17:19 Sep 18, 2011 

... the ginnasio started with the sixth grade, but not anymore as I have always understood it. I quote from wiki, which explains it well:

"Questa scuola fu abolita nel 1940, con una riforma che prevedeva la nascita di una scuola media triennale.

Nell'attuale ordinamento scolastico italiano è rimasta la dizione «ginnasio» (più precisamente «ginnasio superiore») per indicare le prime due classi dell'ordinamento del liceo classico,.."

However, the question here is the precise school in question. I am sure that this "ragazza" (not "nonna") started this school after she finished the "media" at age 13. The Manzoni in Milan for example is still called the "Liceo ginnasio statale", but the first part of the ginnasio is history.

14:49 Sep 18, 2011 

Without trying to be antagonostic I would like to note that:
The "ginnasio" starts with the 6th grade and is the "middle school"
The graduates of the ginnasio, can attend the "liceo" which is the high schoool.
Both ginnasio and liceo are part of the secondary schooling.