More than sixty years ago, I was taught mathematics by a relatively young teacher named Dan Drummond who was responsible for Pure and Applied Mathematics in later grades. One of the things I recall is his advice on written problem solving – “Draw a diagram, boy!”. The assumed logic behind it was that by visualising a problem you were disregarding all the extraneous clutter that came with the problem as stated and could concentrate on the essential elements of the actual problem … which would make it simpler to solve the problem.
The use of diagrams for explaining or defining issues was recognized by Euclid. If it was good enough for one of the math gods, it was good enough for me.
You can read more about the Oxyrhynchus Papyri here
On a more modern note, while staying at the Lan Tian hotel in Shanghai 10 years back there was a problem with the digital alarm clock in my room. My Mandarin wasn’t up to writing a note to the room service lady but a diagram crossed the language barriers and resolved the issue as well as getting a ‘written’ response from the room service lady.