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I have come to know a prominent EU university in which it is an official policy that examination questions will be external to the lectures.

For example, say, they are teaching Probability & statistics. Say, they didn't lecture on Poisson distribution. They will put a question on Poisson distribution. If there are 5 questions to answer, they will somehow keep the questions within the syllabus but external to the lecture slides and/or handouts.

I felt that very strange.

Is this policy very common among universities?

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    Need to edit your question to make it more specific. At my university, the syllabus (or subject outline) is a contract between students and the lecturer. If it says the subject will teach X, then X must appear. Otherwise, students have grounds to complain to upper management, especially when they didn't do well in the subject. – Prof. Santa Claus Feb 3 at 22:31
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    How about a more descriptive title? – user151413 Feb 3 at 22:37
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    @user151413 why does it matter? I went in to buy an iPhone, and you gave me a Samsung. – Prof. Santa Claus Feb 4 at 1:21
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    If there is assigned reading, then you are supposed to know it, even if the professor did not re-read it to you in a lecture. – GEdgar Feb 4 at 12:54
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    Tutions fees in major EU countries... France (170 Euro), Germany (free), Italy (income based means test), Belgium (375-850 euro), Austria (free), Czech(free in czech lanuage, free in English), Denmark (free), Finland (free), Greece (free), Hungary (free), Iceland (free), Ireland (free for first attempt), – Ian Sudbery Feb 4 at 18:00
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If its on the syllabus, then you will be expected to know it. But its not necessary that all material on the syllabus will be taught by lecture.

It might be that the material is part of the prerequisites for the module. It might be part of the recommended reading for the module.

It might be that the question can be solved via application of knowledge taught in the lectures, but this is application of the knowledge to a different situation. For example: I might teach the concepts behind a hypothesis test, and give examples using t-tests. I might then set questions using the Poisson distribution. As long as I have the appropriate formulas or probability tables, I'd except students to be able to transfer the concept of a hypothesis test from the t distribution to the Poisson distribution.

I would also be aware that this was a difficult question, and would be to separate the top students from the good students, but it would demonstrate that someone had understood the concepts rather than just learning to plug numbers into formulae.

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    +1, "the question can be solved via application of knowledge taught in the lectures, but this is application of the knowledge to a different situation" this is the definition of higher levels of questions (problem solving and above) in Bloom's hierarchy. Questions that can be answered by directly repeating lecture material are not problem-solving questions, no matter how difficult. I have seen formal education policies that refer to these levels, so it's most likely that is what the OP's case refers to. – juod Feb 4 at 0:57
  • On the other hand, there are definitely universities where this sort of thing is outright forbidden - if it's on the exam, it has to have been taught in either the lectures or the tutorials. – nick012000 Feb 4 at 12:50
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    @nick012000 so if writing (or reading, or adding) is not taught in lectures or tutorials students can’t write their exams? That would be very convenient. – ZeroTheHero Feb 4 at 13:27
  • An extreme example is the Cambridge English Tripos, where, at least 15 years ago, students only had one lecture a week. – Ian Sudbery Feb 4 at 14:08
  • @IanSudbery Fifteen years ago? Wouldn't that be around the time of the famous BeeGees' Tragedy exam question on the Cambridge English Tripos? – Daniel Hatton Feb 4 at 16:19
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I personally stay away in exams from material not covered in assignments or tutorials, simply out of fairness rather than by a policy requirement. Once can always argue that, if it’s in the course description or the syllabus, it’s also fair game even if not covered in class but to me at least that’s over the line.

There has to be some flexibility to allow instructors to go beyond what was strictly in the lectures: in an absurd example one could argue that, if the instructor showed in class how to multiply 3x5 but not 4x7, then the first example would be legitimate a legitimate exam question but not the second.

A reasonable boundary is to expect that topics covered in class - rather than specific material covered in class - are fair topics. In the example of my previous paragraph, both are examples of multiplication so both would be fair questions in my mind.

Thus, it is possible to have an exam question on the Poisson distribution if the question deals with properties common to distributions rather than a unique property of the Poisson distribution, provided that distributions were a topic covered in class or tutorials.

I do not know examples where allowing exams questions not covered in class is a policy. I know of plenty of instructors (including myself) who make it a habit of not asking in exams the same examples covered in class, although the exam questions are on topics covered in class.

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