If so, that's a much weaker and not terribly interesting claim. The concrete example of counting with Catalan numbers is more compelling; it would be very chall

If so, that's a much weaker and not terribly interesting claim. The concrete example of counting with Catalan numbers is more compelling; it would be very challenging for children who lack experience with recursive definitions and inductive proofs. Systematic enumeration, albeit elementary, is distinctly modern.