I have been working with my daughter on the times tables. One of the things I have realized is that learning the times tables requires two different capacities: (1) the ability to calculate each of the calculations (e.g. 2 X 7) and (2) the ability to simply memorize the correct answer (in my daughter's case, this means memorizing calculations for numbers 1 through 12).
Categorizing these Capacities
I would categorize the calculations capacity as a cognitive skill and the memorization as more of a behavioral response. Because they are fundamentally different types of capacities, they require different instructional practices. The cognitive skill of calculating probably requires lots of explanation, examples, practice and feedback, and lots of hand on activities. In contrast, the memorization simply requires drill and practice through rote memorization. Both are important - the ability to calculate is important for later math skills, and the memorization skill aids greatly in the ability to move quickly with more complex calculations.
I noticed that my daughter was doing great with the calculations but hadn't yet started memorizing the times tables very well. She struggled for a while, but when we changed our strategy to one of direct memorization with drill and practice, and she memorized a dozen calculations in about 40 minutes. I decided to put together this video as a way to further enhance her memorization. I think that this video will work best if we alternate between watching the video a few times (demonstration) and practice with flash cards (application and feedback).
We'll see how it goes...