Does repeated retakes of a test with average score of all attempts allow manipulation? I am working with a computerized Course Management System which provides many options for scoring a test or activity - one of them is "Average of All Attempts". I thought that was: 1) a bad idea, 2) would not be able to be manipulated. But I just saw a student repeatedly get just one question wrong (whether intentionally or not) before finally getting all correct, and it migrated the average upward from the first poor attempt. So, students can "adjust" their own results with this method. Not sure if they know it or not, but I would bet they are smarter than I am! (Or less naive.) 

Has anyone else seen this? I think it would be mitigated by allowing only two attempts. Why would a Course Management System allow unlimited (or many) repeat attempts and an Average Score grading method? Maybe students should be designing the CMS, it would be more fair - perhaps more ruthless!
I have never encountered a computerized exam in which you have an unlimited number of consecutive attempts on the same questions and for which your final score is the average of all attempts.  This does seem to be gameable as you describe as well as perhaps in other ways: depending on the format of the answers, I could imagine many tests in which one could eventually deduce all the correct answers with little or no knowledge of the material being tested.  

This does not seem to be a very meaningful or rigorous way to run an examination.  I have never given an online examination but am rather familiar with online homework: there we often allow unlimited multiple attempts (except if the question is true / false or multiple choice, but most are not) and simply record the best score.  But the goal there is not to assess the students as much as to get them to do their homework.  Anyway, all such systems I know of certainly feature an easily "togglable" maximum number of attempts.  My feeling is that an instructor who sets up an exam as you describe is either unusually naive or -- more likely -- knows what they are doing and has reasons to want or live with an exam which can be gamed in this way.  

Nowadays I and many other academics have to periodically take little computerized exams in which we show ourselves to be familiar with current university policies (ethics, security...) Many of my colleagues are indeed trying to get through them as quickly as possible and trying to minimize the amount of time they have to spend reading background material (or worse, watching in-house informational videos).  Even these exams are not gameable to the extent that you describe.