Dan Willingham is a cognitive scientist, and takes P21 apart step by step.
The Partnership for 21st Century Skills assumes, he says, that first, knowledge and skills are separate. But research shows that not to be true.
Second, P21 assumes that teachers do not have cognitive limits. But, of course, they cannot attend to everything. That's why they aren't embracing problem-based learning, cooperative learning, and small group instruction. These are really, really hard to do well. Maybe even impossible.
Now we're looking for a little red circle on a screen. (OK, you kinda gotta be here for that one...)
The reason that seatwork and whole-class instruction is preferred by teachers is that they can easily tell if their students are paying attention. Small group instruction makes that virtually impossible.
Willingham's bottom line: Teachers like the methods that P-21 is advancing, but they are really hard to implement well. There's a reason that they've been told to teach projects for a century and they haven't done it much.