Should she mention previous applications?

Hmmm. Your post raises interesting questions.

Your note does not indicate whether the new position is the same search, similar position, or distinctly different role. In my view, you do not want to provide information that would lead the committee to reject. As is stated in the Interviewing Series "the purpose of the cover letter is to get your resume read."  (I recommend purchasing the Interviewing Series if you haven't already done so.)

If it is the same search or similar position...the search committee probably already knows.

If a different role I do not see a compelling need to state the previous application...simply state genuine enthusiasm to work at (what is obviously) a great school.

 The only situation I can think of where she should mention the previous application is if it is still 'live' (i.e. still awaiting a response), certainly if there is a strong chance of the hiring manager finding out about the application.  I believe it would be more damaging for the hiring manager to discover the other application, or be informed of it by HR, than if it is mentioned in the cover letter (nothing major, just as short sentence along the lines of "I am currently awaiting a response to an application for... in department ... of your company.").  To not mention an active application may give an impression of something to hide.

If the previous application is no longer 'live', in particular if it was some time ago, I wouldn't mention it but I would be prepared to be asked about it.

Stephen

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Skype: stephenbooth_uk (Please note I'm on UK time)

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Experience is how you avoid failure, failure is what gives you experience.

I concur that the length of time between applications is relevant in whether or not to broach it in an opening missive - and particularly if it's asked directly.  "Have you ever applied here before?"  If they ask, especially on the application itself, she needs to tell the truth.

Interviews are horse races.  I can run the exact same time on the exact same track on a dozen different days but if the track's muddy, if the sun's in my eyes, if the horse gets stung by a bee, if there's a bur under the saddle blanket, if the camera at the finish line is experiencing a shutter malfunction ... well, you get the idea.  There are a lot of factors at play in a horse race as well as an applicant pool.  I could be the exact same candidate a number of times but if the recruiter is different, I may get through this time where I didn't with the other recruiter.  I may have spiffed up my resume.  I may have worked on a project pivotal to my career that may just push me over the finish line a nose ahead of the next guy, er, horse.  The other guy's horse might get stung by a bee so he's flying like the wind (or maybe he's flirting with the hiring manager or is related to the recruiter or something.)  None of that is a reflection of the person applying / in the race on that given day.  It's a horse race and just because you/she didn't place the last time she raced doesn't mean she can't win it this time. 

And trust me, I've used that analogy (a bit less verbose, I'm sure) when I was officially rejected for Manager Position A but based on my outlook and professional handling of it (with that analogy), I was considered for and offered Manager Position B. 

There's no shame whatsoever in being passed over a time or two or six.  In fact, I've been with my current employer for 7 years and it took me at least a half-dozen applications in various offices across the country (MI, IL, CO) before I entered "the right race" against competitors that weren't quite a fast as me, with the right trainer (recruiter), the right judge (hiring manager) and fully functional finish line gear (VP.)  

Persistence pays off.  If they don't ask on the application, I'd say leave it off.  You want to get your foot in the door first and you DON'T want to present anything that could be miscontsrued by a disgruntled or inept recruiter.  It's much easier to share your professional outlook and attitude during an interview - in person or over the phone - than it is to boil it down to fit in a little box on a form.

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Given the number of resumes that can now be submitted, sending multiple apps does not make screeners happy.  But to put this in perspective, have you EVER heard of anyone telling you they were hired because the hiring manager was impressed with how many applications they submitted?