Mr Reid says 16-year-olds should have the vote and citizenship should be part of the core curriculum.
The Scottish Parliament's education service is already "a world centre of educational excellence", he says, and will be further improved when the new Holyrood building is opened. But MSPs could be doing more work among young constituents.
Mr Reid, an SNP member who has been elected presiding officer in succession to Sir David Steel, told The TES Scotland: "When the Parliament was set up, I was determined it would have a good education service. I think we might have a world centre of educational excellence. I believe we are out in front of other legislatures in the UK, the United States and Europe in the service we provide.
"Over 16,000 pupils have visited the Parliament and used our teaching materials. But is this enough to engage young people? Not particularly. I think their disaffection is with the classic party-based process because they are passionate about issues, as witnessed recently during the war in Iraq, and we have to address that.
"The Parliament does a good job but it's up to individual MSPs to promote more outreach among their own young constituents which means going into schools. It's not about telling young people. It's about dialogue, about listening to them and reflecting on what they have to say. We are a rainbow parliament so we should be asking young people: what matters to you?"
In regular visits to primary and secondary schools in his Ochil constituency, which takes in schools from Clackmannanshire, Kinross and Stirling, Mr Reid finds pupils are motivated by issues such as global warming, GM crops, Third World poverty, women's rights, young people's rights, health matters, bullying, war, youth crime and the police.
"They understand complex matters like our voting system and they can be quite sophisticated," he says. "A 14-year-old girl recently asked me why we don't operate open lists, for example."
Mr Reid has promoted votes at 16 from his first days in politics.
"Citizenship, which includes rights and responsibilities and issues like globalisation, should be as important as the three Rs and should be part of the core curriculum but taught across the curriculum. We are not geared up enough for this but in my own constituency schools like Alva Academy are doing this by binding in teachers and departments on a project basis while meeting national guidelines.
"The approach should be international. In talking to young people in schools, for example, I explore issues like globalisation, that there is no longer such a thing as a job for life, that you could be locked into a global company and find that you are as likely to be working in Seville or Munich as in Scotland.
"They raise issues about a branch factory closing and moving to Indonesia and complain it's wrong and we should be doing something about it. So we discuss the question: with globalisation can we have protectionism? How could it work?"
Mr Reid advocates twinning across the world and says that pupil visits and exchanges should be the norm. While contact via e-mail is easy when dealing with schools in countries like Poland or Germany, in countries like Angola and South Africa he suggests we should be willing to help them bear the cost of getting schools online.
At the new Holyrood building the Parliament's education service will be better equipped, he says, and there are plans to engage tertiary and adult education centres and organisations. There is likely to be a local twinning, too - between the new Parliament and its neighbour Dynamic Earth to promote joint visits for schools.
Mr Reid says this illustrates what the Parliament intends to be a holistic approach. "Politics and politicians should never be isolated. We are into exploring new ideas and the education service is open to new ideas coming in from all educational spheres," he says.
Gavin Clark, vice-chair of the Modern Studies Association, says it is a pleasure to see the Parliament's presiding officer putting citizenship so high on the agenda - especially as many Scottish schools lack a modern studies department.
"Citizenship should be taught across the curriculum because it is about social, economic and political literacy. It is about showing young people how they can take part in the system to effect the changes they want. The key aspect for us is political literacy which should be taught in a dynamic way. But that depends on every school in Scotland having a modern studies department.
"A national survey carried out by our association in 2001, which is about to be distributed shows, for example, that in Edinburgh itself only 53 per cent of schools have a modern studies department. It's ironic that, in the city which houses the Parliament, nearly half the pupils are being denied political literacy."