Monday, December 11, 2006

Long division

If you listen in on the math wars, you'll notice that long division is one of the more divisive issues in this war. It's hard to comprehend why fuzzy math zealots are so opposed to teaching long division and making such a fuss. For example, NCTM in its so-called standards calls for "decreased attention" to long division. I've taught long division and the kids caught on quickly.

In a paper called The Role of Long Division in the K-12 Curriculum that should be must-reading for educationists, David Klein and R. James Milgram show that long division is a crucial skill necessary to understand more advanced math concepts:

We discuss the role of long division in the K - 12 mathematics curriculum. We begin by reviewing the reasons that most math educators today depreciate the topic and other topics in the curriculum that derive from it, such as polynomial long division or polynomial factorization. Later we show that this view is simply wrong mathematically. The role of long division is not just to divide one rational number by another, but the algorithm itself contains the initial exposure of topics which become crucial in the core
applications of mathematics in our society today. Following the introduction, we discuss methods for teaching long division in such a way that the underlying concepts can be understood by students. We then provide more details about the ways in which these concepts develop in later mathematics course, and why they are so important.
After reading this, the mysteries of real numbers and the conversion of fractions to decimals will become much clearer. Isn't conceptual understanding what the fuzzies purport to be after? So why are they opposing a tool that leads to a conceptual understanding of major math topics?

UPDATE: Reader Katie has left an incredible link to an actual conversation between a phone customer and a number of customer reps (supervisors) that sounds more like an Abbott and Costello routine. It's about telling the difference between dollars and cents expressed in decimal form. The reps never get it and instead rely on a calculator without realizing what they are doing. This should give pause to NCTM and fellow fuzzies and their enthusiasm for calculators.

What is absolutely hilarious is that at the end the rep (supervisor) declares that the difference between the customer's correct math and the rep's fuzzy math is a matter of opinion.

More here.


Katie said...

This is what happens when they don't learn math, and only use to learn calculators.

(or in print: )

Instructivist said...


Thanks so much for the link, Katie.

I listened to the whole thing. My head is spinning and I am speechless.

You are so right about not learning math and only being able to use the calculator like a robot.

This should blow NCTM's nuttiness out of the water.

Anonymous said...

A press release from the city of Denver earlier this year said:
"The November ballot question asks Denver voters to raise the sales tax rate .0012 percent (1.2 cents on every $10 purchase) to fund a high quality, parental choice preschool program for Denver’s four-year-olds."
Fortunately they changed it before making the ballot language official.

Alexandre Borovik said...

Long Division is indeed the most sophisticated structured algorithm of school mathematics. It deserves to be learned just for the sake of development of algorithmic thinking in children.

Jonathan said...

Much of the value of the algorithm is that it gives intensive repeated practice in estimation, multiplication, and subtraction.

It is indeed strange when I teach polynomial long division, and some students have not done arithmetic long division. I end up teaching both.r

Blank said...

Well, if you want to practice some...

long division worksheets