Well, that's a thirty year time period, and a lot happened in those thirty years, so it's hard to say if this is the information you are looking for.
I'll concentrate on two major changes. In 1954, the Supreme Court ordered schools to be desegregated. The government enforced the ruling and across the South, schools were forced to open their doors to black students as well. By 1970, that process was largely complete.
After Sputnik, a Russian satellite, was launched in 1957, the US passed the National Defense Education Act, which changed all of the graduation requirements, placed an emphasis on math and science, and created the AP program. High school moved away from basic job preparation towards college preparation.