See No Bell Curve, Hear No Bell Curve, Speak No Bell Curve

A great statistics professor I had once joked, “nothing in the world is actually normally distributed, except test scores.” This is not only true for the test scores of individuals; the average district mean of, say, 8th grade math, forms a tidy normally distributed bell curve when you compare all US school districts on a constant scale (as the Stanford Educational Data Archive has now done):


The increasing class and education-based sorting of Americans by school district, and the increasing divergence of upper income and lower income states has, I strongly suspect, widened the base of this curve.

Earlier this week, I half-seriously argued that part of the reason the Middlebury students reacted so aggressively to Charles Murray’s arrival was that they didn’t want to hear how much the current system favors people like them. But another reason is this graph; in the school districts that produce most kids who go to Middlebury, there is simply nothing like a representative distribution of the academic ability of Americans as a whole. A few Middlebury students are no doubt from schools only a little bit above the mean (say, those that attended New York City public schools). But the majority are from a small segment of high achieving school districts, putting aside the large number coming from private and magnet programs.

Fewer than one in fifty students from districts like Harrisburg, Pennsylvania or Youngstown, Ohio score as high in 8th grade math as the average student in Lexington, Massachusetts or West Windsor, New Jersey or Northbrook, Illinois.  Including very low-performing districts in Mississippi or Southern Arizona or rural New Mexico, the differences are even larger: essentially zero students in whole counties are performing at the same level as the average student in some affluent suburbs.   I am not saying this to disparage those places, and at least some of these differences can probably be narrowed (although I continue to think it is nuts for New Mexico and Massachusetts to be giving the same Common Core based tests, especially given the content and difficulty of those tests.) My point is simply that our upper middle class is increasingly insulated from the actual distribution of academic ability. Thinking through what can and cannot be achieved by schools and what kinds of policies are likely to help low-income people is grievously harmed when  the people running the country, like the Middlebury students, are not only ignorant of the distribution of ability but determined, come hell or high water, to keep it that way.

5 thoughts on “See No Bell Curve, Hear No Bell Curve, Speak No Bell Curve

  1. “although I continue to think it is nuts for New Mexico and Massachusetts to be giving the same Common Core based tests, especially given the content and difficulty of those tests.”

    No doubt true about the tests and the textbooks, but I would like to see all students nationwhide get the same basic introductions to world and American history: once in grade school, again in middle school, and finally in high school.

    Slightly off topic, but I also think Bible study should be integrated into that curriculum on secular grounds: not as the world of God but rather, as my rabbi used to say, as the world about God. For not only is the Bible the single most important primary document in our culture and civilization, but the very concept of God with a capital G (meaning the Hebraic conception of God as orignially adumbrated in Genesis*) easily the single most influential idea in Western intellectual history, from which all our liberal ideals are derived: human equality, equality under the law, social justice, political and economic freedom.

    Few educated people today are aware of these facts but they are easily demonstrated in any free, open debate. It reminds me of something Matthew Arnold once wrote (I think it was him), namely, that those who know their history and do not know their Bible do not know their history. The contrary is equally true: those who know theire Bible and do not know their history do not know their Bible.

    * For details see here, the middle parts especially:

    [I’ve since learned that there is an Arabic word, hanifya, for this “original, pure religion of Abraham.” In fact Muhammad himself seems to have ascribed to it in the first part of his career, before he went over to the dark side. He reminds me of Eminem in this regard: nobody would listen to him when he sung about peace and love.]


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