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:
- 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.)
- Flexibility: whenever this is useful, it is easy to 'deviate from the script'.
- 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.
- 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.
- Dynamics: referring to information on the different boards allows me to move through the room, adding a more dynamic aspect to the lecture.
- 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.