I recently read a post by a teacher who was concerned about the Common Core’s apparent focus on making sure that kids are understanding the math they are learning, as opposed to simply being able to just calculate correctly right away.
I have a strongly differing interpretation of a story she shares about her son solving a division problem. He gets an answer only after several minutes have elapsed and he has created his own (correct) method for solving it. She thinks this is an epic fail (why didn’t he just long divide?!), but I think this is an epic educational victory!
Here is my full response: http://havingneweyes.com/2013/01/26/adults-can-calculate-with-fractions/