[Numeracy 183] Re: The double negative language-math link
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Tue Feb 16 13:47:10 EST 2010
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Hello Carol and all,
I don't know whether the "Michael" you are referring to is me (I?) (one easily gets lost in a conversation string, or at least I do...), but what I have written is that negative integers do not exist in physical reality. That is precisely why (perhaps) when we start learning math, we deal with unsigned numbers. They are positive, alright, but not signed as such. To start, we learn of positives and negatives as operators, that's all.
That's why I believe it is important to make learners aware that in the world of math, unsigned numbers are, in fact, positive, because they refer to (or can be related to) concrete objects that exist in concrete physical space - whether whole numbers, parts, or mixed numbers. It's not the numbers that exist per se, but rather quantities of whatever (thus, in language, the notion of count vs. noncount nouns).
It is also why I stated that when, for example, one owes money, the money that one owes, most especially in the minds of those with limited numeracy skills, is a concrete amount of (very positive!) money. Logically, therefore, if you have a negative balance and render it in terms of a balance sheet, and in turn translate back into word-based rather than mathematical language, it can - depending how instruction plays out - defy comprehension how one can owe a negative amount (as displayed on the balance sheet). If I owe negative $10, in fact I either don't owe anything and/or someone in fact owes me $10.
So...the trick continues to lie in establishing the language-math link in a way that help create meaningfulness in the minds of our students. When all is said and done, they are capable of far more than one might expect...
Michael
Michael A. Gyori
Maui International Language School
www.mauilanguage.com
________________________________
From: Carol King <cking at lyon.k12.nv.us>
To: The Math and Numeracy Discussion List <numeracy at nifl.gov>
Sent: Tue, February 16, 2010 7:56:32 AM
Subject: [Numeracy 181] Re: The double negative language-math link
Michael you are right that the negatives have physical reality, but I have students who do not relate to those examples. The concept of a negative even when we talk about temperature does not compute for them. I tend to resort to the double negative in language as the example when I cannot make head way with temperature or holes or number lines. These students really do see it in terms of 15 degrees is cold and negative 15 is really cold and can not bridge the relationship of numbers to see why the range from 15 to -15 should create an addition problem (Yes we count it out, but they will repeatedly look me in the face and say, See its 15!) or if counting works for temperature, they cannot transfer it to algebra for 15 - - 15.
________________________________
From:numeracy-bounces at nifl.gov [mailto:numeracy-bounces at nifl.gov] On Behalf Of Charlie
Sent: Monday, February 15, 2010 1:36 PM
To: The Math and Numeracy Discussion List
Subject: [Numeracy 171] Re: The double negative language-math link
I draw a horizontal line and call it ground level. A pile of dirt can be x feet above ground level (positive). A hole in the ground can be x feet below ground level (negative). You can add a positive value by filling the hole and/or making the pile taller. You can add a negative integer by shoveling off of the pile and/or digging deeper. Subtraction problem are converted to addition. For subtraction, the mantra is "cross the line [change from subtraction to addition] and change the sign [of the second integer]"
Charlie Love
GED/ESOL Instructor
DurangoAdult Education Center
701 Camino del Rio , Room 301
Durango, CO 81301
phone: 970-385-4354 970-385-4354 ext. 110
fax: 970-385-7968
charlie at durangoaec.org
On Feb 15, 2010, at 7:05 AM, mysbooks at aol.com wrote:
Sea level, stocks, money; loans, home equity-especially relevant when mortgages are "under water".
-----Original Message-----
From: Denney, Brooke <denneyb at cowley.edu>
To: numeracy at nifl.gov
Sent: Thu, Feb 11, 2010 10:17 pm
Subject: [Numeracy 151] The double negative language-math link
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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