What software would be good for a parent to use to monitor a screen and record it as needed?

It sounds sketchy, but it's not. O_o 

My son's teacher verbally assigns the class things but won't record his lessons or provide written instructions and isn't available for questions after he's assigned something. I want to record my son's screen so I can listen to the recorded instructions and help him when he doesn't understand something and would like the ability to watch what's happening on his screen live from time to time to make sure he's following along with the class and engaged. 

I tried Team Viewer this morning but it's not really working. I don't want to control the screen and my son gets too many popups from the program while it's running.