[Numeracy 278] Re: History of Negative Numbers

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Chip Burkitt chip.burkitt at orderingchaos.com
Thu Apr 1 16:49:06 EDT 2010

Actually, I do use "opposite" to teach negative numbers. One problem is
that we use the same sign (-) for distinctly different meanings. When it
occurs between two expressions, it indicates a binary operation
(subtraction). When it occurs before a value, it indicates a unary
operation (negative). And when it occurs before a variable, it again
indicates a unary operation (opposite). Many students struggle with the
difference between negative and opposite. To see if a student
understands the difference, just ask if the expression -x is less than
0. Students who don't yet understand the distinction will say yes; those
who do will say not necessarily. I always teach -3 as "negative three"
and -x as "the opposite of x." (I also use the expression additive
inverse explaining that it means the same as opposite.) Of course,
negative three is also the opposite of three, but the opposite of
negative three is just three. We don't generally use the expression
"negative negative three."

On 4/1/2010 3:10 PM, Denney, Brooke wrote:


> Good Day to Everyone:


> I have enjoyed reading the many postings on negative numbers. I

> believe that negative numbers have caused many mathematicians,

> students, instructors, everyday Joes with different levels of

> frustration about what a negative number is and why do they even

> exist. Here is a link to the history of negative numbers that I found

> to be fascinating: http://nrich.maths.org/5961

> <https://exchange.cowley.edu/exchweb/bin/redir.asp?URL=http://nrich.maths.org/5961>



> The language of negatives does seem to boggle the mind; we are taught

> minus, subtraction, and negative. But, this concept might be

> understood better if instead of saying minus, subtraction, and

> negative; we state it as the opposite. Just like the opposite to up

> is down and the opposite of right is left, would this verbiage help

> shift the way learners (and perhaps ourselves) think about negative

> numbers? What are your thoughts?


> Best to all,


> Brooke Denney, M.S.


> Moderator Math and Numeracy List



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