When I first started my Italy Visa Quest, the conventional wisdom was that getting a Student Visa was a piece o' cake. A student visa could be had by enrolling in and paying for 20 hours per week of almost any kind of instruction in almost any private school in the land. Massage therapy school, tai chi school, cooking school...
Then there were the work-studiers. I've heard anecdotes first hand of people enrolling in private schools for 20 hours of Italian language lessons per week and then teaching English for that same school 20 hours a week (allowed within the Student Visa)-- and conveniently forgetting to attend the Italian language lessons.
But the times they are a-changin'. In this era of sea-based and overland poverty-, drought-, or violence-fleeing migrants, wall-builders, and the global passage of translucently-veiled jingoistic government policies, Visa requirements in Italy have been beefed up and enforcement has clamped down.
Today it is difficult to be approved for a Study Visa without enrollment in a University full-time.
This could actually be an interesting option for parents because University tuition in Italy will more than likely be less than the in-state tuition of your local university. But that's a conversation for a different day.
(Visas are apparently no longer issued for private school programs in basic language instruction.)
The Study Visa application needs to be accompanied by two copies of a letter in Italian from the accredited academic institution on official letterhead and bearing the official seal, stating that you have been accepted and admitted, and specifying the exact period of study. It also needs to include an official transcript of the most recent completed studies, and a letter of enrollment from the home academic institution indicating the student’s current status (full-time in good standing) and expected date of graduation.
Further your Student Visa research here.