The supposed goal of our public education system seems to be socialization as much as it is education, however it fails horribly at developing the ability to work effectively as a team.
FIRST Robotics goes a long way towards accomplishing this, however it's an underfunded extra-curricular which is perceived by many as "nerdy".
My specific recommendations are as follows:
Current "group projects" resemble unions in the lack of incentives. They suffer from the "free rider problem" horribly.
#1.Grading on "group projects" should be a 75/25 averaged score with documentation of your own personal contribution to the project comprising the 75, and the 25 being based on the entire group outcome.
#2.Group projects should be based on real problems. I reject the premise that indoctrinating students in to doing work which they do not believe in is a valuable thing to be teaching. There is no shortage of such problems in life and the real world.
#3.Those problems can be sourced from local employers as a source of funding. AKA: local employer's sponsor these group activities as a way of raising money for the school.