As a new teacher, I upheld the longstanding requirement among math teachers that students must always show their work. And like many teachers, I deducted points when students refused to comply. But the more pushback I got from them--"you shouldn't make us work the problems out if we already know the answers"--the more I questioned the wisdom of this rigid requirement. And eventually my message for students changed from you must show your work to you may show your work. Here's why.
A common reason teachers give students to show their work is that "I can't help you if I can't see what you did." But seeing students' work isn't the only way to know what they did. In fact, you can often learn more about students' thinking when they explain--out loud and/or in writing--what they did than when they just show what they did. (See Standard 3 of the CCSS Standards for Mathematical Practice: Construct viable arguments and critique the reasoning of others. Also check out Marilyn Burns and her team conducting Math Reasoning Inventory interviews with students.)
A problem with requiring students to always show their work is that it risks emphasizing mathematical procedures and computation to the exclusion of mathematical thinking. The more programmed students are to show their work, the less likely they are to develop mental math and intuitive problem solving skills.
Of course that's the point with Common Core - to make it look like kids are doing more "rigorous" work when what they're really do is rote procedure that stifles creativity and thought.
We see the same thing happening with the seventeen day units from EngageNY that have kids reading one short story over and over and over and annotating it over and over and over...