noun / verb
doodle
DOO-duhl/dˈudʌl/
A drawing made casually or absentmindedly, or the act of making one.
She doodles loose stars and spirals while listening on the phone.

Etymology
The drawing sense may come from dialectal doodle, “fritter away time, trifle,” shifting from idle activity to aimless drawing. Association with dawdle is another possibility.
In context
When you doodle, those random shapes, lines, or little sketches act like an anchor. Your mind stays lightly engaged, which keeps you tuned in to the conversation or lesson.