[Numeracy 199] Re: The double negative language-math link
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Fri Feb 19 10:48:17 EST 2010
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I am a 2nd grade teacher and we teach negative numbers too. As a school, we use Everyday Math, which is a scienitifically-researched based math curriculum from the University of Chicago. Here are the three artifacts I have in my classroom that show negative numbers. We refer to these daily and they seems to provide concrete examples of negative numbers:
An oversize poster of a number grid (-9 to 110)
An oversize thermometer from -40-140 degress F.
An oversize number grid that wraps around my room from -35 to 180.
They seem to help. They provide a visual for my kids.
From: Linda Hartung <lhartung at csiu.org>
To: The Math and Numeracy Discussion List <numeracy at nifl.gov>
Sent: Fri, Feb 19, 2010 8:04 am
Subject: [Numeracy 197] Re: The double negative language-math link
Claire-- Love the "Yeah, yeah" story--thanks for the chuckle.
SIU Adult Education
A CareerLink Columbia/Montour Counties
51 Tenny Street
loomsburg, PA 17815
70-387-6288, ext 118
From: numeracy-bounces at nifl.gov on behalf of Claire Ludovico and/or TJ DeLuca
ent: Wed 2/17/2010 1:42 AM
o: The Math and Numeracy Discussion List
ubject: [Numeracy 189] Re: The double negative language-math link
talian has the same "problem" with double negatives as Spanish...but I write
ecause this reminds me of something I read a few years ago (wish I had a better
emory for names...now if everyone went by a number...):
omeone was giving a speech and said," Two negatives make a positive, but two
ositives can never make a negative." Someone in the audience responded in a
ather bored voice,"Yeah, yeah."
S As a former science teacher, I find it difficult to talk about thermometers
ithout a quick history of the two temperature scales (I love to mix science,
istory, and math!)
ahrenheit was first. He took a long narrow glass tube and filled it with
omething (I never give away exactly what right away) that would not freeze at
ery cold temperatures. If I don't get any guesses, I mention car radiators and
ntifreeze...eventually we get to...wine! Perhaps that is why we still dye our
lcohol filled thermometers red. Fahrenheit's zero was based on the coldest
emperature he could produce at the time. There was no refrigeration. (Ever
ake homemade ice cream?) He mixed ice and salt to create a (fairly reliable)
ixture colder than pure ice. That was his zero. His 100 degrees was slightly
ff, but a readily available object (subject) to measure...(I make them figure
his one out too)...human body temperature. On his scale, then, pure water
roze at 32 degrees and pure water boiled (at sea level) at 212 degrees. He had
o divide up the area on the thermometer between the zero and the 100 into 100
egments and continue the same spacing to get the other measurements. [To be
ccurate, Fahrenheit's human body temperature was originally 96 degrees; other
cientists tweaked the scale to put exactly 180 degrees between freezing and
oiling...I try to keep it simple though.]
elsius came along in what, at the time, was considered a more scientific age
actually only 18 years later). (I throw in a quick explanation of where the
easurements for feet, an inch, a yard and a few other body based measurements
riginated.) The scientists of Celsius' day were ready to discard this kind of
easurement system and use something more scientific. So using essentially the
ame long, slender glass tube, filled with essentially the same liquid, Celsius
et his zero at the temperature at which pure water froze and his 100 degrees at
he temperature at which pure water boiled (at sea level). [Once again, to be
ccurate, Celsius actually set his zero at the boiling point and his 100 at the
reezing point...Linnaeus is given credit for reversing the two, but there was
till the 100 degree difference. Since the revised system still bears Celsius'
ame, I don't explain the reversal.] When he then marked off his degrees on his
hermometer, he had 100 degrees between freezing and boiling, where Fahrenheit
ad (212-32) 180 degrees in the same space...hence the Celsius degree is a
arger degree...one can even do a ratio to figure out how much larger (9/5) and
roceed to derive the formulas for temperature conversion if students are at
hat level (which generally they are not...but it helps to understand about
hermometers and how temperature could then be negative (because temperatures
an be colder than either man's zero.))
On 2/16/2010 3:52 PM, steinkedb at q.com wrote:
I see a problem with using English grammer as a model for math syntax.
We must remember that not all our students are native English speakers. What
e consider a "double-negative means a positive" in English is a simple negative
n Spanish. A literal translation of a simple negative sentence in Spanish (No
uiero nada.) looks like a "double-negative" in English (I don't want nothing.)
e must be careful that students take in the information in the way that we
From: numeracy-bounces at nifl.gov [mailto:numeracy-bounces at nifl.gov]On
ehalf Of Carol King
Sent: Tuesday, February 16, 2010 2:27 PM
To: The Math and Numeracy Discussion List
Subject: [Numeracy 186] Re: The double negative language-math link
The rule in teaching English is that a double negative statement creates
positive statement, so, for a few students, it makes sense to hang my hat on
he hook they have. Since they know in English " to not not go" creates a
ositive statement that you are going (and must be rewritten as such) it bridges
heir mental block about double negatives in math changing to addition problems.
Fernley Adult Education
cking at lyon.k12.nv.us
From: numeracy-bounces at nifl.gov [mailto:numeracy-bounces at nifl.gov] On
ehalf Of Michael Gyori
Sent: Thursday, February 11, 2010 8:58 AM
To: The Math and Numeracy Discussion List
Subject: [Numeracy 148] The double negative language-math link
Carol King stated,
If I am taking out taking out 8, as in 10 - (-8), then I must be adding
I read it a few times and find myself perplexed by it, as much as I
elieve I understand its intent.
"Taking out" is a positive statement and regardless of how many times
ou say it, it remains positive, and what changes - perhaps, depending on how I
hoose to understand it - is the number of times you (***yes***) "take out."
f I take out once, I have 2 left, and I cannot take take out again, because I
an't take another 8 out of 2.
Alternatively, I can understand the meaning to be that I am "taking
ut" the taking out of 8, which then could leave me to believe that I wanted to
ake out, then decided against it, such that I end up doing nothing. I still
The problem, as I see it, is that we are getting into integers.
egative values have no meaning in the world of the concrete, because once you
ave 0 left, that's it. On the other hand, if we deal with negative balances
such as when you overdraw your balance in your checking account), you create
eaning because it can and does happen. In other words, negatives carry meaning
n mathematical, but not physical (reality) terms...
Michael A. Gyori
Maui International Language School
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