This is not a simple question as you think. We are not allowed to impose restrictions on our fellow Jews on things that may be technically allowed Rabbinically and Biblically. This violates the Torah prohibition of going to the right of what the Torah teaches. Although many religious Jews including me and everyone on this forum don't think it is propper to dance with a single girl and every Rabbi will tell you that it is not propper to do so (and the Jews of old didn't do this), if you investigate the matter, this is going beyond the letter of the law to those that adhere to the Rambam and the Ramban and it is really not violating any Rabbinical or Biblical ruling so we can not make it forbidden, we can just discourage it. This is especially pertinant to Baal Tshuva's and Baal Tshuvah Yeshivas that try to bring close not religious Jews. These Jews want to have a prom and look forward to it and having one will bring them closer to Judaism since they will like the School and not think the religious are fanatics.
But isn't the concept of a "prom" a Gentile concept? Dancing might be permitted but calling it a prom is purely a Gentile concept.
A prom isn't based off of religion at all, Yacov. Here's the definition:
In the United States and Canada
a prom, short for promenade, is used to describe a formal dance held at the end of an academic year. In the United Kingdom, the term is more widely understood to be in reference to a season of classical concerts or "proms", which have been held between July and September since 1895, today run by the BBC. The British synonym for the North American event would be Valedictory Ball, Leavers' Ball, Leavers' Dinner or informally Leavers' Do, closer to the Australian description (see below.) In Canada the terms Grad or Formal are most common and the event is usually only held for those in their graduating year of high school or middle school.
While proms at smaller schools may be open to the entire student body, large high schools may hold two proms, a junior prom for those finishing their 11th grade year and a senior prom for those who are finishing their high school or middle school years. The name is derived from the late nineteenth century practice of a promenade ball. The end of year tradition stemmed from the graduation ball tradition.
Boys usually dress in black tie (a dinner jacket and bow tie), sometimes with brightly colored cummerbunds or vests, though any sort of formal wear can be worn. Traditionally, girls gave boys matching boutonnieres to be worn on their tuxedos or waistcoats. Girls traditionally wear formal gowns or dresses adorned with a corsage given to them by their date. Many boys also match the color of their tie to their date's dress. Often, boys and girls will dress according to the theme of the prom - e.g. pastel suits for a Miami Vice-themed prom.