Explaining mathematics

So I set up all my equipment ready for my tutorial at 11AM last Thursday. We started our Microsoft Teams meeting, I shared my Main Display (Display 1) with a blank DrawBoard PDF document open and copies (screenshots) of the tutorial questions open in a picture viewer. Then I attempted to start an Echo360 recording, and my tablet refused to cooperate!

[Note to self: make sure to restart the tablet in the morning. It sometimes helps!]

There was rather a lot running on my Windows Surface. I always make sure that it is running on mains power (which helps with the processing power), but it was still clearly struggling. The mouse pointer was starting to wander around randomly without me doing anything. When I did manage to get the mouse pointer over the Echo360 record button, it didn’t seem interested when I clicked. Eventually it did respond, and started a partially visible but fragmented visible countdown, before announcing that it was unable to start the recording. In fact I think it did start one recording, and also attempted to start a few other recordings unsuccessfully.

I started up Task Manager (which probably added a bit more to the tablet’s burden), and this confirmed that I had too much running. So I quit a few applications (Echo360, Adobe Acrobat and Chrome). One of my tutees then set a recording going in Microsoft Teams, and we got on with some maths.

I should probably have restarted the tablet, because it was still struggling. When I was writing or sketching curves/regions in the plane, I kept having to stop and wait for the inking to catch up with my pen. And additional random inking filaments were appearing. Nevertheless, we managed to cover some important stuff. And the recording uploaded to Microsoft Streams quickly and successfully at the end.

I should say that there are other reasons why my tablet sometimes has to stop and think about stuff. For example, if I right click and try to use “open with”, the tablet often hangs while it attempts to check all University of Nottingham applications in order to populate the list it (maybe) eventually offers. I am going to have to try to get out of the habit of right clicking.

I hit another problem when I installed PDF Annotator on the tablet. (This was because I wanted to be able to do a few things that the version of DrawBoard PDF I have can’t do. ) Suddenly I found that double-clicking on PDF files was having no effect! I tried quite a few documents. Their properties showed they were supposed to open with DrawBoard PDF. (I set that as my default on the tablet. That is also rather difficult to do at the moment, for similar reasons to the problems with “open with”!) I will admit that I probably overdid the double-clicking. I then uninstalled DrawBoard PDF and reinstalled it. This was almost certainly unnecessary. I had to find and re-enter the activation code DrawBoard had sent me, and then set up all my favourites again, etc..

At some point windows started to open up again and again (10 minutes or so after my spate of double-clicking) asking me whether I wanted to keep using DrawBoard PDF to open this file, or use a different app instead. (In fact the first few of these opened up during the time period when DrawBoard was still uninstalled!) That kept me busy for a while.

I think what happened was that, when I installed PDF Annotator, the tablet decided that I now had some new PDF software. So the next time I double-clicked on a PDF file, it thought it would be a good idea to ask me whether I wanted to continue using DrawBoard PDF to open the file, or another application. But it then had to try to populate the list of available applications, and this took several minutes at least. Anyway, maybe 20 minutes later the last of these windows had opened and closed and things were working again.

OK, so it looked as if recording meetings in Microsoft Teams was the way to go then! Admittedly my first attempt at recording a meeting on 11th March had not given me much confidence. But things appeared to have improved since then…

OK, so next was my 1PM online lecture for my Level 4 module. I set everything up the way I wanted, started the meeting, shared my main display, and started the recording in Teams. Everything seemed to work well, until I checked the recording later. See below!

Soon after my 1PM lecture finished (after grabbing a quick snack) I had an online dissertation supervision meeting with a 4th-year student. It isn’t obvious whether recording project/supervision meetings is necessary: after all, I never used to do that in my office! Still, the students agree that these recordings could be useful, so I’ll try to record them. I also generate PDF files with my annotations, and I make these available to the students too. For this particular meeting, somehow I forgot to start the recording until the middle, but it was still probably better than nothing.

OK, now I had some catching up to do! I distributed the various PDF files I had generated and made sure that the videos had processed on Microsoft Streams. The processing was pretty quick (a big contrast to the long delay I saw back on March 11th). I thought that the students might be more used to accessing videos on Echo360/Moodle, so I downloaded the videos from streams, uploaded them to Echo360.org, and shared them with the relevant students. (Or in the case of the Level 4 Module, I was able to make it available to the students via a link from the Module Moodle page.) However at some point I realised that there was something wrong with one of the recordings. The recordings of the tutorial and the (second half of the) dissertation meeting were both fine. But the recording of the Level 4 Module lecture had gone wrong. Instead of recording the audio and the shared screen where I was annotating a PDF file, Teams had recorded the audio and video of a static screen showing 4 discs containing the initials of the participants at the meeting. The audio may still be useful, in combination with the annotated slides. But the video/screencast showing the annotation happening would be much better!

I assumed that I had done something wrong, and that maybe I should attend a training session. But looking online I found that this was a known issue. See
https://techcommunity.microsoft.com/t5/microsoft-teams/recording-a-team-meeting-screen-share-isn-t-recorded/m-p/227069

The second page of that thread was unavailable (to me at least) yesterday, but it appears to be back today. See
https://techcommunity.microsoft.com/t5/microsoft-teams/recording-a-team-meeting-screen-share-isn-t-recorded/m-p/227069/page/2

I had another lecture at 12 noon yesterday (Friday March 27 2020). I thought it might help if a student started the recording instead of me, but unfortunately that made no difference.

This appears to be an ongoing issue (see continuing discussion and announcements in that thread). However, I have received advice locally that it is best to start the recording BEFORE you share your screen. I have examples showing that it sometimes works if you share the screen first, and some people in the thread above have had problems either way, but it could well be that your chances are improved if you do start the recording before the screen share.

It may also depend on your set-up. For example, I have dual displays: could that contribute to the problem? Does it help if you share a window rather than a display? (Because of my use of Pen Attention as a “digital pointer”, it is better for me to share the screen rather than just the DrawBoard window.)

Anyway, for now it isn’t obvious what I should do. If only everything worked smoothly, recording in Teams should be the way to go. But if the problem persists, I may have to try something else.

[Note added: fortunately Microsoft appear to have fixed this! See
https://explainingmaths.wordpress.com/2020/03/29/microsoft-announce-fix-for-problem-with-recording-screensharing-in-teams/ ]

Well, my living room table is starting to fill up with more and more equipment. There is the surface pro on a stand, the Dock, the second monitor plugged into the Dock, external USB keyboard+mouse+webcam, some old computer speakers, earphones and an old Blue Snowball microphone. (I’ve ordered a new mouse mat …)

I am going to make some test recordings to see which microphone I should use for audio input, since I have quite a few options. I should probably listen to the results on something decent before I decide.

When the audio doesn’t fail completely (as it did for the lecture yesterday), the audio recording can still be distorted if the tablet can’t cope with the demands placed on it. I think that it may be at its limits when I’m recording audio and video with Echo360 at the same time as running a Microsoft Teams meeting, annotating a PDF file using DrawBoard PDF, keeping an eye on Student Confidence using my Google Form (and having lots of equipment attached!). I think I’d better keep an eye on this using Task Manager. It is probably just as well that I’m not recording two simultaneous video streams (for now!).

Perhaps if I allow Microsoft Teams to record the meeting, instead of Echo360, that will help. I had some problems with this before, but maybe I should give it another try.

I recorded two sessions/live meetings today: an undergraduate project supervision meeting, and a lecture. I remembered today that I wanted to use the webcam for audio input, and set that up successfully.

The first meeting and recording were fine, but I hit problems with the second meeting and recording. The students said that they couldn’t hear me. So I switched the audio input on Microsoft Teams back to my tablet microphone, and then they could hear me. But I was using Echo360 for the recording, and I didn’t switch the audio input there. That was a mistake! I think from now on I’ll make sure that Teams and Echo360 are sharing the same audio input, so the students can warn me if there is an issue. The audio on that recording is very strange: just a lot of squeaking and other weird noises.

There was also a problem with connectivity. Teams flashed up some messages to say that my internet connection was slow and so the call would be low quality. Of course the whole family is sharing the broadband connection, and we have some significant backup-to-cloud uploads running on various machines (perhaps I should try to make sure these are paused when I am teaching). I’m not sure whether there was any connection with the other problem though.

I have now rearranged things a bit so that the less demanding USB devices are plugged into the USB ports in my Dock (for my Surface Pro), while the USB webcam is now plugged directly into the USB port on the Surface Pro itself. I would still prefer to use the audio input from the external webcam if possible, to avoid the issue of recording/broadcasting loud tapping and scratching of the tablet pen. I’ll make a couple of test recordings to see how the equipment is behaving.

I now have a USB keyboard plugged into the Dock, rather than using the standard Surface Pro keyboard. This gives me more options when it comes to the physical setup I use for annotating PDF files on my Surface Pro using DrawBoard PDF. My table is getting a bit crowded now though!

Amazingly, after all this time, before today I had never used multiple screens to have an extended monitor!

I got a few things wrong at first, which I don’t fully understand yet. For a while I couldn’t get the mouse pointer from one display to the other! This was, I think, a combination of the display arrangement and the choice of “main display” in the display settings. Once it is all working, it is fine! Currently I have the external monitor (Display 2) to the left of the tablet screen (main screen, Display 1), and I have the screens aligned vertically in the middle, so I can’t get from one screen to the other if I am too high or low on the “taller” display. I may rearrange this to fit more closely with the actual physical relationship between the two screens.

OK, so that’s all working. My next task was to see how this plays with Teams and Echo360. I’m rather pleased to see that Echo360 is happy to record both displays as separate streams. That could possibly be quite useful, though it isn’t currently my top priority.

In Teams, I can now share Display 1, where I will annotate the PDF files, while having separate Teams windows etc. open on Display 2. This should allow me to see my students’ faces during the class, without recording their faces in the video. I can also have the chat window open on Display 2. But I probably need a different keyboard, because I can’t annotate properly on my Windows Surface while the standard keyboard is attached to it. (Of course I could continue to use a second computer and/or my mobile phone.)

I am not sure whether my Student Confidence Google Form is still necessary, but I’ll keep it going for now.

At the moment I haven’t found a way to see my students’ faces while I am sharing my screen with them in Microsoft Teams. So I thought I should look for a simple app that would allow students to indicate, in real time, how confident/confused they were feeling about the material currently under discussion. I would see the summary, and should be able to tell if something needs further explanation, even if no-one says anything aloud or in the text chat window.

Well, I haven’t yet found the right app, so I’ve gone back to Google Forms. You can see a copy of the form I am using at

https://forms.gle/WNW2UpjvEpB5JSR9A

It’s just a very simple scale 1-10 question, with 1 being very confused and 10 meaning very confident. When students submit a response they are invited to go back and edit their response (rather than submit a new response).

This does appear to work in my small Level 4 class, and I was pleased to see confidence levels rise when I provided additional explanation! (On the other hand, students in that class are anyway willing to speak when they have a question.)

I’d still like to be able to see their faces though! So either I have to get better at using Teams, or I should maybe use some other software.

In my recent online classes I have been using (simultaneously) a Windows Surface with an external USB webcam attached, another computer, and my mobile phone. This does at least allow me to see the chat window on one computer while annotating full screen on the Windows Surface (and sharing the screen in Teams and recording a screencast using Echo360) and keeping an eye on the students’ confidence levels on my phone. But so far I haven’t managed to combine this with seeing my students’ faces.

I’m going to see if attaching an extra monitor to my Windows surface provides some more options.

As I mentioned in a previous post, in my teaching I am currently using DrawBoard PDF on a Windows surface to annotate PDF slides with gaps .

My first Windows Surface had DrawBoard PDF included with it. But later generations of Surfaces don’t, and the free trial only lasts 3 days.

The School of Mathematical Sciences (University of Nottingham) purchased a batch of DrawBoard licenses for various members of the School, using their work Microsoft Store accounts, but there were a few issues getting these licenses to work. By the time I started trying to install it (on my new Surface), there was a local troubleshooting guide (thanks Dave!), a link to DrawBoard’s guidance, and a suggestion to contact DrawBoard support if all else fails. Apparently some colleagues had succeeded, but others had given up and purchased the app using a personal Microsoft Store account. (It isn’t very expensive, and there isn’t any hassle that way.)

One of the first steps in the troubleshooting guide is to make sure that you log in to the Microsoft Store using your Work account (given that the license was purchased for your Work account) and not a Personal account. Now I don’t know if it is just me, but I simply could not work out how to log in using my Work account for ages! The instructions I found online all said (when in the Microsoft Store) to click the user icon (top right) and select “Sign in”. When I tried this, it said that there was no account associated with my (work) email address, and would I like to create one? So I tried to create one, and it told me I couldn’t create an account with that email address, because it was a work email address.

I tried this several times, because I couldn’t see what else to do. I began to think that I didn’t and/or couldn’t have a Microsoft Store account associated with my work email. But, by chance, one time when I clicked on the user icon, I spotted that underneath “Sign in” it offered “Add work or school account”. I clicked that, and suddenly I was able to sign in using my work email! (If you start off signed in to a work account, then under “Sign in” it offers “Add personal account” instead.)

I thought that I was home and dry now! I downloaded DrawBoard PDF using my Work Microsoft Store account … but all I got was the three-day free trial, and when this expired I was stuck again.

I followed all the online troubleshooting advice available, but nothing worked. So I finally contacted DrawBoard support, telling them when my license was purchased and for which (work email) Microsoft Store account. They were very helpful. They knew that the usual troubleshooting steps wouldn’t solve the problem (“Unfortunately the steps you took will not fix this, as it is a Microsoft Business Store issue …”), and sent me an activation key to use. 

All is now well! But if I consider the amount of time I spent on this and the price I would have paid to purchase the app myself using a personal account, I don’t think it was the best use of my resources. Unless, of course, this post helps others who have similar problems?

I have a very small Level 4 class, Further Topics in Analysis (FTA), with just 5 students registered. As with all my modules these days, I have been teaching the module using a Windows Surface and DrawBoard PDF to annotate PDF slides with gaps.

I decided that today would be my first attempt at remote, online, live teaching of this module.

Earlier in the day, I had a short test meeting on Microsoft Teams with David Hodge. This gave me a chance to practise sharing my screen or my DrawBoard PDF window during a meeting. There were some problems with my webcam video stream: it was permanently on, but didn’t say so. (The button always said “Turn video on”, but David could see me whatever I did. Be warned!)

I also recorded about four minutes of the meeting using the Teams record meeting button. After the meeting it took a VERY long time before this recording became available on Microsoft Streams. So I decided that this was not the way to go.

Meanwhile, I had set up a team with the five FTA students in it. I contacted the students to say that I would have a test meeting in the hour before the real lecture. That gave me a chance to iron out a few more wrinkles. Then we started the “real” lecture at 3PM. Four of the five registered students joined the meeting.

I was able to use DrawBoard PDF in the usual way to annotate a PDF file which they could see. I had to choose whether to share my whole screen, or just the DrawBoard window. Because I use a digital pointer (PenAttention), in order for the mouse pointer highlighting (red blob) to be visible to the students, I decided to share my whole screen.

I used Echo360 Universal Capture – Personal to record the class.

Now, when I am annotating slides on a tablet, I don’t like to use the tablet’s camera and microphone. The microphone records loud tapping etc. from the tablet pen, and the video from the camera is quite scary! So I needed to attach a USB webcam. I also have a USB mouse attached because it makes a few things easier. But these surfaces only have one USB port. Fortunately I have a Dock for my surface, and that provides a couple of extra USB ports. Otherwise I suppose I would have needed to plug in a USB hub.

Teams and Echo360 were happy to share the audio stream from the USB webcam. But they couldn’t share the video stream. I decided to let Teams have the video stream, and not to bother recording a separate stream dedicated to showing footage of myself today. (In theory I could probably plug in a second USB webcam? But that seems over the top!)

Everything went relatively smoothly, but I found it felt rather strange not to be able to make eye contact with the students. They could see and hear me, and see me annotating my PDF file and using my digital pointer. I could hear them, and we also had a chat window for text chatting (though my windows tended to get in the way of each other a bit). But I couldn’t see them. In theory I could, if they turned their cameras on, but even then when I was annotating my PDF file I wouldn’t have been able to see them. Maybe what I need is a second screen (I don’t know how that fits with Echo360), or perhaps I could log in a second time on my desktop PC and see the students there.

Usually with such a small class, there are lots of easy ways to get some idea of how well they are engaging with and following the material. Today I felt cut off from a lot of the things I would usually be able to do.

I could try different software. What have other people been using? Can you get a more interactive experience?

With a bigger class, I would be using mobile phone voting on multiple choice questions, so I could interact that way. Perhaps I should set something up so that students could keep me informed of their levels of puzzlement as we go. (David Hodge showed me Jitsi Meet, and I could maybe try that.)

Anyway, the class seemed to go OK, and the recording worked fine. (I must remember to turn off Windows Mail notifications before the next class!) But I still think that some things could be better. Next class will be Thursday afternoon. I also have a first-year Group Tutorial (6 students) on Thursday morning. Tomorrow I’ll have a play with various bits of software/mobile apps.

Oh yes, the Surface did struggle to cope with all the software that was open. I can tell when this happens, because you suddenly get unexpected straight lines appearing between two recent places the pen was on the screen. In the past this problem only happened if I wasn’t plugged into mains power. But today the surface was plugged in, and the machine was still struggling. It may be just as well that I didn’t try to record another video stream!

The University of Nottingham is moving to online teaching only (as soon as possible, and from 23rd March at the latest).

Of course, I have complete sets of recordings of my lectures available through various channels. But I haven’t yet tried online-only live teaching. So this afternoon’s class on Further Topics in Analysis will be my first attempt. This is a level 4 module with relatively few students, so it looks like I will be able to use a Team (as in Microsoft Teams). I’ll write about my experiences on this Blog.

At this time of crisis, I would like to wish everyone all the best. Take care of yourselves and those around you.

Best wishes,

Joel Feinstein

Tomorrow I’ll be in Nottingham Central Library with colleagues/postgrads from maths, contributing to the Nottingham Festival of Science and Curiosity.

(See https://nottsfosac.co.uk/)

We’ll have a set of mathematical exhibits, (toys/games/puzzles), and our activity is called Marvellous Mathematics.

There are several other teams from maths contributing various activities at various venues (including Victoria Centre Market).

There’s lots going on, so why not have a look?

 

I have been asked on YouTube about the reading list for my old module G14FUN Functional Analysis. It looks like that is not included in the materials available on UNoW at https://rdmc.nottingham.ac.uk/handle/internal/257 so what I’ll do is I’ll quote the reading list here. To be precise, this is my current reading list for the module Further Topics in Analysis, but the syllabus is very similar. (The main difference is that Further Topics in Analysis includes some material on measure theory, and a slight reduction in the functional analysis content).

Books

The following books are all well worth looking at. Although no single book is ideal for the module, the book of Allan is probably the closest for the material on functional analysis (although the more advanced material in that book goes well beyond the scope of this module). Indeed, I first learned most of the material in this module from the lectures of Allan (on which his book is based). The books by Jameson and Bollobás and Rudin’s book on Real and Complex Analysis are also highly recommended.  In particular, the early chapters of the latter book are a very good source for the material on measure theory in this module.

• Allan, Graham R. (Prepared for publication by H. Garth Dales). Introduction to Banach Spaces and Algebras. Oxford Graduate Texts in Mathematics, 2011.
• Bollobás, Béla. Linear analysis : an introductory course / Béla Bollobás, 2nd ed. Cambridge University Press, 1999.
• Halmos, Paul R. Finite-dimensional vector spaces / Paul R. Halmos, 2nd ed. Springer, 1987.
• Jameson, G. J. O. Topology and normed spaces / G. J. O. Jameson. Chapman and Hall, 1974.
• Pedersen, Gert K. Analysis now / Gert K. Pedersen. Springer, 1989.
• Rudin, Walter. Functional analysis / Walter Rudin, 2nd ed. McGraw-Hill, 1991.
• Rudin, Walter. Real and complex analysis / Walter Rudin, 3rd ed. McGraw-Hill, 1987.
• Simmons, George Finlay. Introduction to topology and modern analysis / George Finlay Simmons. Krieger, 2003.

 

From seeing my children’s school work, it looks as if GCSE maths in the UK uses what looks to me to be confusing notation for composite functions. Essentially they write where I would write . For an example, see the BBC web page

https://www.bbc.com/bitesize/guides/z36vcj6/revision/6

To be precise, they write things like .

Surely this can cause confusion with the pointwise product function given by ?

I suppose that might look weird and frightening?

I sometimes run a session for school children (typically aged 10-12) about the grains of rice on a chessboard, and the Tower of Hanoi puzzle. Here powers of two are relevant, but I wanted a child-friendly name for these numbers, so I have been calling them “doubling numbers”.  At the end of the session I have provided a sheet with the first 65 doubling numbers (starting from 1). But I’m no longer entirely happy with calling them “doubling numbers”.

I don’t want to call them powers of two unless I have to. But “numbers you get by starting from 1 and doubling again and again” is a bit unwieldy.

Maybe I will stick to “powers of two” in the end.