===============================
> casting out nines is a terrific tool to get some students
> interested in pure mathematics. It's easier to use than the written
> explaination makes it seem (and that isn't too bad anyway). It can provide
> a great check on addition, which some on this list believe should be done
> by hand, at least by students. Frankly I've only seen it used for
> multiplication, but it seems that it should work for addition as well.
> Phil Mahler
> Middlesex CC
===============================
The term "casting out nines" may be dead, but the idea is very much alive.
What this process amounts to is a calculating a simple _check-sum_,
taking advantage of a special property of decimal notation. Check sums
and error-detecting codes are extensively used in modern computer
applications, and can make an interesting side-study in a mathematics
class (but it's the computer-science people who study them, of course).
The nines check-sum has a bad flaw, in that it will not detect a digital
transposition (e.g. 3168 as against 3618), an error commonly made when
propagating results manually. I have seen recommendations that this
check be combined with that of an alternating digital sum (casting out
11's, if you will) to increase confidence in a result calculatoed on paper.
Of course this is silly when you have recourse to electronic tools. But
how do you check whether, for example, you have entered a problem
correctly into a calculator, without (say) having transposed a digit?
The _issue_ here has not gone away!
This is where the "graphing calculator", with its recallable multi-line
displays, shines. One of the first things I teach my students to do when
they first get their hands on a graphing calculator is to gain control
over the recall and editing features. Visual inspection of the entered
calculation is often enough to show up an error entry and allow fixing.
Won't help, of course, if the entered calculation is based on a
misunderstanding of calculator syntax. Here is a case where
"reasonableness of results" judgments are called for. If the
result displayed by the calculator looks funny (and just how
much experience does it take before you can see this sort of
thing?) then you can go back and analyze the calculation itself.
RWW Taylor
National Technical Institute for the Deaf
Rochester Institute of Technology
Rochester NY 14623
>>>> The plural of mongoose begins with p. <<<<
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