The answer to the problem with education is "all of the above."
However, good teachers with strong wills can and do meet the challenge and actually do an excellent job of educating their students year-after-year.
My wife and I are in our fifth year of volunteering with a fourth grade teacher Mr Taylor who annually starts with a class of fourth graders, 2/3 of whom are below grade level, and ends the year with most of the class at and above grade level. He gets results by emphasizing reading and writing, and holds students responsible for the work assigned. All the students read the same challenging books, stories and poems; they spend a lot of time on vocabulary, take notes, identify the main chapter idea and write a chapter summary every day. They read about six challenging books a year.
He uses the same basic methods used by the successful KIPP schools. He assigns more homework than any of his peers, and holds students responsible for its timely completion. He stresses civility and respect for authority -- without which learning is nearly impossible.
His Title I students perform as well as students in the nearby "rich" area with all top-rated schools.
He gets little or no recognition from his peers or the administration, despite his outstanding results. He irritates parents of non-performing students by regularly calling them to enlist their help. In turn, they complain to the administration. He sends disruptive students out of class and suspends them when necessary.
His peers and the administration attribute his success to "cheating," "teaching to the test," his volunteers, etc., etc.
Fortunately for his students, he puts them first and is determined that every student will make at least one year of progress in his class. Some students make spectacular gains in reading, writing or math. The average student this past year made about three years academic progress.
So, schools can definitely improve with good-to-great, strong-willed teachers -- and without more money. (Although more money would be nice.)