Jerry - your question:
Isn't Gymnasium a term for lower Elementary School in England? Or is it Germany?

In Germany gymnasium is the secondary school qualifying for University. In my prime it was classical (Latin, English, Greek and one or two more modern languages in the last years, Hebrew at will for future ministers) or modern (sciences, English first, less Latin, no Greek).
Now the classical branch is abandoned, but for qualifying you still need 9 years (5th to 13th) after 4 years of elementary school.

Wilfried