"What role can parents play?" It's hard to believe we have actually gotten so dependent on schools that we ask this. Education is the RESPONSIBILITY of the parents and child, not just something that they can have a "role" in. When you send the child to school, you are designating the school and teacher with educational tasks toward the educational goal, but responsibility still resides with the parents and child.
When you contract out other responsibilities, you oversee the contractor. You make sure when you are having a house built that it is being built according to your desires and requirements. You often recognize that the builder may know more than you do about specifics and technical issues, but you judge how the work is being done, you make sure that it is being done in a timely manner, you make sure it is being done correctly, and, if the builder is not doing it correctly, you fire the builder.
Likewise, you examine the curriculum, your child's progress through it, your child's interest in subjects, your child's FULL educational experience. You make sure that the teacher is teaching your child. If the teacher is trying, but your student is not responding, you should realize there is a problem before a teacher brings it up. It is your responsibility to supplement what the teacher is doing with what your child needs.
Too many parents just assume that if they send their kids to school, they'll be educated correctly. Sadly, this is not a guarantee. The teacher has many students, as does the school. They do not have the time or ability to personally oversee and guarantee that each child is getting the correct education level for that child. An average child that progresses through the curriculum at the rate of the class will get very little attention as to their needs from a teacher, but a parent can know whether the child has abilities that can be cultivated further and encourage their child with supplemental education.
Education is the responsibility of the parents and child working together as a team. The teacher and school have the role of educational consultant hired to provide experienced educational assistance to the parent-child team. When the teacher is assumed to be the one responsible for educating the child, we get the mediocre system in place today.
In other words, stop asking if the child is satisfying school requirements and start asking if the school, in conjunction with other education supplied by parents, tutors, self-driven interests, etc, are satisfying the goals of making the child all that they can be and cultivating abilities and interests in the child. The child does not serve the diploma; the diploma serves the child.