Actually we do teach children the logic behind it. Our main purpose is to let children know that Math is not rocket science, but it's based on very simple logics. The most important thing is to let them understand why and how we can solve a problem.
For our example of multiplication by 11, the method we showed is always accompanied by an explanation why we can do it that way.
We tell children that any number multiplied by 11, is actually equal to the number multiplied by 10 plus the number itself.
So if 23 x 11, it's equal to 230 + 23.
Because of this fixed pattern, it lead to a simplification where placing zero and adding subsequent number works.
Again, at Math Monkey we also emphasize that there's no right way of solving a Math problem. There's many different ways and it's up to the children to decide which way they're most comfortable with.
Hope that our explanation could clear some of your doubts, if not we're more than happy to show more examples