Question: A lot of universities are expecting not to be able to run in-person exams for at least part of the 2020/21 academic year. I believe, for example, that no UK universities is currently planning to hold in-person exams this coming January. I can see how other forms of assessment might be possible for some subjects. But I can't see how this can work for math. 

> 
> For those universities which will not run math exams in-person for this
>  coming year, what are the plans for how to replace them?
> 
> 
>

Answer: 
Here are some examples of how it is done at the University of Copenhagen for the two courses that I have exams in next week.

One course has a written exam: We are given a problem sheet that we write up a solution to and submit to an online portal after a time limit of four hours. We are allowed to use the internet and any other aids we wish, except that we are not allowed to communicate with other people.

Another course has a verbal exam: A verbal exam is performed using Zoom. There is no preparation time.

Both courses were intended to be verbal exams pre-covid-19.
It's not possible to give a universal answer, of course, as that depends on many factors: how many people are available to grade, how many students need to pass the course (solutions that work for 20 students may not work for 200), what technological solutions are available… In our department somewhere in France, the solutions adopted for the various exams are:

* A normal homework, sent electronically by taking a picture of the answers, graded normally, with a long delay (a week or so) to complete. For very low level courses it's also possible to have a fully online exam, with multiple choice questions and short answers.
* A timed exam. This can be the same time for all students, common for low level courses where copying others' answers is trivial. Or it can be an exam available during a whole day, and when the student downloads the exam they are put on a timer and must give back their answers before a time limit (a few hours).
* Oral examinations using visioconference tools. The students connects with the examiner and gets asked questions, usually with the help of a virtual whiteboard.
* A hybrid method: students are given a timed exam, which is then graded (takes a few days). Then students pass a short oral exam about the content of the written exam. Depending on the size of the class, this can either be all students, or students who got above a certain grade on the written exam (to avoid "wasting" time on students who have no chance of passing regardless of how well they perform on the oral exam). The goal is try and bump up students, and detect some cheating.

My preference goes towards the last item, but it's a significant time investment, much more so than a traditional handwritten exam. It takes a lot of organization, there is a lot of cheating anyway, technical issues arise all the time for the video chat, the exam needs to be specially designed...

After a department-wide meeting, we have pretty much all agreed that there was no good solution anyway. Maybe someone here has a better one...