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David Scott Powell

Posts: 54
Registered: 12/6/04
Posted: Aug 9, 1995 2:40 PM
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Chi-Tien said:

>The most important mathematical concept adopted in Tonna's procedure
>is that by multiplying or dividing the same number in both numerator
>and denominator, the value of the fraction is unchanged. This is
>conceptually simple and student should know very well already ( at
>least by dividing the same whole number from both numerator and
>denominator when they do the reducing of fraction ).

I tend to think that almost nothing about a fraction is all that simple(to
the students). Fractions really need to be grounded heavily in a
geometrical context to really make any sence. If you think about it talk
of numerator and denominator is confusing for almost anyone.

>This concept and its extended version:
> operate the same operation and number on both side of equal sign,
> the equal sign is still valid.
>are also the most valuable ones in developing the algebraic
>manipulation algorithm. The beauty is that both these basic concepts can be
>very easily demonstrated and proven.

Easily demonstrated, maybe. Easily proven, uh to who? To you and I? you
are probably right. To an average 4th grader? I don't think so? Why
should they believe it just because we can throw numbers around an equal

>This is may be the reason why it "is" (or "was"?) the "standard"
>algorithm been taught in the "old" classroom world wide.

And the reason why so few understood it:-)


Scott Powell
University of Hawaii
University Labratory School
1776 University Ave.
Honolulu, Hi. 96822

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