[Numeracy 156] Re: The double negative language-math link
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Fri Feb 12 13:07:51 EST 2010
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Actually, you can subtract with money. Think in terms of a credit card. Say
they have charged you a $29 late fee (or is it more now), and you challenge
the fee for a legitimate reason, so they have to remove (subtract) the late
fee. That actually means *adding* the $29.
On Fri, Feb 12, 2010 at 9:18 AM, Leslie Hunten <lhunten at gmail.com> wrote:
> 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
> 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!
> 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.
>> On 2/11/2010 8:17 PM, Denney, Brooke wrote:
>> 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
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