@Iluviaporos - It's all about scaffolding and the way the brain works. It's like a wiki in some ways. You can put a new idea in there but if it doesn't connect to the existing ideas then it's never going to be accessed.
If you teach children multiplication and don't show them how it relates to addition and to physical objects in real life, then it will just be an isolated fact that they memorize.
If you scaffold the idea of multiplication with real examples (we have two boxes of six eggs, how many eggs do we have? how would you find out with addition? How about multiplication?) and show it to them in many different ways, then it will connect up with the ideas they already have in their heads and will be truly accessible.
This might seem slower than just getting them to memorize something, but once they grasp the idea behind multiplication, they will be able to expand on that much more easily than just memorizing formulas.