Human innovation has always been accelerated through competitions. When groups compete, the results of innovation are far better than when individuals compete. For the most part this is how we work in the real job world. However in most schools and classes it is always the individual who is competing against other individuals. More so each individual is also required to perform at their best in all fields (subjects). This is a false model for our kids as this does not train our kids for the real world.
If we look at a real world job scenario, each one of us is very good at one thing (for the most part, i.e. our department) and we then collaborate with others (departments) to achieve combined success (company results). What if, even in the current classrooms, say we divided the class into four corners. Each corner representing broad categories/groups of math, science, languages & social sciences. Each student is given an option to pick their favored group, either by their choice or based on the teachers observation. Then classes/sections compete against each other for the best class with the highest aggregated score. In this model, I believe that every student will not only share their secrets to understanding the subject faster but also learn other subjects from their expert classmates. This model will I think help the students help each to win against the other class for the title. This will also make the role of teacher from being a person required to know all the knowledge to being the coach who brings out the best in their children. This I think would lead to collaborative innovation in anything and everything they do as a team. The children understand their key strengths and their role in the team. They work as one team as opposed to one individual.
This is something we see all the time in any team based sport or well organized groups like the armed forces or companies. Whatever be the task on hand, be a project or just the current form of academics, I think this will lead to innovation in the way learning happens. It is the children teaching other children and the adult facilitating the learning as opposed to the adults teaching children in their own perceived language.
What I have also seen is that collaborative teams with the good age mix in their team perform the best. Teams with at least a 4 yr age group difference or an average of 2.5x (x being the ages/grades of children within the group) performed the best when it came to school children. Schools do not allow this kind of a mix in academics but do so in sports, where children of the school are divided in various school teams of 4-6 teams.