What have we learned from science about the nature of learning?

It is of course difficult to conduct experiments involving learning, especially over an extended period of time, but there are potentially great benefits to what we can learn. Have there been any controlled studies of different approaches to teaching and learning? For example, Howard Gardner has a multiple intelligences theory. He says that some people are better learning visually and others learn better through listening. Has anybody tested this? Related to this, I once saw someone suggest that students may differ in what works best for them, though this may not necessarily be related to different aptitudes. For example, some may prefer a more open learning environment and some may do better using a more rigid approach. It would be nice to know if this is true. It may be that it is wrong to assume that there is one method that works best for everyone. On the other hand, there may be at least some principles that apply universally.