Every situation has to be decided on its own merits.
If it’s just one or two overlooked citations, i generally make a note to the student to be more careful with his/her referencing in the future. If it’s more, and suggests a pattern of laziness or sloppiness, i will make a note of it, and will also start dinging the grade of the paper. I will also, in most of these cases, return the paper and tell the student to get the citations right and resubmit.
Note that, in all above cases, i need to be reasonably sure that any neglected citations are inadvertent, the result of either rushing or simply overlooking a footnote or two. If i suspect any intention to deceive, it’s a different story. My aim in penalizing plagiarists is to penalize cheaters, not to ruin the academic careers of students who are trying to do it right. A sloppy mistake, one or two poorly-cited quotations, an accidental failure to place quotation marks around a quotation—these are things that should be corrected, but that don’t generally warrant any actual punishment beyond fixing the error and dinging the grade on the paper a bit.
Every act of plagiarism where i’ve actually punished the student by failing them on the paper and/or the course, and reporting them to the Dean, has been so egregious that there was no room for doubt about whether or not it was simply a mistake. I’m talking about whole paragraphs copied and pasted from websites or from books, with no attribution.
I had one case last semester where basically every sentence of a 4-page paper on Alexander Hamilton was lifted verbatim from three different websites. I downloaded the pages of the website and converted them to PDFs, and marked the relevant paragraphs using the highlighting feature. I then did the same on the student’s paper. I used a different color highlighting for each website, and used those same colors on the student paper, so you could see at a glance how much had been lifted from each website. Then, after confronting the student and letting him know he would receive an F on the course, i passed the documents, along with an Academic Dishonesty form, along to the Dean.
Where i was teaching last semester, i think that, in addition to failing my course, the first Academic Dishonesty violation gets the student a talking-to from the Dean. they are also placed on some sort of academic probation, and told that a second violation will result in expulsion from the university.
Working out whether a student has been sloppy, or has been trying to deceive you, is usually reasonably easy. Context is important. If the student has 25 other accurate footnotes, and has clearly read and understood the source material, then it’s pretty clear that one or two missing references were probably inadvertent, and deserve nothing more than a “Be more careful next time.”
The most difficult cases to adjudicate, and cases where it’s most difficult to explain to students what they’ve done wrong, are instances where the student essentially lifts their argument straight from the source, but puts it in their own words. No matter how much you explain plagiarism, there are some students who simply can’t get their head around the notion that it is possible to plagiarize even if you don’t copy the sentences verbatim. Taking other people’s ideas without attribution is still academic dishonesty, and it’s a difficult thing to explain sometimes. There are also genuine grey areas between using someone else’s argument to help make your own argument, on the one hand, and simply lifting someone else’s argument and presenting it as your own, on the other.