I had a discussion about teaching long division recently with someone who has thought long and hard about primary-level mathematics. She thought that teaching "short division" by 1-digit numbers would serve most of the purposes that teaching long division does. Short division is similar to long division, except that you don't write all that stuff under the gozinta sign part, and rely more on mental arithmetic and an understanding of place value (number sense!) The method can be souped up to do 2-digit divisors.
It seems to me that one of the main objections to long division is the excessive attention that must be paid to getting the steps of the procedure right when the divisor has several digits. Kids and teachers get so obsessed with the algorithm that all the ideas go out the window.
I am very fond of long division, or at least several important mathematical ideas that it leads to: remainder (modular) arithmetic, infinite sequences (nonterminating decimals), and division of polynomials, for example. And most calculators won't do these things; have you tried to buy a fraction calculator at the drug store, or even at K-Mart? Most people own a calculator, but it's the plain 4-function kind. Susan Addington Academic year 1995-6: The rest of the time: firstname.lastname@example.org The Geometry Center Math Department 1300 South 2nd St., Suite 500 California State University Minneapolis, MN 55454 San Bernardino, CA 92407 (612) 624-5058 fax: (612) 626-7131 WWW at Geometry Center: http://www.geom.umn.edu/~addingto/ ***** NEW MATH GAME! ****** Check my Web pages for The Number Bracelets Game.
On Wed, 22 May 1996, John Sheehan wrote:
> email@example.com says: ...the larger question is why are > we spending time teaching long division. > > Whatever argument you make for not teaching long division can be > applied to addition, subtraction, and multiplication. If you > teach those three, why leave out long division? It's like teaching > how to shift gears, and leaving out reverse. Why is it that when > something's value in the curriculum is questioned, it is always the > slightly-more difficult piece of the puzzle? > > John Sheehan > firstname.lastname@example.org > >