If you watch the video, make sure you also read Mr. Person’s explanation of the problem. It really comes down to this: The traditional method of multiplication is more efficient, as his diagram demonstrates (traditional multiplication on the left, partial products on the right).
But also see Myrtle Hocklemeier’s response:
1. If efficiency is your top priority, get a calculator.
2. Timed arithmetic quizzes don’t measure math smarts. Real problems take longer than 30 seconds per problem to solve.
3. Drilling is what one does to develop a neural pathway, like a reflex, it’s not “higher thinking.”
4. Real math doesn’t have numbers anyway. Calculations are something that bookkeepers and engineers concern themself with. (Said dad to son as he wrote out a proof in point set topology)
On the other hand, I’m the one seeing first hand that if my kid doesn’t have his multiplication table down cold, he can’t factor and reduce fractions. And poor facility with fractions means that he’s clueless in algebra.
It seems to me that the partial products method helps kids understand the principles behind multiplication, while the traditional method just allows kids to work faster. But as Myrtle points out, there are times when being able to multiply quickly in your head is important for “higher math.”
The question is certainly not as simple as the video makes it sound. I think I’d prefer to see kids learn the partial products method first, then learn the “shortcut” later on.