Our DD7 is working on multiplication tables at home, and we're overt about the goal being to memorize them. That was one of the few things I enjoyed when I was in elementary school, because it was the one thing we were allowed to do at our own pace. So not only was I not being held back by the rest of the group for once, but I was internally motivated to show off by being the first one done. Plus, every time we successfully tested out on a new number, we got a Blow Pop.
One of the reasons she's homeschooling now is because her school was doing such an awful job at math... and this was one of the subjects she actually got to go to a gifted program for. They introduced the concept of multiplication through what they called a "matrix", which was just drawing boxes and then counting them.
Okay, teachers, that's fine for an introduction... but if that's the tool you're going to give them, why are you asking them to solve for the total carpeted area in square feet for a reasonably-sized house? Haven't you skipped right past something rather important?
I took one look at what she was working on and how she was attempting to solve it (and getting extraordinarily frustrated at all the counting), and I told her to stop, this is stupid, here's the multiplication table in your folder, use that instead. She got to see the value of that tool immediately. Later on, I quickly demonstrated a 4 digit x 3 digit problem for her, narrating as I worked. Then I drove the lesson home... the first step in learning how to do that is to learn this table.
In order to correct the behavior of her teachers, I recommend they be ordered to clean out the sandbox with a spoon. That'll drive home the lesson of using the right tool for the job.
