[Numeracy 155] Re: The double negative language-math link
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Fri Feb 12 11:18:15 EST 2010
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I like the sea level analogy. If I hike down into Death Valley, I'm going
down below zero in elevation, because sea level is the arbitrary zero and DV
is deeper. However I'm not hiking backwards, nor using an anti-gravity
chair, I'm definitely taking steps and I can count them as an absolute
number in a negative direction. So I might walk a few miles, which are very
real to my feet, but now I'm at a negative number on an elevation map. When
I hike back out, and perhaps even climb to the peak of a mountain, I'm
walking in the positive direction. But it feels the same to my feet - I'm
still walking forward. My total distance could be called the absolute
number of miles I walked, and my elevation change has to be in negative and
positive numbers. I could walk 10 miles and have an average elevation of
zero!
But frankly, I think the most realistic analogy in integers for students is
with "having and owing money". That's a scenario they're all familiar
with. Unfortunately, this only works with adding, not subtracting. But if
you spend quite a while exploring neg & pos with money situations, they
should get a good grasp of the concepts. After that, I tell them, "Sorry,
now you just have to memorize a few rules, because they don't really make
logical sense. Just do it."
By the way, I just joined this list, and I love it already!
Leslie
On Thu, Feb 11, 2010 at 10:57 PM, Claire Ludovico and/or TJ DeLuca <
tjdclaire at cox.net> wrote:
> There is always above and below sea level...
> I use bank accounts as the most likely exposure of my students to negative
> numbers...and the minus a negative example is when one finds a charge (funds
> subtracted) that has been (incorrectly) imposed by the bank that is then
> removed (taken away) from your balance...or in other words, they returned
> your money to you.
>
> I once had to introduce integers to a group in a very limited amount of
> time. I made up a story about the positive tribe and the negative
> tribe...both very warlike but only with the other tribe, never with each
> other. Positives, of course, carry two spears, negatives only one. They
> have very strict rules of warfare: only one positive may fight a negative
> ...no ganging up...and when they fight (so sad) both die. They can hang out
> with their own kind, of course, no problem. (Addition)
>
> Subtraction: They are also both very greedy...so in their wanderings in
> the woods, if they should spy a new spear laying on the ground (the minus
> sign) the positives, who have a spear in each hand, must throw away their
> two spears in order to pick up the new spear (and thus become negative) and
> the negatives, who carry only the one spear, can reach down and pick up the
> new spear...and become positive. Then those former negatives can hang out
> with positives (and vice versa) but can no longer face their former kind
> without "war" breaking out.
>
> Miraculously, the two tribes can marry (multiply) and the *product* of
> their union depends on their signs (multiple marriages allowed (perhaps each
> parent "gifts" the same number of spears as he/she carries)...count the
> negative signs: odd number, the "children" are negative, even number (two
> spears again) the "children" are positive.) Divorce (division) is quite
> possible and the rules are the same as for multiplication.
>
> I don't know if my students always get why I tell the story (but then they
> don't always get the rational explanation.) As I said, I usually back up
> the problems with bank account analogies. But the spear story helps
> sometimes if you have a negative (or minus sign) outside parentheses and you
> can talk about shooting the spear through the parentheses and changing the
> sign of everything inside.
> Also, my students were looking at the problem yesterday: (-6) - (-1) = ?
> I was able to say," If you have six negative guys and you take away one of
> them, how many are left?" They got it.
> Claire
>
>
> On 2/11/2010 8:17 PM, Denney, Brooke wrote:
>
> Michael:
>
>
>
> I disagree with your statement that, “negatives carry meaning in
> mathematical, but not physical (reality) terms”; after all, it is winter in
> the Midwest and negative values mean something in my reality when we are
> talking about wind chill factors and really cold temperatures (perhaps
> living in a really warm climate you may have forgotten). Also, negative
> numbers are used when discussing the grade of the road (i.e., positive or
> negative grade). Does anyone else have examples of negative numbers used in
> reality?
>
>
>
> -Brooke
>
>
>
>
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>
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