Showing Your Work

Joanne has a slew of good posts today, including this one on the difference between "showing your work" and "explaining your answer" in math.  A commenter puts it most clearly for me:

Requiring written “explanations” is also (here I’m generalizing) counterproductive for learning and understanding mathematics by those who do not have such handicaps.

There is a right way to “show understanding” in mathematics. It has been understood for many generations and taught in the best classrooms. Yes, it has also been done poorly, but this is no reason to supplant it with inferior methods.

The whole point of mathematics is to learn efficient and effective ways of doing problems that can be formulated in abstract ways. Natural language is highly inefficient and often ineffective and misleading in doing such tasks. So the objective of math education should be to teach these methods and assist students in honing their skills in the use of these efficient tools.

There are plenty who insist that Common Core mandates the inefficient, and I'm not convinced they're wrong.