Cdtrjyty

I teach mathematics at MSc and PhD levels. My preferred method of teaching is old-fashioned: talking and writing on the blackboard at the same time.

Why? Because it has many advantages:

1. 
   Handwriting: imposes few restrictions on notation and illustration. (Complicated figures I could project from my laptop, but I have no need for this in my courses.)


2. 
   Flexibility: whenever this is useful, it is easy to 'deviate from the script'.


3. 
   Natural speed: it imposes a natural speed on the speaker. Preparing slides using LaTeX or PowerPoint and just clicking through them, I find myself proceeding way too fast.


4. 
   Parallel displays: having several boards available for writing makes it easy to keep some text/examples on display on one board, while writing on another.


5. 
   Dynamics: referring to information on the different boards allows me to move through the room, adding a more dynamic aspect to the lecture.


6. 
   Ease: it is a low-tech way of achieving all these things simultaneously with easily available means.

The main disadvantage of this method is that I spend a significant amount of time of each lecture with my back to the audience.

Question: What would you recommend as a means of communication that combines the six features above (most importantly, the handwriting and parallel displays), but facing the audience?

Obviously, a low-budget solution would be appreciated, but my institute is usually pretty generous in investing in technology that improves teaching, so don't let that restrict you!

What I tried: Many things, including writing by hand on tablets (iPads, Digital Paper, reMarkable, etc) and projecting this in the classroom. Perhaps I haven't found the optimal device for this yet, but it often comes out pixly, delayed, and less readable than my usual handwriting on paper or the blackboard. Using a document camera to project my handwriting on paper. Works well, but can project only about half an A4 paper at a time to keep it readable for people in the back of the room and, like other approaches, has the disadvantage of not having parallel displays: it's hugely important to be able to keep definitions, examples, theorems from earlier on for easy reference.

1. Do not assume that facing the audience is actually better. It depends on the type of content. For example, if you are explaining a diagram (detailed hydraulic system for instance), you want the audience to concentrate on that, not the presenter. The audience is still getting plenty of stimulation by having a live human voice along with visual content. You actually don't want the presenter to distract the eyeballs from the intricate content. (I see this wrong often with recorded talks where the video operator concentrates on the podium versus the charts, or shows both but with inadequate scale to see the slide charts.) If you are doing math (as opposed to history or literature), the content is more intricate and you should have the audience concentrating on the formulas, not the speaker.




2. Take some occasional time to address the class when that is appropriate. Examples are a "sea story" about test performance or industrial application of the math. But these will be a minor amount of time within a math lecture.




3. I mean, if you really wanted to, you could write backwards in grease pencil on plexiglass like in an old Navy combat information center. But really what is the point. People concentrate on the status (content), not the writer anyways. The one advantage is that you don't have a body blocking part of the board. I believe there are now electronic versions that would flip this around for you (or you can use an OHP). But still I think you lose a lot from having a lot less screen space than board space (especially with sliding boards). So, the small advantage of facing is at the loss of huge amounts of content physical space.

The retro-projectors where one wrote on the plastic film allowed one to go "back in time" as it were... rewind...

Of course one could lay a diagram on top then remove it etc

So, you can have a single slide with a particular expression or theorem that you need often and drop it on as necessary.