Dave Marain of MathNotations is running a poll about how to teach multiplication, but the question has broader application:
How should we teach the arithmetic algorithms
— or should we teach them at all?
Algorithms are step-by-step methods for doing something. In arithmetic, we have standard algorithms for addition, subtraction, multiplication, and long division. Once the student masters the steps for any particular algorithm, he can follow the steps to a correct answer without ever thinking about what the numbers mean.
An efficient algorithm can free a student to concentrate mental effort on learning more difficult concepts (such as multiplication or division of polynomials) or thinking through multi-step word problems. But reliance on memorized algorithms can be a “follow the recipe” approach to math that disguises lack of understanding, leading to a student’s eventual crash-and-burn (usually in high school algebra).
What is the solution? Do you have an opinion? Head over to MathNotations and make your voice heard!