The only real wonder is why this hasn’t happened before: Nashville Children’s Theatre summer camp students mount a production of their own, with entertainment value beyond what’s appreciated by the naturally supportive audience of family and friends. Here it is, then, as 20 young persons in grades 6 through 12 take on this somewhat legendary 1959 musical based on Hans Christian Andersen’s fairy tale “The Princess and the Pea.” The music was written by Richard Rodgers’ daughter, Mary, and the original New York production of the show marked Carol Burnett’s Broadway debut. This earnest effort marks the culmination of NCT’s Emerging Actors program, with cast and crew in rehearsal for a month. Sets and costumes also feature major student contributions. NCT education director Alicia Fuss directs, with Shawn Knight as musical director. Recommended for ages 8 and up.