One of the things I disliked most about learning math was the constant requirement that I show my work. If I knew the answer to the math problem, why was I not allowed to simply provide the answer?
As I progressed through school, math became increasingly difficult and I learned that solving some math problems required so many steps that it was no longer possible to do them all in my head and write down the answer. When I later entered the work world and became a typographer, I wrote computer programs using R-DOS, AOS-VS, and Penta Systems' typesetting language to generate typeset material. For example, I wrote programs that figured out how to make a variable amount of text fit a specific shape by either enlarging or reducing the type and the leading in specific increments until the text fit exactly. The formula had to work no matter how much text I input and it had to work no matter what shape I had to fit the text into. In effect, the formula was me showing my work.
Writing successful fiction also involves showing your work.
I've read many short stories by beginning writers where things happen for no apparent reason, where important objects appear out of the blue at the climax of the story, and where characters make important decisions without any of the information necessary for making that decision. These are examples of writers failing to show their work because the information is in the writers' heads and not anywhere on the page.
For example, if our hero pulls out a gun at the end of the story and shoots the villain, where did he get the gun? Somewhere in the early part of the story the writer needs to establish that the hero carries a gun or that the hero keeps a gun in his desk drawer.
If the detective solves the crime because he hears the killer whistling a snippet of Beethoven's Leonore Overture #3, it needs to be established early in the story that the detective has an extensive knowledge of and appreciation for classical music.
If, at the end of the story, the protagonist decides to remove her mother from life support, somewhere early in the story the author needs to establish that the mother has a living will giving her daughter the authority to do this and we need to establish that mother and daughter have, in some way, addressed this issue.
This is, in some sense, the opposite of the advice frequently attributed to Chekov (If there's a shotgun over the mantel in the first act, somebody better fire it by the third act.): If somebody fires a shotgun in the third act, there had better be a shotgun over the mantel in the first act.
In other words: Show your work.