Sometime in elementary school, most of us endured memorizing multiplication tables, up to 12 x 12. However, in the past few decades, people rely more on calculators, and metric measures and decimals have replaced shillings and dozens in much of everyday life. So is there any purpose in learning multiples of twelve? Jon McLoone looks at the question, and finds that mathematical errors are reduced when you learn your "times tables," but only as far as the sevens, then the benefit of knowing more flattens out (see above graph). At least as far as future mathematical errors go, learning the higher tables may be useless.
However, looking back at my own experience, I believe that learning the nines, tens, elevens, and twelves will help a student to see the patterns in numbers. For my children, finding the beauty in mathematical patterns made the difference between hating math and exceling in it. What do you think? McLoone has a lot more to say about multiplication tables at the Wolfram Blog. Link -via b3ta
In my experience, a lot of learning and memorization can come around as a result of needing to use something. I've had students ask why I remember so many atomic numbers and masses and if I sat down to memorize the whole periodic table, when instead it was because there were certain elements I needed to use the numbers for on a daily basis and I just remembered them eventually (but not others I didn't use). At least in some fields, like math and physics, you can re-derive things instead of memorizing them. Although for teaching some basic principles, you need to prime the pump and some memorization is needed, and some more advanced topics can become way too tedious and slow to teach if a student can't recall the basic stuff from memory.