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 Discussion: All Topics in Algebra Topic: Is "variable" confusing to students?

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 Subject: RE: Is 'variable' confusing to students? Author: Peggie Date: May 8 2009
OK for my two cents:

I agree that if you use the word "variable" to mean "something that varies" it
can be confusing to students. In teaching 7th grade math, I simply define a
"variable" as a letter that stands for one or more numbers. While that may be
simplistic, it does work in all three of your cases -- the expression, the
equation, and the slope equation.

On May  8 2009, Susan wrote:
> I'm trying to establish the differences among the following three
> things:

3x + 5

11 = 3x + 5

y = 3x + 5

The first is an
> algebraic expression containing the "variable" x.  In this case, the
> variable x can take on any value.  It “varies”.

The second is an
> equation of one variable.  We call x a variable but truly it doesn't
> vary.  It is just an "unknown".  We can solve for x and determine it
> must equal 2.

In the final case, we have two variables and they
> do 'vary' depending on each other’s values.

Should we call the x
> in the second case an “unknown” and not a variable?   I’ve seen
> books say, “solve for the unknown”.

I think we confuse students
> by calling x “variables” in all of these cases when in case 2, the x
> does not vary at all.