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I would like to know the advantages and disadvantages of open-book exams as compared to closed-book exams, particularly in standard undergraduate courses like calculus or linear algebra.

My practice (about 20 years of teaching) has always been to give open-book open-notes exams, allowing the students to use their books and notes during the exam. Part of my reasoning for this is that I hope to place a greater emphasis on understanding the material, rather than on memorized details. I don't mind if a student has to look up some detail quickly during the exam.

But perhaps there are advantages of closed-book exams I am overlooking.

Question. What are the main advantages and disadvantages of open-book versus closed-book exams?

I would be particularly interested in the result of any math education studies that compare the two exam methods.

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    $\begingroup$ possible duplicate of Formula sheets and books during tests and exams $\endgroup$
    – dtldarek
    Commented Mar 14, 2014 at 1:30
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    $\begingroup$ It does have an overlap with that question, but I find that question to be much wider in scope than what I am asking here, which is more narrowly focused on exams, rather than general teaching philosophy. So let's keep this narrow question, particularly if someone has data from a study comparing the two exam methods. $\endgroup$
    – JDH
    Commented Mar 14, 2014 at 1:38
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    $\begingroup$ My students often have the book in electronic form, and don't own a printed copy. This makes it impractical to give an open-book exam. Re open notes, some classes require more memory work than others. First-semester freshman calc seems to me to be a class where essentially zero memory work is required, so I don't see the point of making exams open book or open notes. $\endgroup$
    – user507
    Commented Oct 7, 2014 at 0:41
  • $\begingroup$ If you can do something without the book, it shows a higher form of proficiency. Of course "in the real world" the book will be available. BBut there are still values in having more internalized proficiency (higher retention, easier grasp of other material to include physics derivations). I think almost all tests are better closed book. (Without even a formula sheet. Just steam tables and periodic table for thermo and chem.) $\endgroup$
    – guest
    Commented Feb 4, 2018 at 21:20

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There is a middle ground: closed-book, with some notes.

The disadvantage to open-book exams is that students will waste time looking for answers in the book. I know this from experience. As I personally have a very bad memory, I wanted to keep that aspect out of it. But I saw many students wasting time during exams, flipping through the book. (Have you not seen that?)

My solution has been to let them use notes. Even a page of notes allowed them to write so much that I watched students searching all over their note page. So now, they get a 3x5 card. (Except calc II. They get a page still.) This seems to offer them enough notes to not worry about memorizing, and keep the searching down.

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    $\begingroup$ I hardly ever see the flipping-through behavior you mention, but probably because I anticipate the problem, and I emphasize during the review that in my experience, students who do that are almost always failing the exam. I explain that the purpose of the open-book exam is to look up something quickly, and students should not expect to find "answers" in the book to the exam question. $\endgroup$
    – JDH
    Commented Mar 14, 2014 at 2:06
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    $\begingroup$ Perhaps we teach different populations. (I teach at a community college.) $\endgroup$
    – Sue VanHattum ♦
    Commented Mar 14, 2014 at 2:39
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    $\begingroup$ It's probably not that different. When I first started giving open-book exams, I did observe the phenomenon; but I noticed in subsequent years that one could easily correct it by explaining during the review that open-book does not mean find-the-answers-in-the-book-during-the-exam, and that such a strategy inevitably is a failing one; in fact one must study hard for an open-book exam. $\endgroup$
    – JDH
    Commented Mar 14, 2014 at 3:27
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    $\begingroup$ I remember (long ago) saying that sort of thing. For me, it didn't help. $\endgroup$
    – Sue VanHattum ♦
    Commented Mar 14, 2014 at 4:17
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I gave a response over at this question Formula sheets and books during tests and exams that might be useful.

Basically, the education literature seems to be divided over the usefulness of open book exams, and there appears to be very little on the maths education front, with much more from medicine or literature-focussed courses.

From personal experience, most students I talk to hate open-book exams because they don't know how to study for them effectively and are worried during the exam that they will miss something important in their answers that they could have found in their book. At least with a fully closed-book exam they know where they stand. Therefore, if you choose to do it, you need to train students in the skill of doing an exam with open-book. You should probably give them lots of advice about exams generally, regardless of the type of exam you do!

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As a student, I learned to hate open book exams... too much time wasted looking around. A case could be made for take-home exams (can look up whatever you want, but not the same time pressure).

I like to construct exams made of several (5 to 7) short questions, each one testing a specific concept. If some technique requires several steps, make a question for each (perhaps even "If the result of step 1 above is , do step 2 ..."). If specific, easy to confuse/forget formulas are involved, they are printed on the back of the exam as official notes.

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This basically comes down to the depth versus breadth debate. With an open book exam, you can assess more content, but not know exactly how well they know it. A closed book exam gives you a much better idea of exactly what they know, but it limits you to a smaller amount of material.

Right now, it occurs to me that an open book exam might work better as a formative assessment.

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    $\begingroup$ That wasn't my experience in college. Professors would make open-book exams really, really hard to compensate for the advantage of having the book. So instead of having some easy definition question or calculation, you'd have to do tricky proofs. In one course we had the option as a class to opt for an open-book or closed-book exam and we chose closed-book because we were afraid of the harder exam. $\endgroup$
    – Rag
    Commented Mar 27, 2014 at 21:12
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The biggest advantage of open-book exams is that they are closer to real world problems. People can look things up in the real world. So why should they not do that during exams? However, the big disadvantage is that students, because they are not used to it, have the common misconception that an open-book (or even open-internet) exam means that "I can just look everything up on the fly", which is bad, but is just that: A misconception.

Make sure to explicitly communicate how you expect them to prepare for this exam. Consider even to ask and guide them on their exam preparations. Give them a recipe for exam success (while, of course, avoiding "teaching to the test"). Also, make sure not to make the open-book exam terribly hard. If you transform a closed-book exam into an open-book exam, but the degree of difficulty stays the same, you have a slight chance of making your students' lives just a little bit easier.

The "exam taker" students might complain, so maybe compensate with "bonus" problems or other goodies (possibly, outside of exams) that compensate people who invest more time, and are actually interested in learning this stuff. What about rewarding students helping other students (outside of exams)?

Having said that, let us re-consider what an exam is and does: Exams exams are short-time, high-stakes, high-pressure turning points in a young person's career. They generate large amounts of stress and disgust in the average young (and old) person's mind, and there is tons of research showing that they barely help the student in understanding things, solving any problems or achieving any other form of goal. Exams do two things:

  1. Exams generate one (and only one) kind of extrinsic motivation in students. We call that kind of motivation "pressure" or "stress". In the world of "carrots and sticks", its the stick.
  2. They generate a grade. Institutions (and thus teachers) are required to generate a student's evaluation, usually in the form of a low-dimensional vector of "grades". As a result, generating "good grades" ends up being the only goal for institutions, and often distracts them from what should be their real goal: To help the students.

Do you think, that open- or closed-book exam can really help students? Regarding your exams, is it more important to "get it right the first time" (because else their grades, and thus their future career and chances to get scholarships will deteriorate), or do you focus on students learning from the exams and the feedback you give them on the exams?

Do you give students a chance to generate good grades, if they have the passion and put in the effort, even if they are not good "exam takers"? Do you think that the quality of being a "good exam taker" correlates with a person's ability to succeed in or contribute to society? What about those who are not good at exams? Do we know anything about those students?

So here are some suggestions: Have you tried non-one-shot (i.e. repeatable) exams? If that's too much effort (or you don't have the infrastructure to make it effortless), did you consider take-home exams? What about project work? Please don't rule it out just because students are bad project managers. No one has taught them yet. Of course, good project work also needs the right kind of structure. The same issues apply to all approaches that diverge from the traditional "lecture, homework, exam" cycle of death - It's hard. Hopefully, we will be able to come up with better approaches that we can also share more easily, soon enough.

PS: Maybe you want to take a look at Robert Talbert's awesome blog on new ideas in teaching Mathematics, flipping the classroom and a lot more?

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  • $\begingroup$ Domi, thanks for the contribution. I feel that a lot of your discussion simply misses the mark with my situation. For example, my open book exams are not "closer to real-world problems," and there is debate in math education circles about whether that is helpful anyway. What I wanted to know was rather specific, namely, whether there were advantages of closed-book exams that I had overlooked. $\endgroup$
    – JDH
    Commented Oct 6, 2014 at 12:07
  • $\begingroup$ @JDH Sorry for not being of more help at this point. The fact that "there is debate in math education circles about whether [having real world problem solving skills] is helpful [to students]" (and similar arguments) are not new to me, but it still hits me every time I hear it. Good luck though! $\endgroup$
    – Domi
    Commented Oct 6, 2014 at 13:02
  • $\begingroup$ @Domi Your remark mischaracterizes the debate. The debate is whether using real-world exercise problems (with all their distracting complications) helps to teach a mathematical concept, and at least some studies provide evidence suggesting that it does not. Meanwhile, I do teach real-world problem-solving skills, like the ability to explain a technical idea with clarity and precision. Indeed, I tend to assume that that is the most important skill I am teaching most of my students. $\endgroup$
    – JDH
    Commented Oct 6, 2014 at 13:04
  • $\begingroup$ @JDH I sincerely apologize for not being clear enough (I rephrased it a bit): My answer does not suggest the use of real-world exercise problems in exams. I merely claim that open-book exams are, by their very nature, closer to real-world situations than closed-book exams, because you get to look stuff up in the real world! FYI, I love your priorities in teaching. $\endgroup$
    – Domi
    Commented Oct 7, 2014 at 16:45
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One minor point: I would not permit books and forbid other print resources (student's prepared notes, reference cards, other text books…) That strikes me as too hard a rule for proctors to enforce, because it is hard to see what a student is flipping through.

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    $\begingroup$ I agree with this, and this is indeed what I usually do. $\endgroup$
    – JDH
    Commented Oct 6, 2014 at 18:47
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Perspective: I'm a lecturer at a large urban community college. My opinion is that open-book tests are fundamentally a trap for students. It reduces complaints and makes it seem like you're a "nice guy", but it gives the impression that students won't have to study in advance, and can just look the answers up in the book during the test. I think what generally happens is that they get lost shuffling pages during the test, unable to get started because they really don't know how.

I feel like we need to communicate the fact that there is some body of conceptual knowledge that practitioners carry around in their head, and can converse and read about with "automaticity", without looking it up. On the other hand, I'm a huge proponent of providing a 2-4 page formula card (in common to all the students) as a tool which is short and clarifying and not likely for someone to get "lost" in.

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    $\begingroup$ I always give open book exams (20+ years at a large urban university), and I find it helpful to emphasize in advance that one should not expect to "find the answers" in the book during the test. I tell my students that the students who are flipping through the book a lot during the test are generally the students who are failing the test. An open book policy, instead, is meant for quickly looking up a fact or formula. Thus, study time is spent on mastering the concepts, rather than memorizing facts. Primed this way, I find that most students usually have the right attitude. $\endgroup$
    – JDH
    Commented Nov 14, 2015 at 0:34
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    $\begingroup$ @JDH: Late comment: I now realize that we were both at the same "large urban university" when we wrote this. :-) However, my experiences at the community college level are likely quite different. Exactly as Sue's comment up above, almost all of my students lack the meta-cognition to pay attention when we tell them that some practice is bad for them (e.g., searching for answers in book during exam), nor are "study time" or "mastering the concepts" things they generally recognize. I find that's a problem for pedagogy research, as effects vary so much by location. $\endgroup$
    – Daniel R. Collins
    Commented Aug 31, 2019 at 17:02

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