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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: stek
Date: May 8 2009
Hi Susan,

You bring up a very important point: our algebraic notation is very elegant and
flexible, allowing us to use it in a wide variety of contexts. The accompanying
risk is that we may gloss over subtle differences in a way that leaves students

On this subject I highly recommend a chapter in NCTM's Research Companion to
Principles and Standards for School Mathematics. The chapter, by Daniel Chazan
and Michal Yerushalmy, is entitled "On the Cognitive Complexity of School
Algebra: Research on Algebra Learning
and Directions of Curricular Change." In particular, p. 125 has some nice
examples of different equations in which the variables may represent known
quantities, unknown quantities, or variable quantities. The article has a nice
analysis of the difficulties (for the student and consequently for the teacher)
and some useful suggestions and recommendations.

Scott Steketee
Sketchpad Projects

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

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