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:
AbstractAfter 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?
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.
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.