[Numeracy 282] Re: Linking word- and number-based language

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Michael Gyori tesolmichael at yahoo.com
Sat Apr 3 02:17:16 EDT 2010

Greetings all,

Chip - sounds like you're throwing a curveball of sorts.  You state that,

(-6) is less than (-4) because it is to the left on the number line. But (-6) is still "bigger" than (-4) because it is further[farther?] from 0.

If we revert back to a particular pedagogic objective, namely to connect word- and number-based language with reference to "concrete" (and thus 3-dimensional) reality, I cannot quite wrap my mind around that statement. If nothing less than zero exists in such a reality, the comparatives of "less than" and "bigger than" could be understood  meaningless - with the possible result of sucking learners into a black hole of sorts.

Yes, we have the makings of a very engaging and stimulating discussion, and I believe we still have quite a ways to go...

Michael

Michael A. Gyori
Maui International Language School
www.mauilanguage.com

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From: Chip Burkitt <chip.burkitt at orderingchaos.com>
To: numeracy at nifl.gov
Sent: Fri, April 2, 2010 10:34:17 AM
Subject: [Numeracy 280] Re: Linking word- and number-based language

Hi Everyone,

This is turning into a fascinating discussion.

A related difficulty is in talking about "less than" and "greater then". In mathematics, these terms are technical and refer to relative position on the number line. However, our intuitive grasp of them comes from a sense of number that recognizes "more" and "fewer." Students know that 4 is less than 6 because 4 is fewer than 6. When it comes to negatives, however, everything is reversed. (-6) is less than (-4) because it is to the left on the number line. But (-6) is still "bigger" than (-4) because it is further from 0. Absolute value gives us a precise way to talk about the "bigness" and "smallness" of numbers without confusing those concepts with "greater than" or "less than." Small numbers are close to 0, regardless of sign, and big numbers are far from 0 regardless of sign.

Chip Burkitt

On 4/2/2010 2:13 PM, Michael Gyori wrote:
Hello Carol and everyone,

>

>The word-based and number-based language link can be quite a task, can't it?

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>There is a fundamental difference between the terms quantities and magnitude. Quantities refer to count nouns (persons, places, things, and ideas). 1, 2, 3 people; 1, 2,3 cities; 1, 2, 3 cups of coffee; 1, 2, 3, insights, etc.).  Magnitude(s), on the other hand, can refer both to count as well as non-count nouns (tons of love - a noncount noun in this case, vs. tons of coffee beans - a count noun in this case).

>

>One of the characteristics of absolute values, at least for pedagogical purposes, is the use of numbers (math) to - ultimately - (to be able to) count, whether it be a sum, difference, product, or quotient that derives from performing operations on numbers (whether whole, part, or mixed).

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>The use of the term magnitude might be potentially confounding for a learner.  Magnitude is a lower-frequency word, and to delve into its meaning while building mathematical awareness might pose a challenge for learners with limited cognitive underlying proficiency levels.  We need to be sensitive to what we wish to accomplish both by teaching and the learning it may trigger.

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>Michael

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>Michael A. Gyori

>Maui International Language School

>www.mauilanguage.com

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________________________________
From: Carol King <cking at lyon.k12.nv.us>

>To: mmanly at earthlink.net; The Math and Numeracy Discussion List <numeracy at nifl.gov>

>Sent: Thu, April 1, 2010 7:30:33 AM

>Subject: [Numeracy 277] Re: Is an absolute value positive?

>

>

>This leads me back to some of the confusion, while I really liked that example, you have now introduced the new term of magnitude into our discussion of absolute values which my text defines as the distance from 0 and it does not mention magnitudes at all. While I personally understand magnitude and I prefer that as the term for what absolute value is showing in the problem, if my struggling student was to try to use another source to help them they might also run into this language and they feel rather than being helped they are led down another rabbit hole. Why are there so many ways to express in language what this one concept is doing rather than a consistent method?

>Carol King

>cking at lyon.k12.nv.us

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