Two student just kissed each other, in public, in front of the other students and me (as the lecturer), in class!
Should I report the case to the administration?!
What am I supposed to do?
I'm a tenured female lecturer, at an american university.
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(Assuming that the kiss was worth noticing: personally, I wouldn't mind) What do you do with, e.g., students who chit-chat in the classroom? With those who play with the phone? With those who look at Youtube videos? With those who eat spreading food everywhere? With those who arrive late giving high fives to their friends?
Do the same.
As I'm sure you're aware, kissing in public is an entirely acceptable part of American culture. It happens at the bus stop, in the restaurant, in movies, on TV, and pretty much everywhere else where people can see you. In itself, it isn't a big deal, and nobody feels offended by it.
It becomes a distraction when it either happens at a time where it's in appropriate (e.g., during a quiet exam) or in a way that makes it inappropriate (e.g., a couple french kissing for an extended period of time in a fancy restaurant) or if the norms within your institutions are different from those elsewhere (e.g., in a strictly Christian college). Your question does not specify whether either was the case. If so, you are within your right to ask the students to not do it in the future. But if it was a peck on the lips somewhere in row 3 during class, or someone hugging and kissing during the break between classes, I don't think that that goes outside the norms of American culture. You can of course put something into your syllabus, or call out the students, but the best you're likely going to achieve this way is to come over as prudish. That's not likely what you're going for. If the students themselves feel distracted or think it goes beyond reasonable bounds, they will feel free to police themselves.
Talk to the students involved privately. (E-mail them, if necessary, to set up an appointment.) Ask them to refrain from over-the-top displays of affection during class. Once you have talked to them, make a concise announcement to the whole class that you do not want to see that kind of display during class (although it may be best not to refer specifically to the event that happened, so as not to embarrass the student involved). In the future, have more detailed notes in your syllabus about what kind of behavior you consider inappropriate for the classroom.