A key theme of the Common Core State Standards for Mathematics is the need for students to use deeper mathematical thinking and reasoning skills (rather than just memorizing procedures) -- and to apply their understanding of mathematics by justifying conclusions and communicating them to others.
What I think this means is that the Common Core math classroom is going to be a much livelier place, full of discussion and teamwork and talk. That's a wonderful thing.
Here's a fun math conversation starter:
Which of the following numbers doesn't belong? 9, 16, 25, 43.
Let us know what you think. And remember, EXPLAIN YOUR REASONING!