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 
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 Mathbased answer is satisfying to your students is
certainly an open question in its own right!
 
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