The Role of Long Division in the K12 Curriculum(长除法的角色在K12的课程体系).pdf
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The Role of Long Division in the K-12
Curriculum
David Klein R. James Milgram
Department of Mathematics Department of Mathematics
California State University, Northridge Stanford University
Abstract
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.
Introduction
There is a long standing consensus among those most knowledgeable in mathematics that
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standard algorithms of arithmetic should be taught to school children. Mathematicians,
along with many parents and teachers, recognize the importance of mastering the standard
methods of addition, subtraction, multiplication, and division in particular. The profound
importance of the long division algorithm and its role as a prerequisite to other parts of K-
12 and university level mathematics will be
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