Developing Students' Understanding of a Variable, by Ana C. Stephens.

This article deals with helping secondary students fully grasp the concept of a variable.  Three secondary classroom teachers were given a mouse thought exercise, where one has to come up with all the various ways that eight mice can be shared between two mouse cages connected by a tunnel.  Students developed charts, tables, even pictures to represent the ways, and they were encouraged to figure out a way to express this concept algebraically.  What struck me most was that so many students could not accept openly that two separate variables, say m and n, could share the same value.  This opens up my deeper concern for myself as a secondary math teacher: because so many math concepts have always come so easily to me, how much will I struggle in adapting concepts to make them more easily assimilated by the average or below average math student.  I recall in my elementary school days that we had math problems to do of the variety, __ + 5=8, and we had to figure out what went in the blank.  Then in middle school the blank was replaced with a letter, a variable, and this was an easy transition for me to make.  When this transition is a difficult one for a student in my classroom, I am hopeful that I will be both creative and understanding enough to allow the student to grasp the concept without completely being turned off by math.