So much this! The problem isn’t the Common Core standards, which, to be clear to the vast majority of critics who haven’t even read them, don’t dictate methods but only learning objectives, but the materials and tests being used to implement them. The worst offender here is Pearson, although for-profit education in general is a problem, as, in the interest of increased profits, they did the minimum, in some cases nothing, possible to update their texts and tests to match the CC standards. Many of the examples used to bash CC by their critics are Pearson materials, sometimes from before the CC was even published.
As Obama finally acknowledged yesterday, testing is the other big issue. As Robert has well elucidated, standardized tests CANNOT properly assess the mastery of math enshrined in the standards. Number sense isn’t testable in a multiple choice format, nor can it be assessed by teachers if they haven’t themselves been trained in all the methods a student who has developed number sense might use. Of course, the cynic in me notes that the US spends a fraction of the time and money on teacher training that countries with high math proficiency do, and the power structures that make those decisions here benefit greatly from an innumerate populace. It’s time we woke up.