Berklee College of Music gave us a look at “American Idol” judge (and Mainer) Kara DioGuardi teaching her “Hit Songwriting” course to students on campus. DioGuardi — who’s written chart-toppers for pop stars such as Katy Perry, Kelly Clarkson, and Gwen Stefani — has been teaching the class all semester. She handpicked the 27 students, who are probably prepping for midterms right about now.