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A math lecture typically works with the professor explaining something, and at the same time writing her theorems on the blackboard, without any Powerpoint slides. When the blackboard is full, its contents are quite close to what should be in the lecture notes.

I think this has advantages over Powerpoint slides, besides being easier to prepare: One blackboard may contain 45 minutes of information, and a reader may look at all the previous information at their own leisure during the talk if they forgot something (or decided they want to prioritize understanding a certain part of the lecture).

How can I approximate this experience in an online lecture? Ideally, I imagine something like this:

  • The audience opens a link to something that looks like a PDF/Word document
  • While I hold the talk, I click my mouse and this makes the next (prepared) sentence appear in real-time for my audience and me,
  • In the end, when everything is revealed, those are the talk's lecture notes.
  • I may still point to certain places of the already-revealed lecture notes during the talk.

Is there a tool that allows for something like this? The best I can think of is using Google Docs and copy-paste, or similar.

(Update: The talk was held to a group of academic quantum information theory researchers [I had actually misunderstood who the audience would be], and the subject was some research of mine related to that subject. I was interested in functionality that would allow me to approximate the experience of a person writing on a blackboard --- either involving writing live, or clicking to make new statements appear.)

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  • Welcome to Academia StackExchange! Could you be a bit more specific about the intended audience and the setting of the lecture? Maybe you could also briefly point out your background? (Many mathematicians use the LaTeX beamer class for the purpose that you describe, but you seem to be unfamiliar with it - so it might help to briefly mention your background.) Feb 27, 2023 at 12:32
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    Hello, and thanks for the welcome! The intended audience is a group of academic/mathematically-sided ML researchers, the setting is an informal seminar talk in which I will present parts of arxiv.org/abs/2212.04606 (not using LaTeX for it was a mistake that is in the process by being corrected) and hopefully have a discussion about whether it can be pushed further. Feb 27, 2023 at 12:42
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    In contrast, I want to "present lecture notes", such that the audience is able to scroll through all of the previously explained things at their own pace during the lecture --- just like a student in a math lecture would be able to look anywhere they like on the blackboard, not just at the things written down in the last few minutes. Feb 27, 2023 at 12:48
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12 Answers 12

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Alright, you might not like this.

The question "How can make the experience of an online talk similar to the experience of a blackboard talk on-site" has the same answer as the question "How can I make streaming a movie online similar to the experience of watching a play in the theatre?":

You simply can't.

A movie is not a play and a screen is not a theatre stage. Both media have their advantages and pecularities, but they are too different to replicate the typical movie streaming experience on a theatre stage or vice versa. Same for an online talk and a blackboard talk.

(You might be able to rescue some of the blackboard spirit if you just give a blackboard talk and stream it via a camera and a microphone. But it will still not be the same experience, and it only works at a reasonable level of quality with the right setting and equipment, which you might or might not have available.)

You say you like blackboard talks (so do I), so let's see what makes this medium so well-suited for math talks; we can check for each point to which extent it can be replicated online. A (probably non-exhaustive) list of relevant points is:

  • Pacing. Writing things on the blackboard limits the speed at which we can discuss material in a talk. Many people seriously need such a limit (as you can see by checking what they do if they use slides, where no such natural limit exists).

    This can be replicated online by writing by hand on a tablet computer instead of using text that has been written before.

    Alternatively, you can use a medium without such a limit (for instance, slides), but force yourself not to put too much material in it. This is absolutely possible if one is really committed to do so.

  • Temporal synchronisation of speaking and writing. When you write something on the board, you will typically talk about what you are writing right now or about what you have just written.

    Again, this can by replicated online by writing via hand on a tablet.

    It can only partially be replicated by using pre-written text that is revealed piecewise as you give the talk. This solution is imperfect (and requires much more work to prepare, in particular if you want to do it really well, i.e. not only reveal things from left to right and top-to-bottom). It should be noted, though, that some people do not like such overlay mechanisms (link 1, link 2). Some other people though (including myself) get seriously annoyed if such overlay mechanisms are not used (e.g., not using them has typically the consequence that I am, as a member of the audience, unable follow which points the speaker is currently talking about. Using somekind of pointer to resolve this does typically not work well, in my experience.)

  • Geometrical synchronisation of speaking and writing. At a blackboard, the speaker will often be physically close to the written content they are currently speaking about, and increase the distance now and then during some elaboration that is not written on the blackboard. A good and experienced speaker can use the distance to the board to direct the audience' attention and to modulate the "density" of the presentation (e.g., move away from the board and insert a number of less technical sentences now and then in order to give the audience time to relax mentally a bit).

    I see no way to replicate this online.

  • Using gestures and movements to keep the audience engaged. One great things about blackboard talks is that somebody is really moving at the blackboard. Personally, I find myself much more motivated to listen carefully if I see that there is something going on phyiscally and in three dimensions.

    This cannot be replicated online. Putting your camera on during the talk, so that people can at least see you talking, is probably better than nothing, but very far from the experience in a lecture hall or seminar room.

  • Ability to correct a mistake. If you write something on the blackboard that turns out to be wrong, you can easily correct it.

    This can be replicated online be some media, but not by others. Generally speaking, writing things on a tablet computer by hand gives you the opportunity to correct things. Whether pre-written text can be fixed on-the-fly depends on the details of the technical solution that you use.

  • Keeping large parts of the text available during the talk. This is a point that you mention as very important in your question. I'll argue that it actually consists of two important points:

    Availability for the audience: As you say, somebody in the audience can just look at another part of the blackboard to recall what, say, "Assumption 1" was. The main point here is that it typcially takes very little time (and thus distraction) to look this up.

    I claim that this can be replicated online only to a very limited degree. The only thing that you can probably do is, as you have already suggested, to send the entire document to your audience before the talk. I think there are two major caveats, though: (i) Looking something up in those notes will often be more distracting for someone in the audience than it would be one the blackboard (because they might have to scroll through the document, and if they use only one screen, then this will cover the talk itself while they do so.) (ii) I strongly suspect (without having checked empirical evidence for it, though) that people are more easily distracted during online talks anyway, and this adds yet another distraction.

    Availability for the speaker: This refers to the possibility that the speaker can refer back to results, assumptions, properties, formulas, and so on, from previous parts of the talk. At the blackboard this is possible since everything (or much of it) is still there; it is also easier to follow since the speaker can move (phyiscally) to the point of reference and point there also physically, for instance with their hand or a stick (just in case that somebody finds the idea of a stick "old-fashioned": if something is located to high for your arms and you have the choice between using a stick or a laser pointer - please use the stick, it is so much easier to follow than those tiny points of light.)

    I'll argue that - and that's the part that you might not like - it is not possible to replicate this online.

    Going back in slides is, as you have already observed, extremely confusing. If you use slides, don't do it. If you use a longer document - say, one which you write by hand via the talk - and scroll down during the talk, you might try to scroll up to refer to something that you have written earlier. I have done so in the past now and then, but my impression was that it does not work well during lectures for students - and it does not work at all during research talks, since the density of the material is typically much higher there.

    So the situation is from my perspective as simple as that: if you give an online research talk, you are not allowed to go back (no matter which technology or software you use). If, say, "property (a)" is no longer on screen, you are not allowed to refer to it; instead, you have to put it there again (either by writing it by hand again, or by revealing a prepared version of it). This is the only way to ensure that many people in the audience will be able to follow you.

    (In case that this seems like an exaggeration: no, I'm dead serious - Don't go back!)

Bottom line. An online talk is not a blackboard talk, and you won't be able to generate the same experience for your audience.

So rather than trying hard to achieve something which is not possible (with a high risk of messing it up), I suggest to choose an online medium which you think is most suitable for your presonal way to give a talk, and then adjust your talk such that it works well with that particular medium.

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    I like lots of parts of this, but let me suggest something to handle "availability for the audience": Use a tablet to write on an online document, to which you can provide your audience a link so that they can scroll it separately. I like miro.com for this and have given many lectures this way; I know other people who like google jamboards, creating a new board as they fill each one. Feb 28, 2023 at 3:10
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    I do agree with the guidance that you, the speaker, are not allowed to go back and must restate things in place. What I am pointing out is ways to let the audience go back, if they want to check an old point. Feb 28, 2023 at 3:12
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    Regarding the third and fourth point, these two can be replicated by writing on paper and filming that, instead of e.g. using a tablet, as this will put the hand itself in the frame to mark position and gesture at things. To be fair, I have never seen this tried in a live lecture context, as the setup is probably a prone to have technical issues, but there are some math explanation videos on youtube that use this style to great effect.
    – mlk
    Feb 28, 2023 at 7:56
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    @mlk I vaguely remember one of my lecturers in undergrad writing on overhead projector slides instead of using a blackboard, which bears a lot of similarity to that idea, and from what I remember it worked reasonably well
    – llama
    Feb 28, 2023 at 14:45
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    @llama In secondary school we had a couple of teachers do this exclusively, having overhead projectors with rolls of "film" attached that they could scroll up and down. Very neat.
    – arne
    Feb 28, 2023 at 19:20
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A graphics tablet or a tablet computer with a stylus will let you have an approximation of the pace of writing on a board.

It's impossible to display all of the information you would on multiple blackboards legibly because a computer screen that a viewer uses is not large enough. My personal recommendation if you're concerned is to have written notes that you pre-distribute, and then also write your notes again on a tablet during the presentation.

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    You probably have not seen the bad blackboard setting in my lecture halls;)
    – user111388
    Feb 28, 2023 at 7:59
  • @user111388 I'm sympathetic. Went from a room with 6 boards of visibility last semester to 2 this one.
    – user137975
    Feb 28, 2023 at 16:07
  • We also have two - but one is in front of the other, which is totally useless.
    – user111388
    Feb 28, 2023 at 18:56
  • Does not answer the question, cf. the following: "While I hold the talk, I click my mouse and this makes the next (prepared) sentence appear in real-time for my audience and me". The asker does not want to write on a digital blackboard in real time. Mar 1, 2023 at 9:47
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    @FerventHippo (1) I think you need to re-read the question. The asker described that mechanism speculatively. (2) This answer was also a slight frame challenge. The asker wanted an approach that left most of the lecture visible all the time. But this isn't possible to do legibly on a computer screen, from experience.
    – user137975
    Mar 1, 2023 at 12:51
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Your description sounds close to the kind of videos produced by the Khan Academy for teaching students. This video, for example, opens with a prepared view of something (a plot of a function) but then, starting around 18 seconds into the video, the teacher begins to write on the "board".

They are probably using a graphics tablet as the user interface for the pen/pencil style of writing.

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  • Thank you for that link, but my setting is a live lecture, not a prepared YouTube video - so I would like the reader to have access to a larger quantity of information than fits on one screen. I think the solution that I'll probably use is to scan the writeup I have and OCR it as far as it makes sense, share the entire scan with everyone in the beginning, and then just scroll in the notes and share my screen. Feb 27, 2023 at 13:02
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    @DuY: I don't have time right now to right a full answer, but I would strongly recommend not to scroll through a document in order to present a talk. I've seen this a number of times (while I was out in the audience, either onsite or online) and in most cases it turned out to be a really bad experience. Feb 27, 2023 at 13:12
  • Thanks for that hint... If you have time: Were these documents specially prepared for the lecture? I'll be careful that I don't need to "wildly scroll around", but the formatting is so that pressing the "down key' once corresponds to what would be one more bullet point in a slides presentation. I'll maybe try the google docs copy-paste thing then. I would just really like to recreate the writing-on-blackboard experience, I personally don't like slides very much either (being in the audience). Feb 27, 2023 at 13:43
  • You could present a live YouTube video lecture, with annotations on a blackboard or whiteboard, but you would need a production crew and at least two cameras. You'd probably have to practice the presentation with the crew as well. I'm sure this is impractically expensive for you, but there are YouTube channels that do this.
    – Wastrel
    Feb 28, 2023 at 15:24
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It's not mathematics, but I use OneNote for writing my notes on the screen and displaying it.

Screenshot of OneNote for Circuit Analysis

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  • Does not answer the question, cf. the following: "While I hold the talk, I click my mouse and this makes the next (prepared) sentence appear in real-time for my audience and me". The asker does not want to write on a digital blackboard in real time. Mar 1, 2023 at 9:47
  • @FerventHippo The OneNote I use does precisely what the OP asks: approximates the experience of writing on a white board. The “click” can be approximated by simply scrolling to pre-prepared content. But that seems counter to the start of the question.
    – Peter K.
    Mar 2, 2023 at 11:45
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    I did something similar, using Microsoft Whiteboard with a touchscreen laptop and pen. Benefit of this is that other users can join and see/scroll through/save the screen in real time (which OP wanted their students to be able to do)
    – Esther
    Mar 2, 2023 at 14:47
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I find a document camera combined with pen and paper is a good way to create a naturally paced writing experience in an online lecture. It allows you to use any kind of writing tools, such as differently coloured pens, a ruler, etc., and in my opinion tends to look better than most methods for handwriting input to a computer.

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  • Does not answer the question, cf. the following: "While I hold the talk, I click my mouse and this makes the next (prepared) sentence appear in real-time for my audience and me". The asker does not want to write on a digital blackboard in real time. Mar 1, 2023 at 9:47
  • I'd argue it does answer the question in the title about "the online analogue of writing lecture notes on a blackboard". The mouse-click method was given as an example, and in my opinion it would be a rather inadequate replication of the blackboard experience. But people may disagree about that, of course.
    – zrnzvxxy
    Mar 1, 2023 at 13:09
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Tactile tablet with blackboard app

If you have a graphic tablet, there exist apps specifically to emulate a blackboard. These can be linked either to a video-projector, if you ever need to teach in an amphitheater that has a video-projector but no blackboard, or to a video-conference call.

Usually, these apps are designed so that you can "turn the page", which has the same effect as erasing the blackboard, except the previous blackboard is saved, and at the end of the class you have a multiple-page pdf compiling all the blackboards you've filled during the session. You can distribute it to the students.

Jupyter notebook

Prepare a Jupyter notebook before the class. A Jupyter notebook is a document that can be opened into your browser. It consists in a series of cells; each cell can hold either markdown, or latex/mathjax, or python code (or code in some other programming language).

You can prepare the cells in advance, and leave some cells blanks to fill them during the class.

  • The markdown is super useful to have structure, with titles and subtitles, enumerations and bold.
  • The latex is super useful for all the math equations.
  • Both latex and markdown work almost-exactly like on stackexchange, so you will feel at home.
  • You can use pre-written python code to graph functions, plot probability distributions, and a lot of stuff.
  • You can also include pictures.

The reason I like Jupyter notebooks so much for math class is that they give the perfect balance:

  • You can prepare the document in advance;
  • You can edit the document live, in front of the students;
  • At the end of the class the document is available to the students; they don't even need to install Jupyter on their computer, if the server you use can handle Jupyter notebook. Even github handles jupyter notebooks, so you can host the document on your github and the students will be able to read it without installing anything on their computer.

When I prepare the document in advance:

  • At the beginning of the document, I use latex's \newcommand to define shortcut that I know I will need to be able to write latex fast during class, such as $\newcommand{\P}[1]{\mathbb{P}\left( #1 \right)}$ if I'm doing probabilities or $\newcommand{\N}{\mathbb{N}}$ if I'm doing arithmetic;
  • If I have exercises to solve, I will prepare the text of the problems in advance, and leave blank cells for the solution;
  • I'll prepare the titles and subtitles in markdown.
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Sharepoint access and a copy of Microsoft Word for everybody could do that. So could Google Docs.

Both systems provide simultaneous viewing of a document being edited. And both provide equation objects you can add to the document which take a modified form of LaTeX math syntax for keyboard entry. It might take a lot of practice to get fast enough to do a lecture but it's sound enough to use for notes and coursework in my experience.

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I like to build presentations using LaTeX and the beamer package. The result is a PDF that, when viewed fullscreen, looks just like a normal slideshow. You get an incredible level of control over the output, though. I build mine where content is progressively revealed as I'm talking. I probably hit the spacebar every 5-10 seconds to reveal the next bullet point in the list or the next step of an equation. That gives a more chalkboard-like feel, where it's more like the slides are recording what I'm saying and less like I'm reading the slides to the audience. Besides progressive display of a page, you can also have page elements appear and disappear, highlights and colors can change, etc. Since the output is a PDF file, you get all the advantages that format brings (your last two bullets).

There's a question on the LaTeX user's Stack Exchange site that demonstrates how to do it. It's a bit odd the first time you try it but once you get the hang of it, you can build some very impressive-looking presentations.

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  • In my experience, slides and beamer are awesome for presentations. But terrible for teaching.
    – Stef
    Mar 1, 2023 at 10:59
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How can I approximate this [black board] experience in an online lecture?

There is a low-tech answer to this question that is not covered in the other answers.

Place a webcam in front of the black/white board.

This way you can more or less keep teaching as you normally would in the classroom if you had a group of students in front of you. I did this in my teaching throughout the pandemic with great success, and it is now my go-to for online teaching. All the points listed in @Jochen Gluecks answer are retained in this method. I therefore do not agree with their assessment that You simply can't.

I teach language and linguistics, so my requirements may be slightly different from those in mathematics.

Some things I learned from experience with this method:

  • You need a high resolution camera. Otherwise things you write on the board will not be clearly visible in the image. I use the built in webcam on my MacBook Pro. Colleges that have tried this with laptops with lower quality webcams have had problems with the resolution. My university has cameras at the far end of some lecture halls for this very purpose, but they are too far away with too low resolution for things written on the board to be visible, so I ended up not using them.

  • A decent every-day bluetooth headset will do. I use my Bose QC3 that I bought for listening to music. The sound quality of the microphones is not fantastic, but it is good enough. The wirelessness allows me to move around as I would in a normal lecture. I have also used the inbuilt microphone on my laptop (MacBook Pro), which works well provided that the laptop is on the table in front of me.

  • Place the camera/laptop at about chest height in front of the board. This gives the best framing and perspective. If I can't adjust the height of the table in front of the board I simply put a chair on the table with the laptop with the webcam on top of that. This also allows you to have a (somewhat) natural view and emulated eye-contact with the students in the zoom room. (Natural interaction with students and the reading of their reactions is the bit I think you really cannot fully compensate for. I often ask student to exaggerate body language by nodding and using thumbs up and the like for me to read it better, but it still of course is not the same thing.)

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While re-iterating Jochen Glueck's exhortation to "embrace the medium" of online lecturing, it is worth noting that since this medium is novel, the technology is evolving.

Thus, you may wish to keep asking for and looking for features that give you and your audience the engagement that is being sought.

In particular, multiple mechanisms for keeping the material available for the speaker and the audience are possible.

  1. Links: One can use hyperlinks. How such a link works depends on the software used to create it and the software used to display it. The actual display could merely pop-up as a small box on the screen almost like one would walk to the relevant place on the board and point out the relevant portion. Alternatively, the link may directly go to an earlier slide. Such a mechanism does not exist in Google's Jamboard (for example), but one could ask them to create it!

  2. Audience access: As David E. Speyer has mentioned there are tools that can make slides available online for the audience, even as they are written. In one talk I attended, the slides were "minified" and placed at the top of the screen still (more or less) legible. This successively reduces the available screen space, which may also be a good way for the speaker to realise that they are "using up space and time"! Again, it would be nice for such a feature to be added to various tools that are currently available for online talks.

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    It is also very technically feasible to have a large spatial plane where the lecturer can write and the students can zoom and pan around to refer to earlier scribblings - exactly in the manner of students moving their eyes around an array of blackboards. The question is merely whether a software vendor will produce such a solution, and expressed demand for it makes that more likely.
    – Willa
    Mar 2, 2023 at 15:27
  • @John I often use Xodo for online lectures and one can make a "blackboard" with a large writing area which one can move a "window" around in as you have suggested. However, as of now, I don't know how to share it with the audience in "live" mode.
    – Kapil
    Mar 2, 2023 at 15:35
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The most effective online lectures I've seen (actually some of the best lectures of any sort), have had the lecturer standing behind a glass or plexiglas screen. As they spoke they wrote on the screen. But wait! Won't the writing all be mirror reversed for the audience? No, it was all perfectly legible.

At first I marveled that the lecturer had taught themselves to mirror write in real time. Then I realized that the producers had simply mirror transformed the video in post-production.

It may sound like a cheap trick, but I thought the end product combined the best aspects of recorded talks and live talks. I had the ability to stop and rewind at points that seemed unclear and I could time shift viewing to a time that was convenient for me. It provided the engagement of a live chalk talk while avoiding the perennial problem of the lecturer talking into the board and loosing eye contact with the audience.

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If you are quite tech-savvy, you can achieve the desired effect in a RevealJS presentation with the Chalkboard plugin, run from a touchscreen-enabled PC. Combine this with the Multiplex plugin to allow viewers to follow on their own devices, and author the presentation in Quarto to add on LaTeX rendering and, if you're mad enough, responsive cells coded in Python or Julia.

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