Hi Rhon,  This is good question.  I've passed this on to a few teachers and parents in effort to get you a few perspectives.  The response below is from a teacher based in NYC.  Other responses should follow.  Good luck and I hope this is helpful.

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It seems this issue comes up quite often in competitive districts offering rigorous classes like AP calculus.  In theory, the testing process should be a level playing field for all.  I would think that an extra day might give some advantage in prep time to the students not in attendance.
No matter what the reason for the absence.

The district, the school, the teacher should have a clear policy regarding test-day absences for these high-stake situations.  A poor analogy is professional athletes with steroids, when you have everyone on the same ability level competing, a degree or two of separation can make the difference.

I am sure the district has some sort of arbitration process.  In the end a dramatically more difficult test is unfair, however, it is also unfair for the students who have one less day of preparation.  The prep time is measurable, however, the degree of difficulty for the make up is subjective.

Good luck,
BW

Hi Rhon,
When I first read your question, I was all prepared to talk about differentiation, and modifying tests to students' abilities.  But your further description of the story throws all of that out the window.

I can certainly understand the teacher giving a different test.  Regardless of the innocence of the absent children, the teacher probably didn't want to take the chance that the kids who took the test would tell their friends what to look for.

However, I'm very surprised to hear that not even the principal or even the superintendent (!) would take your claims under consideration.  I'm not really sure who you can take this to beyond the superintendent!

I guess my best advice would be (barring moving your child to another school) to have your daughter be on her absolute best behavior for the rest of the year, ask for extra credit opportunities as often as possible, and maybe eventually soften the teacher into believing that she wasn't just playing hooky.