FLORENCE, Italy—Svetlana Cojochru feels hurt. The Moldovan has lived here seven years as a caregiver to Italian kids and the elderly, but in order to stay she’s had to prove her language skills by taking a test which requires her to write a postcard to an imaginary friend and answer a fictional job ad. Italy is the latest Western European country trying to control a growing immigrant population by demanding language skills in exchange for work permits, or in some cases, citizenship. Some immigrant advocates worry that as hard financial times make it more difficult for natives to keep jobs, such measures will become more a vehicle for intolerance than integration. Others say it’s only natural that newcomers learn the language of their host nation, seeing it as a condition to ensure they can contribute to society. Other European countries laid down a similar requirement for immigrants, and some terms are even tougher. The governments argue that this will help foreigners better join the society and promote understanding across cultures. Italy, which has a much weaker tradition of immigration, has witnessed a sharp increase in immigration in recent years. In 1990, immigrants numbered some 1.14 million out of Italy’s then 56.7 million people, or about 2 percent. At the start of this year, foreigners living in Italy amounted to 4.56 million of a total population of 60.6 million, or 7.5 percent, with immigrants’ children accounting for an even larger percentage of births in Italy. Cojochru, the Moldovan caregiver, hoped obtaining permanent residence would help her bring her two children to Italy; they live with her sister in Moldova, where salaries are among the lowest in Europe. She was skeptical that the language requirement would encourage integration. Italians always “see me as a foreigner,” an outsider, even though she’s stayed in the country for years and can speak the local language fluently, she said.