We've gone back to deciphering Harriet Ball's meter rap. Here's another video featuring Harriet Ball:
This is interesting because it's a tutoring situation -- one-on-one with a bright little girl. But it's still all about memorization, instead of understanding why multiplying with negative numbers must work the way it does. The rules of mathematics are not arbitrary.
There's some useful explanations of multiplying with negative numbers at Ask Dr. Math.