Studies have shown that people are more likely to learn whilst tutored by someone from their own peer group i.e. other pupils/ students. A concept in Scandinavian schools follows pupils that tutor each other. That can be a 5th grader helping an eighth grader get along in math and the eighth grader on the other hand helping the fifth grader with languages. This is because they have "floating" classes, where students choose the subjects and in which order they fulfill their own curriculum.
People learn quicker when trained by someone who "speaks their language". When a student understands a concept he or she is able to simplify and explain it more accessible to other students.
A trainer comes to the company and teaches small groups of up to ten people on any given subject. The participants should be from different teams, so that there are no more than two people of one team in class. After they are trained in their subject, they become "experts" in said subject and can now teach other people of their team (or whoever is interested and couldn't book a session with the trainer). The employees who are taught by "experts" become "2nd experts" and can also teach others.
How would you stage or advertise your hack?
My hack could be promoted as a time saving device. If only one person per team goes to the course he or she can teach others afterwards. This can possibly happen during a lunch conversation or during several coffee breaks. Always depending on the topic. Courses on programs are bound to be explained at the desk, but here the social factor can be a trigger. They don't spend much time with fellow colleagues, here's their chance to change that. If employees are "experts" on a certain topic they could get a plaque with the topic on it which they could put on their desk for people to see. It would also be possible to put the expert knowledge in their internal email signature so that people they are corresponding with, see that they are an expert and feel free to ask for advice on that topic. The same goes for the social intranet. People could post their expert knowledge and connect with others to teach them. There could also be a reward system implemented.