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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: Craig
Date: May 8 2009
Interesting question.

An approach we have used (I believe this dates to the New Math era) is to
describe an equation involving a variable as "an open sentence," one whose truth
or falsehood hinges upont the particular value assigned to the variable.  In a
language example, consider the open sentence "X is my name."  If I think of X as
a variable, then different values of X might make the sentence true or false.
Those values that make the sentence true are called solutions.  Thus, one
definition of a "solution" is a value (or set of values) for variable(s) that
make the statement true.  We then can define an identity as a statement that is
true for all possible values of the variable.

I suppose I would describe the "X" in your second equation, 11 = 3x + 5, as a
variable, but say that only when x = 2 is the equation a true statement.

Now, whether a New Math-based answer is satisfying to your students is
certainly an open question in its own right!

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