Common Core - First Impression

My favorite part of the Core Curriculum reading was the third standard for mathematical practice: "Construct viable arguments and critique the reasoning of others." I am a major proponent of this standard, because from personal experience I have found that it greatly enhances understanding of mathematical concepts. In my Calculus class in high school, my teacher required that we spend 2 hours each week outside of class in a study group with other students from our class. I have never learned a subject in math so thoroughly, and I attribute much of that to those study groups. I learned how to communicate and justify my thoughts, and how to reason through mathematical arguments. I only regret that I learned this for the first time in my last high school math class. I think this is essential to implement in math classes of all levels.
One thing in the curriculum that surprised (and pleased) me was the section titled "High School - Number and Quantity." The basic tenets of this section are number systems, quantities, and vectors and matrices. Maybe this was just a hole in my personal education, but I never remember learning about different number systems in any real depth or drawing any connections between them until I got to college. It is so fundamental to understand the fundamentals! Math makes so much more sense if you can see how everything is based in an underlying structure (this also supports the seventh standard for mathematical practice: "Look for and make use of structure"). I am very excited that this is such a large part of the curriculum.