[/quote]

As a mathematician I have to say that this approach is absolutely appalling. [/quote]

Can you give some feedback as to why you feel this way? These methods aren't sound for teaching the foundation of multiplication, sure, but for memorizing..well I don't see how it differs from rote practice whatever method you use, flashcards, games, chanting, etc.
It would be helpful to explain the reasoning behind your comment. In our case, using this method has worked and finally we have moved onto long division and multiplication.