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The Covid-19 pandemic has changed our work-lives in ways few of us could have anticipated. These exceptional circumstances have forced each one of us and each one of our institutions to adapt, sometimes in creative ways. I would like to compile a list of those changes and adaptations at all levels of the mathematical ecosystem (all the way from the lives of math undergrads to the working of national funding bodies).

For each entry, please discuss the advantages and disadvantages of the new setup, compared to the previous way of doing things. Be as specific as possible.

Where relevant, please discuss issues of accessibility of events/resources to people who would otherwise have less access to them, and issues of climate change (less traveling means fewer emissions).

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    I hope that this will remain open; I have put a question at https://meta.mathoverflow.net/questions/5047/ in case people want to discuss that. – Neil Strickland May 28 '21 at 09:21
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    I did not downvote but would be happier if the question would pinpoint issues specific to research mathematics per se. – მამუკა ჯიბლაძე May 28 '21 at 10:34
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    This seems both too broad and subjective and argumentative, unfortunately. "Please discuss" questions usually are not a good fit on a platform like MO. Even though I find the question interesting, I don't think this is the right place for it. – Federico Poloni May 28 '21 at 11:23
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    Well, the usage of the Internet also has an impact on the climate. Are there any studies comparing the difference between the emissions caused by the traveling and the emissions caused by the "smart working"? – Francesco Polizzi May 28 '21 at 14:52
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    @FrancescoPolizzi "A single return flight from London to New York contributes to almost a quarter of an average UK citizen’s annual carbon emissions": tinyurl.com/yce7aud5 (internet usage is not discussed in the linked article – that very fact is probably an indication that its impact on the climate is significantly smaller) – André Henriques May 28 '21 at 15:11
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    @RayButterworth. I understand your feelings: I removed "social justice" (I kept "climate change" though). – André Henriques May 28 '21 at 15:29
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    I agree with the closure: there's not enough specific to research mathematics here -- and asking about "the lives of math undergrads" is outside the scope of MathOverflow. –  May 28 '21 at 16:28
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    On my opinion, this is not an appropriate forum to discuss these questions, therefore I vote to close. – Alexandre Eremenko May 28 '21 at 19:32
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    I VOTE TO CLOSE – alesia May 29 '21 at 00:06
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    I have not voted to close, nor to reopen, but I think one problem is that "the mathematical ecosystem" looks pretty different in different parts of the world, and some might even say that the Golden Triangle in England has its own ecosystem which is pretty damn different from the rest of England (I can't speak for Scotland) when it comes to teaching, grant-hunting, leverage+profile, demands, etc – Yemon Choi May 30 '21 at 14:36
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    I really wonder about these theoretical open-close-discussions. Have a look at the answers so far. They are very useful and interesting, not just to mathematicians but to everyone who is interested how mathematics is changing right now. It is a (so far) unique point in history, and here professional mathematicians document what is changing in their area. I think it's great. – Martin Brandenburg May 31 '21 at 13:31
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    @MartinBrandenburg Thank you Martin. It was quite tough being on the receiving end of this unrelenting stream of negative feedback. (It left my stomach pretty upset for a day or two.) I'm happy that, despite all the closures, people were able to submit this nice collection of informative answers. – André Henriques May 31 '21 at 17:07
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    @alesia: I vote not to capitalize whole sentences. – Jochen Glueck May 31 '21 at 21:36
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    (Note that OP has un-protected this question three times, after three different users tried protecting it. This can be confirmed in the revision history.) – Federico Poloni Jun 01 '21 at 21:18
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    @FedericoPoloni I feel strongly that everybody should be able to share with the community on this topic. For example, after I became aware of Joel Rosenfeld's video about SpatialChat (I learned about it in the reddit post of AngelTC), I contacted Joel by email, told him that I really liked what I had learned in his video, and asked him whether he'd be willing to post an answer to my post describing his experience. His answer: "I tried to post an answer to the thread, but I guess I’m not active enough". Someone had protected the question, thus preventing him from sharing his experience... :-/ – André Henriques Jun 01 '21 at 22:11

10 Answers10

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Online seminars

Research (and other) seminars have gone virtual. The obvious advantage is, that anyone can attend from basically all over the world. The page https://researchseminars.org/ compiles a huge list of talks and you may visit some mathematical talk basically all around the clock. A further advantage is that no travelling is involved, so speakers are much more flexible. Moreover, the virtual format makes it very simple to record the talk and make it available afterwards.

Among the disadvantages is the missing personal contact and possibilities for one-on-one discussion. Also, virtual seminars do not serve as meeting points for groups and departments as much as classical seminars do.

The additional ability to have public and private chats during the talk is at least different to classical talks, but I am not sure if chats provide an advantage or disadvantage.

My personal conclusion is, that virtual seminars are here to stay, but that classical seminars will come back as well and both are going to exist in parallel.

Dirk
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    And now everyone is using Zoom which appeared out of nowhere and originally had very bad security issues. – Joseph Van Name May 28 '21 at 09:40
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    Well, I don't (most of the time…). Our university provides self-hosted BigBlueButton conference rooms which I find very nice (tbh, superior to Zoom…). But in general, I wanted to keep technology out of the answer - it changes fast and I expect that technical solutions will be quite different in a few years from now. – Dirk May 28 '21 at 10:16
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    So what will happen? Probably everyone will ensure that their seminar rooms have good cameras and microphones and (perhaps multiple) projectors. All seminars will be streamed and recorded. Live audiences will be smaller but nonzero. Virtual audiences for the best seminars will be larger. Speakers will be invited to visit in person; some will choose to do that, but others will present by video, which will be projected in the seminar room. Very few people will travel to seminars that are not at their home institution. Travel budgets will be partly redirected to equipment. Anything else? – Neil Strickland May 28 '21 at 10:16
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    @NeilStrickland, maybe it's a function of the institution at which you work, but this seems like a very rosy view to me. At least where I am, I feel that the tendency was to stick with in-person-like ways of doing things even when given the opportunity to try to find advantages to working online, and the current push seems to be to forget our online adventures as soon as possible, rather than to mine them for any guidance they might offer. – LSpice May 28 '21 at 15:54
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    (Which is a shame, because our travel budgets never were big and will now be smaller, and it would be great to be able to get some world-class seminar speakers whose travel we can't subsidise. I do feel that the math department has been more open than some to exploring changes, so maybe my pessimistic view can be tempered by restricting it to my department.) – LSpice May 28 '21 at 15:56
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    @LSpice I'd be interested to see the distribution of attitudes in different institutions. Certainly in my university there is a strong push from the Vice-Chancellor etc that we should learn as many new lessons as possible and "not let a good crisis go to waste". – Neil Strickland May 28 '21 at 16:04
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    I hope virtual seminars continue alongside traditional seminars when this is all over (although I am not a huge fan of Zoom). – Hollis Williams May 28 '21 at 20:02
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    @NeilStrickland Archaeology – Yemon Choi May 30 '21 at 14:54
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    @NeilStrickland I actually don't think that the travel budget will be impacted that much. A lot of the equipment is already there. I haven't seen a lecture hall or seminar room without at least one projector in years and a lot of people will at least have tried to redirect their unused 2020 travel budget towards buying a camera and a microphone, which aren't as expensive as they used to be anyway. There will be some extra work involved, but I expect this to be just pushed on someone without a change in budget. The only real cost I can see is paying for streaming software and recording storage. – mlk May 31 '21 at 09:07
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Here's something almost trivial:

Writing on a tablet instead of a piece of paper

I think many mathematicians probably acquired a tablet (e.g. something with its own screen like an iPad, or the kind without a screen that plugs into your computer like a Wacom - forgive me for using brand names here) for the first time as a result of the pandemic, in order to simulate the 'chalkboard' teaching experience online.

Now, many of us have the opportunity to continue writing our not-fully-formed mathematical thoughts on a tablet, as opposed to say on a physical notebook that we were using before.

There are pluses and minuses. The pluses are that it's nice to have a systemic and organized record on your computer of various mathematical thoughts you've been exploring, and it's easier to edit notes on the computer. The one big minus I can think of is that I still find it slightly slower to write on a tablet than with a pen and paper.

Sam Hopkins
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  • I still cannot write quickly and tidily on a tablet. I was much happier with paper and a visualiser, though I had to write extra software to get the visualiser snapshots on the web in semi-real time and organise them in a structured way. – Neil Strickland May 28 '21 at 15:48
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    For me a related change has been learning to make do with pdfs rather than printouts of papers, which after the adjustment period has definitely been a net positive, even ignoring paper waste. – Pulcinella May 28 '21 at 21:15
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    The latest generation of tablets and styluses (e.g., the iPad Pro + Apple Pencil 2 or the reMarkable 2) really are very good, to the point that someone used to writing with a fountain pen on paper can adjust with surprisingly little frustration. – Branimir Ćaćić May 30 '21 at 13:23
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    Yep, this did force me to learn to write on a tablet, and now, reviewing papers / grading is much more convenient. – Per Alexandersson May 31 '21 at 07:55
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    @NeilStrickland look into matte screen protectors. The bellemond made a world of difference for me. – Andrea May 31 '21 at 12:14
  • I also started to use a tablet at the beginning of the pandemic. One of the stated benefits is that it allows to store handwritten notes without a massive accumulation of papers. I found out that this is a red herring, though. During last year I tended to store everything, even the more unintelligible jottings, and now I have a big mass of electronic junk which is next to useless. I switched back to take notes in Latex. – Giuseppe Negro Jun 07 '21 at 19:36
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Professional cheating

For me the biggest change in dealing with the pandemic professionally was organized and professional cheating. Of course cheating is nothing new but when I first started in this businesses my impression was that a few bad apples cheated and I could usually detect it because some student had an incredibly silly incoherent answer that is copied word for word by a student sitting next to them.

Over the years it became clear that students could get their homework answered by finding solution keys or by question and answer sites and so I started making homework only worth a token amount of points.

But I honestly had been unaware of the truly professional cheating opportunities now available until online testing began during the pandemic without proctoring. I was also shocked by the percentage of students willing to cheat given the opportunity to do so. All my exam questions would appear and be answered during the exam on sites like Chegg, Course Hero and Slader. A student just has to send a photo of their exam question and they get a photo of a complete solution back in 5-40 minutes. While the solutions are not always correct they are semi-professional. Also I discovered students used group chats like Discord and Whatsapp to share their answers, either obtained from the above websites or via a divide and conquer scheme. In one of my exams a student I caught cheating informed me that 90% of my students were cheating on Discord often with fake names so they could not be identified. This matches 90% of students using an answer identical to Chegg using a different method than we did in class or in the book. Most students register for these sites with fake names and emails or use somebody else's account so even launching an investigation with the site is not very effective at catching people. On timed exams where students got the questions in random order and could not return to a question I found students took 50 minutes to answer the first question and once the solutions became available on Chegg answered the remaining questions in no time flat.

While in person exams will resolve some of this, I now will have to carefully check students do not have phones when they go for bathroom breaks or disallow them and I don't think I will give take-home exams again.

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    This resonates with me, for reasons I am not sure I am "allowed" to mention but to some extent I wonder if the pandemic merely crystallized a longer-term trend: increasingly students believe that the point of assessment is "pass to the next level of the game" and that the definition of understanding is "knowing how to look up online how to do it" (these are not specific to mathematics education) – Yemon Choi May 30 '21 at 15:01
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    Note that the last point is a defensible approach to getting things done in life; I've recently had to hack together a shell script to automate some Moodle->human conversion for exam marking workflow, and needless to say I cut+pasted+tweaked various selected things found on online forums and stackexchanges. So how can we convince our UG students, rather than coerce them, that they should be taking a different approach to the work that we assign? – Yemon Choi May 30 '21 at 15:04
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    @YemonChoi, what bothers me is not so much looking something up on Wikipedia. Even MSE usually requires the asker to engage with the answerer and understand something and requires typing the question of you hope to he an answer. But Chegg and it's compatriots that give immediate answers to obvious exam questions (sometimes it the photo the student sends clearly states the time remaining and that they cannot return to the question) and the immediate sharing of answers between students on group chats really irks me. I honestly felt bad for students who did badly honestly. – Benjamin Steinberg May 30 '21 at 15:23
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    When I taught a fully online class last fall, I noticed that some of my students were posting my exam questions to Chegg etc. as well. It made a bad year feel even worse. I don't know of any good solution. – Donu Arapura May 30 '21 at 16:23
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    In the long term, sites like Chegg will be self-correcting, like any other predator-prey situation. If there are no students who actually understand what they have been taught, there will be nobody to provide the answers for the cheats :) – alephzero May 30 '21 at 19:12
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    Well, there certainly still are some (indeed many!) students who have great academic merit and fully master the material in their courses. If even 5% of students achieve good understanding, this will easily be enough to staff chegg and the like. A single chegg post requires only one answer, but can help hundreds of students cheat. – diracdeltafunk May 30 '21 at 20:42
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    Maybe cheating is notably harder in a face-to-face oral examination by camera, where one sees the student, and they don't have time to send the question to some cheating site and to wait for the answer? (Of course for courses with many students, the workload for giving such exam may be prohibitively high.) – Stefan Kohl May 30 '21 at 20:44
  • @StefanKohl, yes this is a problem for a large course. Also in the US where I teach there isn't much of a tradition for oral exams – Benjamin Steinberg May 30 '21 at 22:37
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    It's not just universities any more that Chegg is giving trouble now. – darij grinberg May 31 '21 at 08:23
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Automated assessment

In Sheffield we have increased our use of online automated assessment. We used to use a home-grown system, but have now switched to STACK with some home-grown extensions. Various other systems are available (e.g. WebWork, Numbas) but in my opinion STACK is significantly more intelligent and more able to give meaningful feedback to students based on detailed analysis of mathematical properties of their answers (provided that you put in the work to code that analysis). While the use of such systems is certainly not new, I am aware of a number of places that have significantly increased their engagement in the last year, and my guess is that the momentum will be sustained.

We have a large dataset from the last academic year consisting answers provided by students, feedback given in response, and answers modified in the light of that feedback. I am hoping to do some extensive analysis of this dataset over the summer, and it will be interesting to see what we can learn.

We have also made some initial attempts to assess and provide feedback on student attempts to write proofs. In most cases we provide a pool of phrases, from which they can select a subset and arrange them in appropriate order. I hope to do this much more extensively next year.

(In terms of social justice etc, I also helped a friend at the University of Nairobi to set up STACK there. It's easy to become blasé about working on a server in Kenya by ssh from the UK, but it is quite astonishing when you think about it.)

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Prerecorded lectures

Many universities have been forced to give their lectures online. Some students seem to prefer physical lectures, and some online lectures.

Overwhelmingly the biggest (potential) long-term advantage is that there now exist entire degrees' worth of prerecorded lectures, many times over. This has the possibility to give a meteoric rise to the scale of maths accessibility and outreach.

However, as far as I can tell most of these lectures are currently sitting behind university login pages, and I suspect that the main reason is basically institutional inertia/a prisoners' dilemma situation. If a few universities' lecture recordings were released, this would probably make others less reticent to release theirs, and cause a culture shift. Note that the same thing happened a while ago with lecture notes.

Needless to say if nothing happens and the recordings are just deleted in a couple of years, it will have been a collosal missed opportunity.

Pulcinella
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    I think that a lot of professors are hesitant to release COVID-19 lecture videos simply because they were put together in an unexpected pandemic crunch, so they aren't up to the standards that the professor feels comfortable having the general public viewing and judging them. Many of us had never recorded, let alone edited, a video a year ago. – Nathaniel Johnston May 28 '21 at 14:30
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    Of course, but I feel like the conclusion is the same, except that professors should naturally be allowed to opt out. In Europe there have been 4 or 5 semesters of lockdown by now, so I imagine that a fair number would be happy with the quality of their more recent courses. – Pulcinella May 28 '21 at 17:11
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    By my count it's the third online semester. On a different note, I have all my (live) lectures freely available online even though they contain errors and glitches. Everybody knows under what circumstances they have been produced... – Dirk May 28 '21 at 18:37
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    "biggest (potential) long-term advantage" from the viewpoint of the administration and students. From faculty's viewpoint, I've created my replacement. Even if I'm kept around for research and teaching new/non-recorded classes, there is a big loss of leverage. – Hasse1987 May 28 '21 at 21:15
  • A disadvantage of prerecorded lectures, from a teaching standpoint, is that human time teaching, can often be reduced. The lectures are there, supervision time exists for questions. That may change the pressures on teacher numbers, or the split between teaching and other work time. – Stilez May 30 '21 at 18:28
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    Another reason for them to be not published publically is that it can incur significant cost to make such lectures ADA compliant. I believe some number of years ago Berkeley pulled freely available online lectures for this reason. I am of course not trying to bad mouth the ADA, just saying that making the lectures freely available is not as simple as removing a password from some page. – Mark Schultz-Wu May 30 '21 at 22:20
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I am not a mathematics professional or a student, but rather a lay person with a great interest in math. Personally, my available time to consume mathematics literature, lectures, and video content has increased. I suspect this is true for millions of lay mathematicians. If true, that could lead to:

  • An increased interest in the field
  • More math content consumed, which could lead to
  • More advertising dollars spent on math content, which could ultimately bring
  • More funding into the field

And increased funding can change any field.

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Flexible work hours

With a physical workplace, and commuting, work hours are standardized. Now, my work hours are divided into two blocks, one block in the evening after kids are asleep. This allows me to be more flexible when it comes to collaboration with different time zones.

Starting collaborations with people far away is now less of a mental hurdle (this last month, I have discussed research with people from at least 5 different countries on three different continents).

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Lightboard

I build a lightboard at home last summer in order to give my classes (this was inspired by Ivo Vekemans - here's an example of him lecturing). I recorded three whole classes so far, and a bunch of seminar talks. Here's a talk of mine. Overall, I'm very happy with the setup.

Advantage: The result is really beautiful to watch.

Disadvantages: The lightboard + recording equipment uses up a whole room in my house. Also, it's a bit time-consuming to clean the board (if you don't clean it well, it leaves lots of shiny smudges). This makes it essentially impossible to give live talks on it.

This youtube video compares two different types of markers for lightboards, including how they erase. (Btw, to erase, just use a dry cotton cloth – certainly no window-cleaning products.)

  • Looks awesome! Sorry for the stupid question, but does this mean you have to write everything mirrored when recording? Or do you just mirror the recording in the edit? – Martin Brandenburg May 31 '21 at 13:50
  • @MartinBrandenburg. The software does the reflection for me. But some people use a physical mirror to do the reflection. – André Henriques May 31 '21 at 15:30
  • I bought a Vileda WindoMatic Power Window Vacuum Cleaner. That works quite well to clean the board quickly and effectively - you can use a wet cloth and be quite generous with water and then suck it up with the vacuum cleaner. It doesn't take much longer than cleaning a blackboard in the ordinary way. – Neil Strickland Jun 01 '21 at 08:27
  • Hi André, glad to see you've been able to add this answer after all! The videos are great, and this technique (which I hadn't seen before) is certainly worth popularization – Jules Lamers Jun 04 '21 at 05:59
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Lives of undergrads

There's an interesting discussion here which provides some insights into the issues faced by math undergrads: https://old.reddit.com/r/math/comments/nnc1v3/changes_forced_by_the_pandemic/

Here are a couple of excerpts which I found interesting:

For reasons I can't fathom, it was decided that the content should go in pre-recorded lectures the students would have to watch on their own time, but that there would still be the same number of contact hours, which would be given over to either examples, going over the lecture notes that were published and which we were told to read, or just repeating the exact same content as in the videos. This has killed me.

And here's another one:

"The material in the exams will be similar to other years and should only take the participant 3 hours to complete" This is what we were told in our 24 hours exams (last year we had 48 hour exams for exceptionally easy exams). What the board of examiners managed to produce this year is unfathomable. Almost every student in every department ended up taking at a Minimum 18 hours if not more and some even spent the whole 23-24 hours to complete these exams. [...] we had questions never before seen, and extraordinaryily difficult some taking up to 5 pages to write up. Not only did we have to answer these tough questions but we had to make sure it was all neat as well since we had 24 hours so sloppy presentation would not have been acceptable. I was up for hours at end grasping at straws. Out of 500 student who talk a pole 80% spent over 16hours.

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    Speaking as someone from the opposite end: 1) the wonderful nature of UKHE means that, erm, the university gets to dictate how you teach and examine 2) in that second excerpt it is claimed that "It would have been impossible to finish that exam in 3 hours even for the lecturers" – Yemon Choi May 30 '21 at 14:34
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Interactive virtual poster sessions

In this video, Joel Rosenfeld conpares his experience at two different online conferences.

► He describes the fist conference as disappointing because he wasn't able to establish any of the connections that he had hoped to be able to establish through the workshop. In his words:

Speakers come, give their talk, and then "poof", they're gone.

► He then proceeds to discuss another online conference that he attended, with special attention to a certain poster session that was organised in a particularly creative way. He calls it "that spatial chat thing" (I don't know the official name). It's really hard to describe the setup using words, so I won't describe it here${}^\dagger$ and thus force you to you watch Joel Rosenfeld's video. He says:

I initially thought that this virtual setting was absolutely ludicrous.

But later, he says:

It turned out to be a lot closer to a regular poster session than I had anticipated. Being able to isolate yourself from the rest of the room and talk to somebody made a huge difference as far as having one-on-one conversations.

And finally:

Honestly, it was surprisingly effective. [...] At first, I thought this was a circus. [...] It was better than most of the other conferences I've been to. [...] This added a whole degree of interactivity and engagement that I didn't really think was going to be possible.


${}^\dagger$If someone could edit my answer to include the official name of "that spatial chat thing", it would be great.
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    I guess the official name is actually SpatialChat, at least that website seems to have a product very much like what he describes. Another somewhat similar concept is gather.town. – Martin Hairer May 31 '21 at 17:31
  • @MartinHairer Haha! That's funny :) Thanks for the clarification. – André Henriques May 31 '21 at 18:34
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    In the last year or so I have participated in online meetings that used gather.town and wonder.me . I expect there will be other 'spatial chat things' beyond these too. (Of course it's not the same as face to face mingling, but I think it's still much better than the first type of conference mentioned.) – Jules Lamers Jun 04 '21 at 06:07