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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.

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    $\begingroup$ Also posted at Academia Stack Exchange. $\endgroup$
    – JRN
    Mar 20, 2019 at 8:31
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    $\begingroup$ I see that your question at Academia is currently on the Hot Network Questions list, so since it is not appropriate to have questions that are exact duplicates at different sites, I think it is better to close this question here. $\endgroup$
    – JRN
    Mar 20, 2019 at 11:10
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    $\begingroup$ I'm voting to close this question as off-topic because it is already asked at Academia Stack Exchange. $\endgroup$
    – JRN
    Mar 20, 2019 at 11:11
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    $\begingroup$ Makes sense. Too bad, though, because there are some subtle differences with math - but it's mentioned in the academia question, so hopefully answers will be good there. $\endgroup$
    – kcrisman
    Mar 20, 2019 at 17:50
  • $\begingroup$ You can work with an overhead-projector, which projects on the blackboard or whiteboard, and write what you'd want to write on the blackboard, instead, on "transparencies" (which you'd be free to do in real time, and/or, with basic preparation ahead of a lecture.) You can then face the audience while writing on/using the transparencies. $\endgroup$
    – amWhy
    Mar 23, 2019 at 20:02

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