“All propaganda must be presented in a popular form and must fix its intellectual level so as not to be above the heads of the least intellectual of those to whom it is directed. (…) The broad masses of the people are not made up of diplomats or professors of public jurisprudence nor simply of persons who are able to form reasoned judgment in given cases, but a vacillating crowd of human children who are constantly wavering between one idea and another.”
While some written math problems are easier solved if you draw a diagram, some written math problems are beyond solution. Not because they are intractably difficult, but because the author is an idiot, the publisher is an idiot, the ‘education’ body that chose the idiot question by the idiot author, and the idiot teacher (using that word in it’s broadest sense), is innumerate and unable to see that the question cannot be solved with the information given. Here’s an example:
Go ahead. There is no solution to the problem as presented. If you see crap like this showing up in assignments then COMPLAIN long and hard. Ask your child’s math ‘teacher’ how to solve it with only the information given. Students aren’t born stupid but crap like that make them give up math ASAP.
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.