Teacher2Teacher |
Q&A #12679 |
From: Pat Ballew
(for Teacher2Teacher Service)
Date: Dec 09, 2003 at 02:59:15
Subject: Re: Language - "reduce" fractions
I don't know if it is possible for language to be mathematically incorrect, but it certainly can make certain concepts more difficult to understand if we use language which is imprecise or misleading. The problem that many people have with using the word "reduce" when we work with fractions is that it gives the idea we are making the fraction smaller, when in fact we are keeping it the same. What is being reduced, in a sense, is the values of numerator and denominator to the smallest values which make an equivalent proportion to the original. The fear is that when you tell a student to "reduce 4/8" he/she may somehow come to believe that 1/2 is smaller than 4/8 because it has been "reduced". I have seen no real evidence that this is true, but I also see no reason to preserve the historical use of a term that can be replaced so simply with more appropriate terms. "Simplify" seems to be a good, short replacement, and for test directions or when we wish to be very exact, we might actually say something like "Express each fraction as an equivalent fraction using the smallest possible denominator." I just wouldn't think that would make it in typical conversation. It may be that teachers who use "reduce" are doing no real harm, or are only slightly delaying an understanding of what is happening in the re-expression of rational fractions, but with the myriad misunderstandings students have about fractions, their order and size, it would seem worth the effort to make this minor adjustment in language. Hope some of this is of benefit. Good luck. -Pat Ballew, for the T2T service
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