We frequently hear the term social construction, one meaning of which is that alleged natural differences turn out to be enforced by those in power. Certainly there was (and alas, still is) an effort to socially construct a world where Black people are inferior. In the first half of the 20th century, many potentially talented Blacks were kept by institutionalized (and sometimes internalized) racism from developing into all they could be. In the 1950s John W. Campbell wrote an Astounding editorial asking why there were no Black geniuses. Harry Harrison wrote a story, "Mute Milton," in which a Black man in the South invents perpetual motion or somesuch, but before he can tell anyone, he is beaten to death for using a Whites-Only restroom. (Note to younger readers: This part was realistic. The past is a different country, and often a barbarous one.) The story was not published in Astounding.
Worse yet, many African Americans internalized this social construction, believing that they were inferior, believing that science and logic were white people's things, believing that they would always need special help. Unfortunately, much of that sort of thinking remains in the Black community as John McWhorter, Barack Obama, and others have pointed out.
But even when the social construction of dumb blacks was at its worst, Richard Wright and Zora Neale Hurston, to name just two, refused to be constructed that way. Social construction resembles the idea many of us encountered in Illuminatus!, that of creating one's own reality.
I don't know anyone who believes that there is nothing but construction. (Maybe a true solipsist would.) I certainly do not. Social construction operates on something, that which, as Philip K. Dick defined reality, "does not go away when we stop believing it."
Popper suggests that our social constructs get better. (Foucault seems to think they don't, and Kuhn isn't sure.) Some ways of pattern making are particularly good for fitting reality; physics and chemistry are two of these. (I recently encountered ane elegant metaphor: Good scientific theories, such as the periodic table of the elements,cut the world at the joints.) Maybe one reality that didn't go away when White America tried to construct black stupidity was blacks with the smart gene. 
I doubt that there was a fall of standards in the 60s and Blacks were its beneficiaries. Let me suggest instead that there was a fall of standards in the 30s, and Blacks were its victims.
In the 30s, idealistic leftists, believing that class determined intellectual achievement, gave social promotions to virtually the entire White working class (or at least all they could get their hands on), in the pious hope that their children, growing up in a higher class, would come out with the higher level of achievement their new status would promise. Unfortunately the children came out no brighter than their parents, which wasn't saying much. Some—probably more than otherwise—profited from their opportunities; many didn't. In fact, standards had to be lowered even further.
Then, the same or other idealists set up new teaching programs like the New Math and see-say reading. These made sense; it has been said that the New Math was designed by sci-fi readers who as a result of their pet sleazo input believed that someday there would be cheap, pocket-sized machines that could do arithmetic better and faster than people, so incredibly enough, there would be no point having people add columns of figures over and over again.
But while the old boring rote methods could be pretty much taught and learned by anyone who wasn't brain-damaged, the new approaches had to be understood by the teachers, just when there was a new group of teachers who understood less than might have been expected, so the New Math came out like gibberish with random mention of topics like sets and computers, while reading literally seemed like Chinese, with a necessity of recognizing whole words without having learned letters. In another horrendous irony, Blacks started getting a decent chance at public education just in time for this disaster, to be badly taught by socially promoted White people and told that the results were their own fault.