Thus states 5.NBT.5 of the Common Core standards.
No doubt, I find it positive to include multiplication of multi-digit whole numbers, and I believe the intention of the statement is that people should be able to do it mentally or on paper, but without calculators. But to mandate "the standard algorithm", whatever that is, and require "fluent" use is way out of line.
I suspect that by standard algorithm they mean something like this:
What I find interesting is the inclusion of the phrase "using the standard algorithm". That, together with the word "fluently".
I learned it that way. So did millions of others. But many did not master it.
In my teaching days it hit me that in a world that reads and writes left-to-right, we were expecting students to work right-to-left in their arithmetic. I consider that one of the great fertilizing factors of math phobia. Left-to-right processes can be helpful for several reasons:
- The chance of error increases the further you get in an algorithm, and with numbers the most significant figures are to the left.
- Estimation is much easier for a brain trained left-to-right.
- Mental calculation skills improve when using the ability to read, write, and say numbers the same way.
- When using the above algorithm, the brain focuses on digits and not numbers.
Lattice multiplication is kind of neat, but I would not call it an algorithm that leads to greater understanding.
Back to Common Core: time to do a rewrite. Get Pearson out of the way, get big business to the sidelines, and get some math people covering the gamut from K to 12. Just make sure that they all have at least a BA in math. Just because Common Core means well doesn't mean it is doing it yet.
The web site freetestprep.net acknowledges this on one of their pages (see here).