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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: proofpad
Date: May 13 2009
Looking at all of these posts, it seems that most of my statements are taken,
but a quick recap (with some additional thoughts) may be helpful for some.
These are, btw, just the pieces I agree with.

"Is Variable Confusing to Students?"  The answer is yes.  Both the concept (try
using something other than 'x' and really see the fur fly!) and the definition.
As many said, it is in the definition of the variable and the SUBTLETIES of that
definition that create the confusion.  One thing I've done in setting up the
different methods of solving equations is to use the statement "Find the value
of x/a/u to make this sentence true."  This is quite important when discussing
the graphical implications of the equation statement.

Granted, I am teaching an honors level Algebra 2 class, but even in the regular
level I discuss the graphical method of solving equations and inequalities.  I
feel that it is important for them to have that tool so they can have a visual
aid when faced with equations that they don't necessarily know how to solve
algebraically, but can graph.

Taking an example equivalent (another word that too few students are exposed to)
to the one posed in the beginning:  

3x + 5 = 8

In the graphical method, I tell my students to use the transitive property
(we've discussed this in Geometry the year before) in reverse:

3x + 5 = y  and y = 8

Then we graph both parts and look for where the two functions (lines in this
case) are equal and discuss the graphical meaning of the world "equal."  Then I
bring them back to the original problem:  

3x + 5 = 8  --> Find the value of "x" that makes this sentence true.

In the graphical method, we demonstrate the idea that "x" is still a variable,
that it causes varying degrees of equality and that there is one (in this case)
value for the variable to make the statement true.  Of course, later on in the
year we discuss cases (quadratics for instance) where the variable has more than
one possible value to make the statement true.  In that case, we get to discuss
the mathematical uses of the words "and" as well as "or" (not JUST limited to

I will go further to state that some of these ideas I've used with other
students who may have had Geometry already, but weren't ready for Algebra 2 yet.
At that time we had to create a class for them (I teach at a private school
where we are allowed that luxury) and even there I presented the ideas of "what
is a variable" using the graphical method above.  

When introducing the topic at the start, it's a great opportunity to discuss the
vocabulary of mathematicians and how important it is to be careful with your
words.  The sooner we can get the students to speak mathematics, not just "do
mathematics" (whatever that means), the sooner we are preparing their brains for
new ways of thinking across the curriculum.
     -Gabriel Edge

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