The NCTM process standards, Adding it Up mathematical proficiency strands, and Common Core State Standards for mathematical practices are all saying the same thing but why do I get the feeling that the Mathematical Practices Standards is out to get the math teachers.
The NCTM’s process standards of problem solving, reasoning and proof, communication, representation, and connections describe for me the nature of mathematics. They are not easy to understand especially when you think that school mathematics is about stuffing students with knowledge of content of mathematics. But, over time you find yourselves slowly shifting towards structuring your teaching in a way that students will understand and appreciate the nature of mathematics. I must admit that my exposure to the way math is taught in Japan also helped me understand what the Standards look like in the actual teaching. At the time when some parents and politicians in the US were busy criticising the NCTM Standards for not reflecting the math they knew and understood, the Japanese were happily restructuring their math teaching to give more focus on the process standards of the NCTM. It is not an uncommon knowledge in the math education community that the best implementer of the NCTM process standards are the Japanese!
The five strands of proficiency was also a great help to me as a teacher/ teachertrainer because it gave me the vocabulary to describe what is important to focus on in teaching mathematics.
With the Mathematical Practices Standards I had this picture of myself in the classroom with a checklist of the standards in one hand and a lens on the other looking for evidence of proficiency. The NCTM and Adding it Up standards actually said more about math. The ones in Common Core are saying more about what students should attain. I wonder which will encourage ‘teaching to the test’. The day teachers start to ‘teach to the test’ is the beginning of the end of any education reform.
NCTM Process Standards 
Five Strands of Mathematical Proficiency 
CCSS Mathematical Practices 
Problem Solving
Reasoning and Proof
Communication:
Connections
Representation

Conceptual Understanding refers to the “integrated and functional grasp of mathematical ideas”, which “enables them [students] Procedural fluency is defined as the skill in carrying out procedures flexibly, accurately, efficiently, and Strategic competence is the ability to formulate, represent, and solve mathematical problems. Adaptive reasoning is the capacity for logical thought, reflection, explanation, and justification. Productive disposition is the 
Mathematically proficient students …

Image from 123RF
Does your “exposure” mean you personally watched Japanese classrooms or were you told/did you read how classes are taught?
Yes, including development of materials with Japanese math educators. We had a project with them. AlSo, the APEC (Asia Pacific…) project about Lesson Study for math which concluded last year devoted each year of the project for each of the process standards. I think the last one was about representation and communication. If you are familiar with Teaching Gap, the TIMSS video study by Stigler an Hiebert, you’ll get a picture of the Japanese math class. Of course, it doesn’t mean it’s happening they all teach that way.
We teachers are under tremendous pressure to be accountable for what students attain, which means insuring students do well on tests. It’s all about ‘data’ and Grade Level Content Expectations now. I fear both teachers and students will blow a fuse.
Really a nice addition in Mathematics Education