But staff at the Barrhead school, which gained 11 "excellents" and four "very goods", are in no doubt that it does. "It reduces the queues of kids waiting for staff to sort out problems," says Anne Hall, depute head.
High achievement in East Renfrewshire schools is often attributed to leafy suburb locations. But St Mark's has an above-average free meal entitlement, so it must be doing something right. East Renfrewshire has decided to roll out peer mediation to every primary school over the next two years, the first authority in Scotland to do so. Edinburgh-based Sacro will provide the training.
"We see this as a very positive step," says Richard Hendry, national schools co-ordinator for the charity that aims to improve community safety.
Peer mediation looks natural. Disputants sit down with a pair of mediators, chat about their problems and try to reach an amicable resolution. But, in reality, it is a fundamentally different approach to conflict from that normally taken in schools.
Mediation is not about right and wrong. It is not about punishments and rewards. It is not about adults handing down judgments on children. So it does take time for pupils to absorb the shift in thinking needed to make peer mediation a success, says Angela Feherty, a Sacro trainer. "We take them out of class for two days' intensive training. We introduce them to peer mediation, do role-playing exercises, get them to think about conflict in a different way. We show them it is a normal part of life.
"We get them to think back to a time when they were in conflict and remember their feelings. Then we show them how to take away the scare factor and learn ways of dealing with conflict day to day. You can see their brains ticking over; you can see when they get it."
One of the hardest parts to get is learning not to tell people what to do, says pupil mediator Lisa Lochrie, 11. "They can make up with each other or they can go their separate ways. We don't decide for them."
The role-play was interesting and fun, says Lauren Dunne, 11. "You've got to experience both sides. Being a mediator wasn't as hard as I thought it would be."
Most of the St Mark's mediators agree and have few worries, now they're trained, about handling whatever they meet during real mediation. But they did express concerns initially, says Christine Healey, class teacher and peer mediator co-ordinator. "They worried they might not be able to solve a problem, that they wouldn't be able to get them to be friends again, that they wouldn't be good at mediation. But during the training they learned that their job was to help people reach agreement for themselves - not do it for them. After the training, we asked them again and most of their worries had disappeared."
When people in dispute come to mediators, there is a structure that participants follow. Once everyone is settled, the mediators invite each party to tell their story. No interruptions at this stage is one of relatively few rules. Experienced mediators say this part of the process can be therapeutic, pointing the way to a resolution, by allowing each party to hear the other in a way that doesn't happen when emotions run high.
But to new mediators, it can be confusing. "Sometimes they tell a completely different story," says David Munro, 11. "So you're not sure what happened."
David can't put his finger on exactly why he decided to become a mediator, but remembers that he "really wanted to do it". Colleagues suggest that it's because he is a "very helpful person". As the only male in the group, David brings a valuably different perspective - even if only an estimated 20 per cent of those seeking mediation at St Mark's are boys.
"We need to encourage more boys into mediation, and get them to talk more and to understand their feelings," says Ms Hall.
Part of the problem is that this type of activity is still regarded as more appropriate for females, says Charlie Johnston, quality improvement officer. "These kinds of roles are almost invariably filled by women in society. That is a challenge. Mediation is about learning to become emotionally intelligent. That is something we all need to do."
Boys who have the courage to take part do respond well to mediation training, says Angela Feherty. "They can have tremendous insights. It may not come as easily to boys. I've heard teachers say that schools are more geared to how females learn, and there's possibly a bit of that in mediation training.
"You are asking them to be emotionally literate, to express how they're feeling, to participate in role-play. But David, for instance, he took to it really well."
Once participants have told their stories during a mediation session, the mediators try to draw out ideas for the way ahead. There are general guidelines - don't take sides; don't tell people what to do - and certain situations become familiar to experienced mediators. But some scenarios are harder than others, says Lynne Armstrong, 11. "The problems the P1-3s bring might be a bit easier. It's more complicated with older children, I think, because there is more talking and persuasion, though you do have to take the young ones seriously.
While peer mediation is about pupils solving their own problems, with the assistance of trained colleagues, adults may on occasion have to get involved. At St Mark's, an extension has been built, looking out on the playground, specifically for mediation sessions. Day-to-day monitoring and mentoring is the responsibility of Rhona Macdonald, pupil support assistant. "I'm in the playground at playtimes and lunchtimes every day when sessions are on, so I can keep an eye on things. Mediators come to me with problems that can't be resolved or issues about children's safety the school needs to respond to."
Over time, the benefits of mediation to a school are very clear, says Ms Healey. "We used to have endless trails of problems after lunch, which could take 15-20 minutes to sort out. Now, most get sorted before they escalate."
But the benefits to children - mediators and participants - are even more important, says depute head Anne Hall. "They are learning vital life skills. The big message is that nobody can sort out children's disagreements for them. They have to learn to do it themselves."