Epistemology Comics

Melody Byrne links to Frazz's Sunday comic which is an epistemology issue. But the comic and Melody under-state the problem.

The problem was something like: 5/8 divided by 2 1/2
The answer was 1/4
The problem was that the student didn't flip the 5/2 to 2/5 before multiplying.
The student said it was an opinion about whether to flip the fraction.
The teacher said test that on the next quiz.

GAHHH!

Issue #1: 5/8 divided by 2 1/2 means something. What does it mean? There's no quiz that will tell you...you have to understand the problem. 5/8 divided by 2 1/2 means that you have a pizza in 8 slices, and you want to split 5 of those slices so that 2 people get the same amount, and a 3rd person who isn't very hungry get's half that much. How do you do it? Understood as a question about the world...it's obvious that the not-flipped answer of 25/16 is silly. Understood as symbols on a page? Not so much.

Issue #2: 5/8 divided by 2 1/2 only has meaning by convention. Just like the russians use the symbol P to make the same sound as the american R symbol.

Issue #3: 5/8 divided by 2 1/2 is not understood to mean a DAMN THING by 99% of math students, and most elementary teachers. It's purely a stupid pet trick for "smart" kids to impress teachers, not a statement about the world.