[Numeracy 259] Re: Is an absolute value positive?
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Wed Mar 31 09:23:50 EDT 2010
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Wow! I wish I could get my bank to agree that negative numbers have no
existence. I'd never be overdrawn again.
On 3/31/2010 1:38 AM, Michael Gyori wrote:
> Greetings Carol and all,
> I suppose the question is what is meant by "positive." If we view
> numbers to represent quantities (of whatever), then they are
> intrinsically positive. Negative quantities have no existence, and
> perhaps we can regard the notion of absolute value to reflect just that.
> As for teaching absolute values to "struggling" learners, my sense is
> we shouldn't underestimate their ability to make sense of things.
> Quite on the contrary, the challenge lies in our (educators') ability
> to facilitate meaning.
> Michael
>
> Michael A. Gyori
>
> Maui International Language School
>
> www.mauilanguage.com <http://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, March 30, 2010 9:12:47 AM
> *Subject:* [Numeracy 250] Re: what is the difference between....
>
> I would point out that technically an absolute value is not a positive
> number. It represents the distance from 0 either negatively or
> positively on the number line. It operates mathematically like a
> positive number, but it is not the same as the positive number. I
> don’t know if I would share that with struggling students.
>
> Carol King
>
> cking at lyon.k12.nv.us <mailto:cking at lyon.k12.nv.us>
>
> Fernley Adult Education.
>
> ------------------------------------------------------------------------
>
> *From:* numeracy-bounces at nifl.gov [mailto:numeracy-bounces at nifl.gov]
> *On Behalf Of *Michael Gyori
> *Sent:* Monday, March 29, 2010 4:55 PM
> *To:* The Math and Numeracy Discussion List
> *Subject:* [Numeracy 241] Re: what is the difference between....
>
> Hi again George and all,
>
> If /-6/ means the absolute value of negative 6, then I stand
> corrected. I didn't realize the forward slashes might have been bars.
>
> In that case, absolute values are positive. So, the negative of the
> absolute value of -6, which is +6, = -6. On the other hand, -(-6)
> [i.e, in parentheses] would be positive 6.
>
> Also, I always teach part numbers (fractions, decimals, and percents)
> before I teach integers. I find it interesting that you delve into
> integers first. Do you have a reason for doing so?
>
> Michael
>
>
> Michael A. Gyori
>
> Maui International Language School
>
> www.mauilanguage.com <http://www.mauilanguage.com/>
>
> ------------------------------------------------------------------------
>
> *From:* Michael Gyori <tesolmichael at yahoo.com>
> *To:* The Math and Numeracy Discussion List <numeracy at nifl.gov>
> *Sent:* Mon, March 29, 2010 1:30:03 PM
> *Subject:* [Numeracy 237] Re: what is the difference between....
>
> Hello George and all,
>
> See my attempt at making sense of your message. I will embed my
> thoughts in green into your post below:
>
> Michael
>
> Michael A. Gyori
>
> Maui International Language School
>
> www.mauilanguage.com <http://www.mauilanguage.com/>
>
> ------------------------------------------------------------------------
>
> *From:* George Demetrion < gdemetrion at msn.com >
> *To:* Numeracy List <numeracy at nifl.gov>
> *Sent:* Mon, March 29, 2010 10:18:55 AM
> *Subject:* [Numeracy 235] what is the difference between....
>
> Good afternoon colleagues.
>
> In my newly articulated and highly pleasant role as a Transition to
> College math teacher, I've come ac ross the following
>
> **-2^2 **^
>
> ^ ^When a number is positive, we don't sign it. For example, 2+2=4
> really means +2 (+) + 2 = + 4.
>
> ^ In that vein, we really have negative **times** _positive 2_
> squared (or the negative **of** positive 2 squared) equals -4.
>
> **(-2)^2 **
>
> ^In this case, the 2 is signed as a negative, or you can see it as the
> negative of positive 2 = negative two, times itself, = +4.
>
> ^I teach my students rather early on that unsigned numbers are
> actually signed by an invisible "+" before them, just like whole
> number have an invisible point (.) to their right, which is the border
> separating whole numbers from decimals (part numbers). 345 is the
> same as 345 **^. **^
>
> ^Something "of something" is always multiplication. In the case of -
> +, we are saying the negative** of** positive, which leads me to
> negative **times** positive. That leads me to teach (also quite early
> on) the **golden rules**, namely, positive x positive and negative x
> negative = positive, while negative times positive or positive times
> negative = negative.
>
> According to my book the answer to the first problem is -4 while the
> answer to the second is 4. The examples are easy enough to follow,
> but a little light on the explanation. In the first problem the
> notation in the book states that 2 is the base; thus (2.2)=4 and, I
> assume, we keep the negative sign, so that the answer becomes -4. The
> second problem is easy enough. I get (-2.-2)=4.
>
> What's missing as far as I'm concerned is a clear and simple
> explanation of the reasoning behind the first problem - 2^2 d
>
> I deduced that the second problem is based on an order of operations
> problem solving menthodology and I'm thinking the same thing for the
> first problem in which the negative sign indicated a -1. Thus, on
> this hypothesis, I am carrying out an order of operation (exponent
> first, including the implied paranthesis (2.2) multiplied by -1 in
> which this later stage is last on the order of operations process.
>
> Questions:
>
> 1. Is my hypothesis for problem #1 correct?
>
> 2. If not, what would be the correct explanation?
>
> 3. Whether or not the hypothesis is correct what woould be the
> simplist accurate explanation to provide my students with?
>
> One more question -/-6/= -6, which I translate to mean is that the
> opposite of the absolute number -6 has an absolute value of 6;
> therefore its opposite is -6.
>
> **-/-6/ = -6 strikes me as being incorrect. If I'm wrong, PLEASE
> CORRECT ME: In language, the equations reads to me, negative times
> negative 6 = POSITIVE 6, because a negative times a negative = a
> positive.**
>
> a) is this correct
>
> b) If so, is there an easier way to state it?
>
> c) If it is correct what is the best way to teach it to TCC students
> with limited mathematical experience
>
> d) If it is incorrect, what would be the correct answer?
>
> Okay, we're just about through with integers. Onto fractions.
>
> Best,
>
> George Demetrion
>
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