My latest epistle to the Head of School at Natural Friends:
Teacher Cranium -- I recently had the following conversation with a "New New Math" educated kid:
Me: You know the shortcut for multiplying by 10?
Kid: Yeah, you just add a zero.
Me: OK, what's 53.5 x 10?
Kid: Um... 53.50?
Me (horrified): That's the same value!
Kid: Oh, right. Is it 530.5?
Kids need to understand that it's not just about "adding a zero", it's about shifting the place value. In an ideal world, you should be able to ask the kid, "why does 10 have this special property, but not, for instance, 8?" and eventually get the answer, "... because we're in base 10."