Diploma di Abilitazione all'Insegnamento nelle Scuole del Grado Preparatorio (Diploma of Qualification to Teach in Preparatory-Level Schools)
http://www.nafsa.org/_/file/_/ges/italy.pdf

These include scuola materna (pre-school) and asilo nido (nursery school).


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Note added at 10 hrs (2014-10-15 10:09:54 GMT)
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It was not until the Gentile reform and the Single Text of 1928 were introduced that nursery schools obtained a precise collocation within the framework of public education. With that reform they took on the official denomination of scuole del grado preparatorio, i.e. preparatory schools to primary education.
http://www.nevermoredst.paesi.com/italeducsysdetailF.htm

International Academic Credentials Resource Sheet
Diploma di Abilitazione all’Insegnamento nelle Scuole del Grado Preparatorio (diploma of qualification for teaching in preparatory-level schools).
http://www.slu.edu/Documents/admission_undergraduate/Intl_Ac...

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Note added at 10 hrs (2014-10-15 10:15:35 GMT)
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looks like it does not include pre-school (elementary school) after all, but just nursery school.

The rules governing the school system were radically changed by the Gentile reform introduced in 1923 which established the following organisation:
● preparatory school (scuola del grado preparatorio) to elementary school, neither compulsory nor free nor state school, except for the giardini d'infanzia annexed to some state istituti magistrali;
● primary school (5 years), divided into two cycles (lower and upper cycles);
● lower secondary education, including six different institutions;
● upper secondary education, including five different institutions;
● lower secondary school, subdivided into a vocational training path (scuola di avviamento), lasting 2-3 years, an academic path called gymnasium (a lower 3-year cycle and an upper 2-year cycle), technical institute (a 4-year lower level course) and istituto magistrale (a 4-year upper level course); art school (3 years);
● upper secondary school, subdivided into liceo specializing in classical studies (3 years), liceo specializing in scientific studies (4 years), technical institute for economics and commercial school (4-year upper level course), technical institute for geometers (4-year upper level course), istituto magistrale (3-year
upper level course), liceo specializing in art subjects (4 years);
● higher education, including state-funded universities and ''free'' (private) universities, without state funding.
http://www.indire.it/lucabas/lkmw_file/eurydice///IT_EN.pdf

I suppose they call it "scuola del grado preparatorio" since they introduced pre-writing activities for pre-schooler (5 y children)