It is so great to read the responses above.  Sometimes, as a teacher, I feel so isolated but that can't be helped with the current systems we have in place.  When it comes to what really happens in our classroom, it's up to us.  I too wish that all teachers read a book like this to get a picture of what needs to be done with the teaching of mathematics.  I think the whole U.S. approach to education is in trouble and something needs to happen to make the changes that are necessary or we are going to continue to fail as a whole. There are so many amazing teachers out there but we can't control what teacher a child has before they get to us or after the leave us.  We could do an amazing job teaching mathematics but that could all fall apart as soon as they step into another teacher's classroom that isn't on the same page.

I think about the education my own daughters had.  When my oldest left high school, at the top of her class, she could do calculus, physics and use a scientific calculator like no other.  But she had to go out and take a class on her own to learn about finances, credit, saving money and making a budget.  There needs to be a balance in what we teach students so that they can relate it to the real world around them.  Information is at the tip of our fingertips now and many jobs that are around today we couldn't have even imagined 20 years ago.  We need to change with the times and start implementing sensible mathematics in our schools as soon as possible.

Thanks to everyone for the thoughtful posts.  One of my take-aways from this book discussion is a renewed commitment to focusing on strengthening students' ability to explain their thinking and to connect their thinking to one another.  Yes, getting the correct answer is important, but the ability to reason and to debate are certainly as important.  

I had little hope for the Common Core changing teaching of mathematics in any significant way.  The previous NCTM standards also emphasized understanding of the logic behind mathematics, but they didn't result in much change.  What I hope the CC can do is change instruction.  New standards without appropriate materials and professional support will not be able to move us forward.

One area that the CC seems to be resulting in is changing assessments away from multiple choice to a new format that will emphasize math practices.  This will provide leverage to move instruction, but by itself is not enough.  I hope we see a real push to focusing on instructional practices.  As Steve mentions, and as has been noted in previous posts, "It's the classroom, stupid."