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Topic: Concepts vs. Algorithms
Replies: 3   Last Post: Jul 9, 1995 11:56 AM

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Norm Krumpe

Posts: 53
Registered: 12/6/04
Concepts vs. Algorithms
Posted: Jul 9, 1995 2:28 AM
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Chi-Tien Hsu wrote:

>Again, I don't understand how one can separate concepts from algorithms.

There is, I feel, an enormous difference between concepts and algorithms.

To understand the concept of division is to understand what it means to
group things, compare things (as in ratios), etc. A child in first grade
shows some basic understanding of the concept of division when the child
shares something fairly with a friend. And this child can do it without
knowing anything about a long division algorithm.

An algorithm is simply a step by step procedure that "gets a job done". But
there are many many algorithms that accomplish finding quotients. Yet, we
find it necessary to spend so much time teaching the one long division
algorithm to nearly all our students.

Ask a student who has learned the long division algorithm to find 2 divided
by 8. I guarantee that in nearly any class of 5th or 6th grade students,
some students will answer "4", indicating that they may know an algorithm,
but don't understand the concept. On the other hand, give a 5th or 6th
grade student two dollars and ask that student to divide the money fairly
among eight people, and chances are that student will find a way to do it,
indicating that they understand the concept of division, regardless of
whether they know the long division algorithm.

Sorry, but right now, I just feel that our students are capable and deserve
to spend their time on more important mathematics than that long division
algorithm. With all the mathematics that exists in the world, the long
division algorithm hardly deserves the attention it is given.

Norm Krumpe

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