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Topic: Origins of negative numbers
Replies: 6   Last Post: Apr 1, 1996 10:33 PM

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Kreg A. Sherbine

Posts: 26
Registered: 12/6/04
Re: Origins of negative numbers
Posted: Apr 1, 1996 9:49 PM
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I'm concerned about the double-sided chip explanation offered by Judy's
textbook. Representing multiplication as "putting in" and "taking out"
seems as contrived as the "rule," or at least I think a student would see
it that way. Students often have very distinct interpretations of the
"-" sign; my students typically and explicitly figure out whether this
dash signifies subtraction or negativeness, and their interpretations of
an expression depend largely on their interpretations of this symbol.

I'm therefore leery of introducing -2 * -3 as taking away two sets of
negative three each, simply because this asks us to read one "-" in one
way and the other "-" in another way. Also, the notion of taking away
is, in my mind, reserved for subtraction.

Unfortunately, I associate multiplication with the idea of quantities of
quantities: 6 sets of 8, for example. This does not lend itself well to
the shift into negative numbers, and I'm eager to know of how other
teachers make this shift. I suspect that it *can't* be done smoothly,
i.e., that the shift requires thinking about numbers in a totally
different way than we (students) have thought about them when our binary
operations were on positive numbers. So perhaps instead of stretching
(and breaking) conceptualizations of positive numbers to make them fit
the "rules" of negatives, we should develop ideas about why these "rules"
make sense with respect to themselves. Perhaps the history buffs on the
list can help us here.

Kreg A. Sherbine | To doubt everything or to believe
Apollo Middle School | everything are two equally convenient
Nashville, Tennessee | solutions; both dispense with the
sherbine@math.vanderbilt.edu | necessity of reflection. -H. Poincare

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