School of Mathematics Teaching

Open book examinations

Information about open book examinations.

Open Book Examinations

The rules and reasons for running open book examinations in the School of Mathematics.

Standard Rules

We run many of our examinations as "open book". Our standard rules for this form of examination are are that you may bring into the exam:

  • 3 x A4 pages containing your personal notes
  • a calculator

And we note that:

  • Permission for dictionaries (language translation or English) is normally granted, if requested.

 

Why we use open book exams

We are interested in testing what students have understood, not what they have been able to memorise in a few days of frantic revision.

In most real-life situations, the important thing is what you can achieve given a normal working situation with access to sources of information.

Open book examining encourages learning (and teaching styles) that target understanding. It also encourages students to buy and study the required reading and produce sensible, organised notes and summaries.

The effect of open book exams

Open book makes far less difference to overall results than you might expect. Even if the exam is similar to one that might be given in a closed book format, it will not lead to a huge difference in mark distribution.

This is because students who have not engaged with the material may not even be able to find the appropriate section of their book or notes explaining a relevant method. It is almost impossible to use a book or other course materials successfully in an examination without properly studying these beforehand.

A book or notes can help, however, if examinees have forgotten the details of something that they do generally understand well. Observations show that students tend to use materials brought in to examinations relatively little and mainly as a check.

 

Modifying closed-book exams for use as open-book exams

 

Lecturer’s FAQ

I think it is important that students memorise some proofs. How can I test this using the open book format?

Do you want them to memorise proofs in the sense of being able to write them down, possibly without really understanding? Or would you prefer that they learn proofs as a professional mathematician would, by remembering a couple of key ideas and reconstructing the detail on demand?

The problem with the former is that students may simply memorise key proofs by rote the night before the exam and forget them on a similar timescale. Many studies show very fast decay rates for information memorised without understanding.

What about giving the proof and asking examinees some questions on their understanding of it: "At what stage in the proof are we using the fact that the sequence tends to zero?", for example?

Students need to be able to carry out certain calculations, such as finding eigenvalues or integration by parts, without looking things up.  How can I ensure this?

If a student has no idea how to compute eigenvalues, it will take them a long time in an examination to compute these following an example in a book or notes.

To ask a question in the opposite direction, do we want to harshly penalise a student who essentially knows how to carry out the procedure but in the stress of an examination has forgotten whether a certain sign is a plus or a minus?

Consider also the typical question styles for closed book examinations: do we end up asking too often for standard processes to be carried out and too rarely for understanding of what the process or its result actually mean?