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I teach in the school of sciences and engineering in the university where I work. I have asked professors several times if the final exams have to be comprehensive, and I usually get mixed answers.

So I want to ask, for a course with two midterms and a final:

  1. If there is some criteria or organizations that require the final exams to be comprehensive (for instance, does ABET accreditation or legal statute require it?), or does it depend on the school or the professor?!)

  2. What are the pros and cons of having a comprehensive final?

  3. Will your answers to the above questions be different if the course components were 2 best out of 3 midterms plus a final, or if the course was a graduate course instead of undergrad?

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TRQ is "should final exams exist?" If a student hasn't shown via progressive tests/quizzes, homework, or other projects that he has learned the material, what good is a final exam? The rest of your comments are offtopic, as accreditation or licensing is different from academics. –  Carl Witthoft Apr 12 at 21:48
@CarlWitthoft: I strongly disagree: Like it or not, accreditation is one of the (ahem) inescapable joys of academia. –  JeffE Apr 12 at 22:45
@CarlWitthoft except that you are assuming such things as homework/progressive tests exists in the first place. This might be true in the US where university is more high-school like but, for example, in Italy there is no such a thing as homework for a course. Projects are done only if the course explicitly has a laboratory associated with it (only few have them). Also attendance is almost never required in most of the courses. Courses tend to have only a final written + oral test. –  Bakuriu Apr 13 at 10:18
@CarlWitthoft Actually I prefer Italian-style university, because at least you are not treated as a 10 years old that still needs a baby-sitter... you have the choice of taking the responsibility of your studies or not. –  Bakuriu Apr 13 at 12:21
@MikeJohn Erm because teachers give homework at high-school but not at university (in the US you still get homework => more high-school like). In the school you have to do tests like every month but at the university you have exams sessions once every 6 months and you have one exam for each course, not so in the US (=> more high-school like). Attendance in highschool is mandatory (even by law), not so in university apart from few exceptions, not so in the US (=> more high-school like). –  Bakuriu Apr 13 at 12:25

4 Answers 4

To address 1, I've never heard of any such policy on cumulative exams. In my experience, such pedagogical decisions are made solely by the course instructor. They make the decision as to what material appears on the final exam, or even whether to have a final exam at all.

In the case of large multi-section coordinated courses, this decision might be made by the course coordinator (especially if all sections give a common final exam) or by agreement of the various instructors. There might be some expectation that they will respect precedent unless they feel strongly that it should change, in which case they might be expected to discuss it at the department level.

Otherwise, I think any explicit rule about the content or format of exams would be seen as a serious infringement on the instructor's autonomy, which is a central aspect of university teaching.

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All of my final exams are cumulative, for a couple reasons:

1) I've always felt odd about non-cumulative exams. It seems to send a message I'd rather not send: “It's okay to forget about what you learned earlier in the course – you won't need that any more.”

2) Often, what gets taught later in the course builds on earlier concepts. If A lays the foundation for B, and B lays the foundation for C, it can be rather challenging to test on C without testing on A and B also.

That said, I try very hard to test on higher-level concepts rather than on minutia, so a cumulative final fits my teaching style. I expect my students to be able to speak intelligently to the main themes of the course. I've told students many times: “Come to class ready to learn, and be ready to engage with the material via the in-class discussions. That's the best way to prep for the exams.”

My goal is to structure my exams so that students who have paid attention in class and learned the material through other assignments should do quite well on the test – without the need to cram or commit the material to short-term memory. “By the last week of the term, you either know this stuff, or you don't,” I tell them. Many of my exam questions are essay questions that require students to analyze a scenario, and synthesize material from different parts of the course.

That might not always work, depending on the nature of the material; some material doesn't lend itself well to such questions. This approach may not be scalable, either. (It's not uncommon for me to have six or seven pages of essay questions per exam. Most of the time, I have between 15 and 30 students per course, which keeps grading manageable. If I had 50 or 60 students, however, I might have to rethink this approach.)

As a footnote, most of my courses are 400/600-level courses. I don't know if the style I've outlined would be a good fit for freshmen and 100-level material.

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At my large public research university (in the US):

In physics, exams are nearly always non-cumulative. The finals are treated essentially as a third midterm, none of which are cumulative.

In math, the it depends on the professor and the course. If it is one of the "common"/high-enrollment courses that students in e.g. biology, chemistry, also have to take, then the final is usually cumulative. In courses designed for upper-level math majors only (e.g. topology, graph theory) it is up to the professor, but usually cumulative (usually the courses are very linear; it would be impossible to pass a test over the final material without knowing the material from the midterms).

In humanities, usually not cumulative. Or if cumulative, trivially so (e.g., one or two basic questions about the early material).

edit: I should clarity, it's always up to the professor, I'm just outlining general departmental tendencies

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This is pretty much my same experience at a private university in the US. I was once told by a physics professor that he couldn't make the final cumulative and still keep it a reasonable length, while a math one said "it doesn't matter" because compared to other courses, more of it builds on top of what was in the midterm. –  Izkata Apr 13 at 4:27
Every single physics exam I've ever taken has been cumulative, and it's been my understanding that that is the norm in physics classes at US universities. I don't have explicit statistics on it, but I would bet your experience is relatively unusual. –  David Z Apr 13 at 7:44
@Izkata - RE: "I was once told by a physics professor that he couldn't make the final cumulative and still keep it a reasonable length." Interesting. I've interpreted "cumulative exam" to mean ‘anything taught in the course could be on the exam,’ not ‘everything taught in the course will be on the exam.’ –  J.R. Apr 13 at 16:04
@J.R. Comprehensive exams were the norm here, presumably since not doing so would skew the final scores higher for students who just coincidentally better understood the chosen topics on the exam. –  Izkata Apr 13 at 16:17
In physics, exams are nearly always non-cumulative. This doesn't really make a lot of sense. When I teach first-semester freshman physics, we do kinematics, Newton's laws, conservation laws, and vibrations and waves. How could a final test the student on vibrations and waves without using the preceding concepts? E.g., I can't ask a question about the energy content of the wave without using the previously introduced concept of energy. –  Ben Crowell Apr 14 at 14:19

I'm responding to #2 and 3, as there are no rules regarding #1 that I'm aware of.

Pedagogically, there is evidence that repeated testing improves learning. Most of the literature is via authors Karpicke and Roediger. Here's a list of resources from a research project at Washington University, and a rather overwhelming overview of student learning and good teaching by John Kihlstrom at Berkeley.

I don't see why the benefits of a comprehensive final would be lessened by a "two out of three" midterm organization or different for undergrad vs grad level students.

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I suspect that "repeated testing"'s impact is akin to "repeated threats", which cause students to study and/or review. It's not the testing itself that improves learning, but the fact that it "induces" students to study. –  paul garrett Apr 12 at 22:21

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