Monday, February 23, 2009

Why teach long division: part II

In my previous post, I discussed one reason for teaching a general algorithm for long division: namely that reliance on calculators and estimation doesn't give you enough feedback about wrong answers.

Reason #2 for teaching a general algorithm for long division is that this lays a foundation for a key topic in algebra: polynomial division. Algebra teachers, including Mrs. H, report that in teaching how to divide polynomials, it's helpful to begin with concrete examples of the algorithm in question that involve numbers instead of variables.

Indeed, with complex problems in general, it's helpful to start students off with analogous problems involving small, simple numbers. Since many general algebraic procedures are analogous to general arithmetic ones, all the more reason to teach the standard algorithms to mastery--and to start doing so well in advance of algebra.

Next up: reasons for teaching the traditional long division algorithm in particular.