It was time to focus on community engagement.
"Schools need to understand that their own effectiveness is dependent on the effectiveness of civil society as a whole - families, playgroups, community centres, youth clubs, neighbouring schools. Schools need to develop the language and institutional structures to engage with their communities. Values have to be identified, shared and put into action," Mr Jeyes said.
Too many schools had displayed a "lack of moral confidence" in their partnership with their communities, which may be down to a "lack of professional confidence".
It was more straightforward in Roman Catholic schools which were clear about their value base, even if the majority of pupils did not attend mass.
"Too many of our schools do not work on this because it is harder.
How do we take this forward in a multi-denominational school setting? But schools that do it, irrespective of their denominational base, and are confident about their values base and have a language to discuss that with their parents are more successful," Mr Jeyes said.
Philip Rycroft, head of schools in the Scottish Executive, said the key to lifting the long tail of underachievement was to tackle issues around the whole child.
Bill Gatherer, of the Gordon Cook Foundation which funded visits to Maine, said that good as Scottish education was, "we are not good enough at helping young people grow up as responsible, caring adults". The foundation would continue to encourage schools to build their core values.