A few years ago, I reported a student for academic dishonesty (in a graduate-level mathematics course, they were copying solutions off the internet, nearly verbatim). After acknowledging their wrong-doing with the Academic Integrity office on campus, they were allowed to drop the course.
The next year, the student re-enrolled in my course, and did reasonably well. I had no qualms about the originality of their work this time.
They recently asked me whether I would be willing to write them a recommendation letter for PhD programs in mathematics.
If I write a letter, am I obligated to write about the academic dishonesty incident? It appears to me that the student has already faced the consequences of their actions (they had to drop the course); however, this was a significant part of my interactions with the student and it seems dishonest to not mention it.
(I am aware that I could simply tell the student that I am not comfortable writing a letter, but I am curious to know what one should do in this situation if one did write a letter.)
Some facts: when the incident occured, the student was in their first semester of our masters program. They are also an international student, and this was their first semester in the US.
ETA: Look, I framed the question to be as general as possible so that it can be useful to the community as a whole. Since some commentors are choosing to attack my teaching practices, below are some more specifics, where once again I am trying to not reveal the identity of this student, myself, the course, the university, etc. I am actively trying to do what's best for the student here (note that I clearly state that I think the student has faced consequences for their actions; I am also not using my usual ac.se account to post this), and I don't understand where comments about "shutting down a student's career" are coming from.
I clearly state in my syllabus and on the first day of class that copying solutions off the internet (or any written source) is not allowed. I do this because I encountered this situation as a TA in graduate school. In particular, students are allowed to talk to anyone they like about problems, but I believe that when they just copy a solution, they are not learning. You are welcome to disagree with my policy, but it is my policy and my class, and it was clearly stated in two separate venues.
The copied solutions were virtually indistinguishable from the solutions online. This was not a matter of simply "being inspired". This was not isolated - three out of six solutions were copied, and those were just the ones I spotted. When I noticed this, I asked the student to come talk to me. I told them that I had noticed similarities between their work and solutions I had found online. I told them that I was not accusing them of anything, and they did not have to tell me anything; I reiterated that copying solutions from the internet was not permitted; I invited them to come to my office hours to talk about future problem sets; but that if I noticed such similarities again I would report them to Academic Integrity. They did it again on the next problem set (four out of six solutions).
Although they denied everything once via email, after talking with Academic Integrity (where they owned up to everything), they did find me and apologize. I was cordial to them throughout this event, and continued to be so afterward. We remain on good terms now. I consciously try to ensure that I do not let this incident color my interactions and behavior with them. They made a mistake once but people make mistakes and I am trying hard not to take it personally.
In summary, the incident itself was pretty blatant, the policy was clearly stated, and they had an opportunity to stop such that I would not have reported them if they had. I did not take reporting the student lightly. Nonetheless, I think academic dishonesty is a serious matter and it is our responsibility as faculty members to not turn a blind eye to it.
Answer
TL; DR: The student probably wants you to write a letter to mitigate the harm of the incident because they already expect admissions committees to know about it. In that case, mention it briefly and move on to your standard letter.
There are only three reasons I can think of why a student would ask you to write a letter in this situation. How you respond depends on the reason.
Despite, or perhaps because, of the incident you have become a mentor to the student and genuinely know the student very well. The student knows that they have regained your trust and confidence, and that you're in a good position to give them a solid recommendation.
A. If this is the case, and you truly do now trust the student and want to offer a strong recommendation, you can mention that the two of you got off to a rocky start, and allude to the issue without going into detail (you don't need to use the words "misconduct" or "cheating"). You could say that the student worked hard to regain your confidence, and that you are now happy to strongly recommend etc.
B. If this is only sort of true, and you don't think very highly of this student and/or have reason to think they might cheat again given the right circumstances, you should decline to write the letter.
It doesn't sound like your situation falls into the first category, however, which brings us to the second possibility.
The student knows that this incident will appear on their record, and that their prospective programs will see it. They believe they have at least somewhat redeemed themselves in your eyes, and are hoping that a generally positive letter from you will mitigate the harm of the incident. I suspect that this is what's actually going on. If so, you should confirm this. Ask the student specifically whether the incident will already be known to admissions committees.
A. If the answer is yes, write whatever letter you would have written absent the misconduct but with an additional paragraph noting that you were involved in the incident and believe that the student has faced sufficient consequences, and that your letter focuses on their performance in the subsequent class. If you have reason to think the student has learned from the incident and it's not likely to be repeated, include that in the paragraph acknowledging the misconduct, but don't dwell on it.
B. If the answer is no, the misconduct is sealed or otherwise unlikely to become know to prospective programs, we come to the third possibility.The student is extremely naive, and doesn't realize the potential harm you could do to their admissions chances by writing about the misconduct.
A. In this case, absent any particularly strong admiration for the student, I would decline to write the letter. At the very least, you need to strongly caution the student about how bad a letter from you could be for them.
B. If you really still want to write the letter and your student still wants you to write it after being warned: You could take either approach above, depending on what feels more comfortable to you—either allude to the issue in the most general terms, or mention it but state specifically that it is not the focus of your letter. You should definitely warn your student about this beforehand, though, and perhaps allow them to see the letter before you send it.
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