Need class to be variableized ; )

No matter how I revisit my application, I cannot find a simple way to:

var thisOne:myVariable = new myVariable;

where myVariable is a name of one of my sprites in my library.  I considered creating a class myVariable and rewriting the above line as

var thisOne:myVariable = new myVariable(spriteName);

but then I run into the same problem internally

...

public function myVariable(s:String):void {

     var thisOne:String = new String;   <<<<<<<<<------ this obviously does not work and resembles the above only one step removed.

}

Everytime I think I figured it out using arrays, I end up with only one instantiation being referenced multiple times.  Understandable since arrays access by reference.  So how about it?

A little background in case my approach is orthogonal to best practice (i.e. I'm totally whack).

In each lesson I may create hundreds of identical Sprites that are displayed so the student can count or subquan them.

Followup lessons are similar except for the quantity and the Sprite.  Therefore, I only need to pass the variables quantity and Sprite (which are sometimes animated) to my program.  But I can not figure out to instantiate the Sprite via a variable or string reference.

I hope I didn't miss the obvious in the on-line Adobe references or that my web searches are brain-dead so please bear with me (and, if possible, bear me up.)