I am personally very familiar with both the NCTM Process Standards and with the strands of proficiency from the National Research Council. I’m curious if you know of the Standards for Mathematical Practice, the eight K-12 standards written in conjunction with the Common Core State Standards Mathematics Content Standards. These eight statements were derived from the two sources your rising AP Calculus students are exploring this summer, and in my opinion, are the most important part of the CCSS-M standards. Without deliberate attention to the Standards for Mathematical Practice, the transformation in math education intended by the writers of CCSS will not be realized.