[Numeracy 493] Re: What does equality mean?

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Chip Burkitt chip.burkitt at orderingchaos.com
Sat Aug 14 12:59:24 EDT 2010


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/ = 3/x/ − 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 <http://www.mauilanguage.com/>

>

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