One of the changes that was still happening in the 40s and even into the late 50s was the fulfillment of the idea of compulsory education throughout the entire United States. Up until that time, the process had reached much of the US but was still absent in some very rural areas as well as others. During the 50s it became just about as universal as it is today.
Those three decades also saw a creeping standardization that has certainly sped up more recently, but there was a desire to find more standardized ways of knowing what a student had or hadn't done and finding ways to rank them based on test scores, grades, etc. The further adoption of the credit hour and the connection of competency with seat time over perhaps an exam of some sort was another happening in the field of education.
Also, teacher training programs became more and more standardized and the certification of teachers became a far more widespread practice as schools of education came into being at more and more universities.
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.