First principle: Understand the problem
Second principle: Devise a plan
Third principle: Carry out the plan
Fourth principle: Review/extend
CCSS.Math.Practice.MP7 Look for and make use of structure.
Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property.
Other innovations include emphasizing more nonfiction in English classes and more statistics in Math classes. (Both are reasonable suggestions for evening out the sex biases in traditional curricula: boys favor nonfiction, while girls find it hard to stay interested in higher level continuous math, which is aimed at producing engineers, whereas discrete math is more immediately useful for things like measuring human behavior.)
My impression from reading some of the Common Core is of a fairly masculine intelligence behind it. A Google search doesn't indicate anybody else has noticed this, however.
Still, the discreetly sensible side of some aspects of the Common Core isn't likely to have much impact on practice. Instead, people in positions of influence in public education simply won't notice the better stuff, and will instead use the commotion mostly as justifying whatever fads they are into at the moment. For example, the LAUSD superintendent has used the prospect of the Common Core to rationalize his spending a billion dollars on iPads right away without any clue what's involved in such a massive rollout.
Update: Breaking news, the LAUSD superintendent just resigned.
UpUpdate: Now he appears to be only threatening to resign if he doesn't get a big vote of support.
High stakes testing could, theoretically, change the practices of public schools by encouraging teaching to the test. But, public education is largely missing the kind of brainpower and realism that could think through how to rewrite the upcoming Common Core-based state tests to encourage better practices in schools. If they put Charles Murray in charge of Common Core testing they might get somewhere, but that isn't going to happen.