There are so many fads concerning learning the multiplication tables, that it's hard to sift through them and figure out which one makes the most sense for you, your child, or your students.
There are a few things to take into consideration when you are searching for the best methods for your needs. Keep in mind that whenever you learn anything, it's good to try more than one method.
The "just-shut-up-and-memorize-it" method is the one used by most American public schools. That's one of the reasons why American elementary school children pretty much suck at math compared to most of the world. There's no need to let your child be at that low level.
When looking for a method to learn multiplication facts, keep these things in mind:
The method should:
* Be based on understanding that multiplication of whole numbers is an extension of addition, but is not exactly repeated addition. (There is a subtle but important difference that you can read about at It Ain't No Repeated Addition)
* Use and develop the "number sense." In other words, it should show the child relationships between the numbers s/he is multiplying, and other familiar numbers, like the number ten. For instance, 8 x 5 is like half of 8 x 10.
* Be based on more than one sense. Just doing worksheets is not enough. If you repeatedly hear multiplication problems as well as see them, you learn how to deal with them with more than one sense. That "locks in" the skill.
* Stress understanding of what one is doing, not just memorizing random facts.
The method should not:
* Not be such drudgery that the child will forever look on math as a boring chore.
* Not be based on some corporate Saturday morning cartoon characters. The "math-is-fun" school of thought is basically sound. But it should be about the math itself being fun, not because Barney says so. Be careful that your child doesn't get trained to like math only if it comes with a cartoon character.
* Not strictly based on mnemonic (memory) devices like songs, rhymes, etc. They may work in the short term, but most of them neither develop the number sense, nor are they well-developed mnemonic techniques. If you use only them, the child will have learned only superficial information, and nothing about multiplication, or how to use mnemonics, for that matter. (Mnemonics for much more advanced calculation is a great help - just not for things as basic as the multiplication tables, and not as songs or rhymes.)
* Never, ever, ever be learned from a calculator. Using calculators to teach simple multiplication is like shooting squirrels with an elephant gun. You may hit the squirrel, but won't get dinner. Calculators are crutches. Would you give a healthy child crutches before s/he learns to walk?
Children appreciate having their minds valued, and not being pandered to. One effective method of teaching/learning the multiplication tables that offers just that can be found at Learn2Multiply.com
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