Unable to access parent constants through subclass

Greetings folks, I hope all (or at least most) is well with you and express my immense gratitude that I’ve been able to find this forum. Now then, I’ve defined two classes, one of which extends the other. The superclass defines a constant and I can’t seem to access it through the subclass.

public class BigClass
  public static const BIG_CLASS_CONSTANT:String = "Hi Mom.";

  public function BigClass():void
    //do random constructor stuff

public class SmallClass extends BigClass
  public static const SMALL_CLASS_CONSTANT:String = "Hello World!";

  public function SmallClass():void
    //do more random constructor stuff

Now, the following calls work as I expect:

trace(SmallClass.SMALL_CLASS_CONSTANT); //Hello World!
trace(BigClass.BIG_CLASS_CONSTANT); //Hi Mom.
trace(BigClass.SMALL_CLASS_CONSTANT); //error

However, the final combination does not:

//Expect "Hi Mom."
//Receive "1119: Access of possibly undefined property BIG_CLASS_CONSTANT through a reference with static type Class."

It’s probably worth noting that when I attempt to access BIG_CLASS_CONSTANT from within SmallClass that the String I expect is returned, it’s only external calls that muddle things up.

Shouldn’t polymorphism allow a subclass to access constants of the classes they extend? Does the subclass have to reference the parent constant in some other way than a simple extension? Do I actually have to declare that constant in each and every class that decided to extend from that parent (but then how would the parent refer to it?)? Or (and this is the most likely) is there something completely different that I’m missing?

Thank you very much in advance for any time and effort put forth in assisting me on this issue.