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Topic: Re: Teaching Dev Mathematics Conceptually: practical ideas
Replies: 96   Last Post: May 4, 2009 5:07 AM

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Wayne Mackey

Posts: 312
Registered: 12/4/04
RE: Teaching Dev Mathematics Conceptually: practical ideas
Posted: Feb 18, 2009 11:37 PM
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It is just to make it a little easier to understand. I also told
students that most people would use minus to mean negative, opposite
of, and subtract since they are all indicated by "-". So many
students think -x is negative that is worth giving them some different
words to use in the different contexts to help them keep it straight.

wayne

Quoting Martin Weissman <mathprof@hotmail.com>:

>
> What's the difference whether a "-"
> means minus or 'the opposite of'
> if the answers are the same?
>
> Besides, don't 'minus'
> and 'the opposite of' actually
> mean the same thing?
>
>
> Professor Martin Weissman
>
> Prof Weissman's Software
>
> 246 Crafton Avenue
>
> Staten Island, NY 10314
>
> Cell: 347-528-7837
>
> mathprof@hotmail.com
>
> www.math911.com
>
>
>
>
>
>
>
>
>
>
>

>> From: kathy.mowers@kctcs.edu
>> To: mahlerp@middlesex.mass.edu; mathedcc@mathforum.org
>> Date: Wed, 18 Feb 2009 16:54:42 -0500
>> Subject: RE: Teaching Dev Mathematics Conceptually: practical ideas
>>
>> At one point, according to what I've seen there was a movement to
>> try to use different symbols to mean "the opposite" and "minus."
>> It didn't catch on, obviously. In one case, the opposite was
>> higher on the line and smaller than the minus. I cannot reproduce
>> it on the keyboard.
>>
>> -----Original Message-----
>> From: owner-mathedcc@mathforum.org
>> [mailto:owner-mathedcc@mathforum.org] On Behalf Of Philip Mahler
>> Sent: Wednesday, February 18, 2009 3:45 PM
>> To: mathedcc@mathforum.org
>> Subject: Re: Teaching Dev Mathematics Conceptually: practical ideas
>>
>> On 2/18/09 3:32 PM, "wmackey" <wmackey@uark.edu> wrote:
>>

>> > Well, I don't think the expression -3^2 is undefined if - is properly
>> > defined. It should be read as the opposite of 3^2 which is clearly
>> > negative 9 or -9. The - symbol has three different meanings depending
>> > on context. In front of a natural number it means "negative", in
>> > front of anything else it means "opposite". If it is between 2 things
>> > it means subtract. Since no books except mine bother to define the
>> > symbol it leaves everyone confused.
>> >
>> > wayne

>>
>>
>> I like the fact that you confront this situation head on. You are saying, I
>> think, that - in front of any expression where it doesn't mean subtraction,
>> or not in front of a single numeral, means -(expression). In some ways it
>> implies a symbol of grouping. I guess it could be extended to even a numeral
>> since the opposite of what a numeral represents is a negative number?
>>
>> That can add a little extra work to something like -6(-4), since you have to
>> think of it as -[6(-4)] rather than the product of two negatives. But of
>> course in practice it probably would not be an impediment, people would just
>> think of it as the product of two negatives, and I grant it helps immensely
>> with -3^2. Though demonstrably one cannot depend on entering -3^2 into
>> calculating devices and getting the defined result. But at least it tells
>> one to enter it as -(3^2).
>>
>> I might be able to live with that because that just might stick with
>> students (I imagine that is your experience?). And I realize that everyone
>> else on the list lives with -3^2 without a problem already. :-)
>>
>> Phil
>>
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>


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