[Numeracy 494] Re: What does equality mean?

Chip,

I fail to understand why the definition of equality is subject to variation - 
say in relation to the level of numeracy of our students.  I have 
always understood equality in math to signify equality in value. If you perform 
the same operation on identical values with different expressions, of 
course doing so might result in inequality, as you appear to state in your post 
below.  My question is, why can we not apply a consistent definition to equality 
when teaching math at whatever level we may be doing so?

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




________________________________
From: Chip Burkitt <chip.burkitt at orderingchaos.com>
To: numeracy at nifl.gov
Sent: Sat, August 14, 2010 6:59:24 AM
Subject: [Numeracy 493] Re: What does equality mean?

I think the difficulty is that mathematics requires rigorous definitions and 
logic, especially as one advances in it. However, for ABE or GED students, it is 
usually enough to know that the equal sign is like a balance scale. In order for 
the sides to be in balance, the expressions on both sides must have the same 
value. If you add something to one side, you must add it to the other side as 
well to maintain the balance. If you subtract from one side, you must subtract 
it from the other side as well. When students get into algebra, they need to 
know that some transformations of an expression can change the character of the 
equality. For example (−a)^2 = a^2, but it does NOT follow by taking the square 
root of both sides that −a = a. Likewise, y/(x − 1) = 3 needs to be qualified by 
x ≠ 1, even though the equation can be transformed to y = 3x − 3, which has a 
solution for x = 1 at y = 0. For most purposes in ABE or GED classes, the 
balance analogy works well without getting into abstract discussions about 
various kinds of equivalence relations and the transformations that change the 
relation or leave it unchanged. If anyone has a better explanation of the equal 
sign for ABE and GED students, I would like to hear it.

Chip Burkitt

On 8/14/2010 1:04 AM, Michael Gyori wrote: 
Greetings all,

>

>After all this discussion about what the equal sign (or equality) means, I find 

>myself somewhat in a maze.  A discussion of equality takes us into a potentially 

>esoteric realm from the perspective of our students.

>

>Might it be time to attempt to more clearly (and simply!) define terms among 

>those who teach math? 

>

>

>Michael 

> 

>Michael A. Gyori

>Maui International Language School

>www.mauilanguage.com



      
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