Resolution for webcam for recording lectures when writing on paper?
For online delivery and viewing on laptops/tablets, 720P should be sufficient for capturing the entire sheet in a legible way, but resolution isn't the only factor to consider...

A 1080P camera would capture higher-resolution images, but a 1-hr lecture at that size would probably result in a file size around 1GB. Assuming the intended delivery is online, the resolution/quality should probably be reduced anyway for ease of viewing/upload/download - the benefits of a better camera would likely be lost.

I'd also suggest that proper lighting &amp; contrast are greater concerns than camera resolution. 

A webcam may have issues if the room is too dark, or if the paper is too brightly illuminated (or not illuminated enough). Similarly, a black marker would be much more legible than, say, a ballpoint pen, but you can't fit as much writing on the page.

Exposure/contrast would also vary depending on if you only intend to include the white paper/writing in the frame, or yourself lecturing as well. This would be the 1 area where  resolution might matter - how much of the screen is actual writing? 

I'd recommend buying the (presumably cheaper) 720p one at a store with a 30-day return policy &amp; do some test lessons in the actual environment. Play with lighting, camera position, etc. If students are happy viewing them, you're all set. If not, try 1080p :)