[Numeracy 189] Re: The double negative language-math link

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Claire Ludovico and/or TJ DeLuca tjdclaire at cox.net
Wed Feb 17 01:42:47 EST 2010


Italian has the same "problem" with double negatives as Spanish...but I
write because this reminds me of something I read a few years ago (wish
I had a better memory for names...now if everyone went by a number...):
Someone was giving a speech and said," Two negatives make a positive,
but two positives can never make a negative." Someone in the audience
responded in a rather bored voice,"Yeah, yeah."
Claire Ludovico
PS As a former science teacher, I find it difficult to talk about
thermometers without a quick history of the two temperature scales (I
love to mix science, history, and math!)
Fahrenheit was first. He took a long narrow glass tube and filled it
with something (I never give away exactly /what/ right away) that would
not freeze at very cold temperatures. If I don't get any guesses, I
mention car radiators and antifreeze...eventually we get to...wine!
Perhaps that is why we still dye our alcohol filled thermometers red.
Fahrenheit's zero was based on the coldest temperature he could produce
at the time. There was no refrigeration. (Ever make homemade ice
cream?) He mixed ice and salt to create a (fairly reliable) mixture
colder than pure ice. That was his zero. His 100 degrees was slightly
off, but a readily available object (subject) to measure...(I make them
figure this one out too)...human body temperature. On his scale, then,
pure water froze at 32 degrees and pure water boiled (at sea level) at
212 degrees. He had to divide up the area on the thermometer between
the zero and the 100 into 100 segments and continue the same spacing to
get the other measurements. [To be accurate, Fahrenheit's human body
temperature was originally 96 degrees; other scientists tweaked the
scale to put exactly 180 degrees between freezing and boiling...I try to
keep it simple though.]
Celsius 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 measurements for feet, an inch, a yard and a
few other body based measurements originated.) The scientists of
Celsius' day were ready to discard this kind of measurement system and
use something more scientific. So using essentially the same long,
slender glass tube, filled with essentially the same liquid, Celsius set
his zero at the temperature at which pure water froze and his 100
degrees at the temperature at which pure water boiled (at sea level).
[Once again, to be accurate, Celsius actually set his zero at the
boiling point and his 100 at the freezing point...Linnaeus is given
credit for reversing the two, but there was still the 100 degree
difference. Since the revised system still bears Celsius' name, I don't
explain the reversal.] When he then marked off his degrees on his
thermometer, he had 100 degrees between freezing and boiling, where
Fahrenheit had (212-32) 180 degrees in the same space...hence the
Celsius degree is a larger degree...one can even do a ratio to figure
out how much larger (9/5) and proceed to derive the formulas for
temperature conversion if students are at that level (which generally
they are not...but it helps to understand about thermometers and how
temperature could then be negative (because temperatures can 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 we consider a "double-negative means a positive" in

> English is a simple negative in Spanish. A literal translation of a

> simple negative sentence in Spanish (No quiero nada.) looks like a

> "double-negative" in English (I don't want nothing.) We must be

> careful that students take in the information in the way that we

> intend it.

> Dorothea Steinke

>

> -----Original Message-----

> *From:* numeracy-bounces at nifl.gov

> [mailto:numeracy-bounces at nifl.gov]*On Behalf 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 a positive statement, so, for a few students, it makes

> sense to hang my hat on the hook they have. Since they know in

> English " to not not go" creates a positive statement that you

> are going (and must be rewritten as such) it bridges their mental

> block about double negatives in math changing to addition problems.

>

> Carol King

>

> Fernley Adult Education

>

> cking at lyon.k12.nv.us

>

> ------------------------------------------------------------------------

>

> *From:* numeracy-bounces at nifl.gov

> [mailto:numeracy-bounces at nifl.gov] *On Behalf 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

>

> Greetings everone,

>

> Carol King stated,

>

> If I am taking out taking out 8, as in 10 -- (-8), then I must be

> adding it.

>

> I read it a few times and find myself perplexed by it, as much as

> I believe I understand its intent.

>

> "Taking out" is a positive statement and regardless of how many

> times you say it, it remains positive, and what changes - perhaps,

> depending on how I choose to understand it - is the number of

> times you (***yes***) "take out." If I take out once, I have 2

> left, and I cannot take take out again, because I can't take

> another 8 out of 2.

>

> Alternatively, I can understand the meaning to be that I am

> "taking out" the taking out of 8, which then could leave me to

> believe that I wanted to take out, then decided against it, such

> that I end up doing nothing. I still have 10.

>

> The problem, as I see it, is that we are getting into integers.

> Negative values have no meaning in the world of the concrete,

> because once you have 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 meaning because it

> can and does happen. In other words, negatives carry meaning in

> mathematical, but not physical (reality) terms...

>

> Thoughts?

>

> Michael

>

>

> Michael A. Gyori

>

> Maui International Language School

>

> www.mauilanguage.com <http://www.mauilanguage.com/>

>

>

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