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[quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous]The way I explained it to my kid was that 
(1) the teacher didn't actually need to know the answer to the problem.  They need to know whether the kid understands the math.  If you do it in your head and make a mistake, the teacher doesn't know whether you understand or whether you just made a careless mistake. They can't see where you went wrong.
(2) At some point, you won't be able to do the math in your head.  The numbers will be too big or there will be too many steps.  Best to get in the habit of showing your work.
(3) You can get partial credit if you show your work.  [/quote]
1) and 3) don't explain why correct answers lose points for not having shown work.[/quote]

Because the work is considered part of a correct answer. Do you understand what a proof is? Many times a correct answer is not one number, it is all of the steps written in the correct way leading logically to a single number. Do you also think English teachers should only assess spelling and ignore grammar and syntax?[/quote]
This is fine if the student is actually asked to solve a challenging problem, but being asked to write "proofs" for, say, 2 digit multiplication which are just two numbers which happen to add up to the answer doesn't teach any more than any other form of busy work. The "proof" is contingent upon the reader already understanding the algorithm, which negates the need for a proof in the first place. If you know the algorithm well enough to interpret the shown work, you know it well enough to verify and answer without any shown work.

Proofs only make sense for problems that require [i]some[/i] shred or semblance of critical thinking (which is what the proof is meant to communicate), which most kids sadly won't see until highschool or even college[/quote]

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