>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 sign?
>This is may be the reason why it "is" (or "was"?) the "standard" >algorithm been taught in the "old" classroom world wide. > >Chi-Tien
And the reason why so few understood it:-)
Scott Powell University of Hawaii University Labratory School 1776 University Ave. Honolulu, Hi. 96822 firstname.lastname@example.org