Twice as good - again?

After writing the blog about school examinations being sat twice in order both to gve students an increased chance of achieving a desired level of qualification before leaving school, and to try and boost the school's performance record, I have been given further suggestions about a school's strategy in such a case.

First, there is the constraint of cost, and also the potential benefit.  Entering a school pupil for an examination costs the school money.  Schools are constrained in their finances, and might need some constructive accounting to justify a practice of recording N pupils in year 10, with M>N entries to the maths GCSE examination.  Therefore, the school has to estimate the value of an extra GCSE pass which might enhance its reputation (which then can lead to financial reward for one or more academic years) and relate that to the cost of entering a student for an extra examination.  This looks like a messy problem (see here).  Input the current cohort of students, with estimates of each one's probability of success.  Given constants are the current reputation and the financial model that relates rewards and reputation.  Output - a probability distribution for the future rewards for various scenarios of entering the current cohort into examinations.

Second, obtaining a "C" grade pass at GCSE is not the only statistic that the school may be interested in.  What about the high-flyers?  There is kudos for pupil and school in obtaining a starred "A" grade, so why not enter the high-flyers twice?  I have heard of parents who pay for their very able child to take an exam twice in this sort of case ... but might it not be in the school's interest as well?

Finally, some students in my experience came to university with the ingrained idea that they could take examinations in series until they were satisfied with the result.  And some of them actually asked their tutors, after the result of final examinations, whether they could retake the examinations because they wanted to get a better degree classification.  No, the tutors said, final means final.


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