I would say that parents are responsible (but not accountable) for helping their children learn, especially prior to Kindergarten and during off hours (after school, the weekend, holidays, summer, etc.). Once a child enters the public school system, schools are both responsible and accountable for student learning, and I think that this responsibility and accountability can be described irrespective of parents' responsibility. Take Child A above: did his school do everything possible to head off his failure? Were early intervention systems in place to support him academically, was a guidance counselor or social worker brought in to address attendance issues, was transportation made available so that he could stay after school for tutoring, was a formative assessment system in place in the classroom to specifically identify areas of academic weakness, was the need for special education ruled out, etc. And, when a child fails and a school can honestly say to itself "We did everything we could for that student, and he failed despite all of our best efforts", then the school has a further responsibility: to figure out, if an identical student were to attend the school the next year, what new systems, interventions, personnel, etc. could be put in place so that the same type of student would be successful the next time around. That is, schools and school personnel are responsible for continually learning and improving.