Ability Differences - Differences in Degree and Differences in Kind (II):

"[Ability differences] consist of two types: differences in degree, and differences in kind. Bodily-kinesthetic ability offers many examples. People with a wide range of bodily-kinesthetic ability can play tennis. The difference between the way most people play tennis and the way that profes­sionals play it is huge, but it is a difference of degree. In contrast, doing a somersault with a full twist off a pommel horse is impossible for most people, no matter how much they might practice. The differ­ence in what they can do and what the proficient gymnast can do is one of kind. 

This point needs emphasizing. Educational measures such as test scores and grades tend to make differences among schoolchildren look as though they are ones of degree when in reality some of them are differences in kind. For example, a timed math test limited to problems of addition and subtraction, administered to a random cross-section of fourth-graders, yields scores that place children along a continuum distributed in a shape resembling a bell curve. Those scores appropriately reflect differences in degree: Some fourth-graders can add and subtract faster and more accurately than others, but they are all doing the same thing and almost all children can be taught to add and subtract to some degree. The same is not true of calculus. If all children were put on a mathematics track that took them through calculus, and then were given a test of calculus problems, the resulting scores would not look like a bell curve. For a large proportion of children, the scores would not be merely low. They would be zero. Grasping calculus requires a certain level of logical-mathematical ability. Children below that level will never learn calculus, no matter how hard they study. It is a difference in kind. Not only that: The child without the logical-mathematical abil­ity to learn calculus cannot do a wide variety of other things in math­ematics that are open to the child with the requisite level of logical-mathematical ability.

The same distinction applies to linguistic ability. Reading is something that almost everyone can be taught to some degree, and scores on tests of reading achievement will form a continuum with a distribution resembling a bell curve. But if we are talking about a classroom discussion of Macbeth among high-school seniors at the 20th percentile and 90th percentile in linguistic ability, the difference is more accurately seen as a difference in kind than as a difference in degree. Those at the 20th percentile will completely fail to under­stand the text in the same way that someone at the 20th percentile of bodily-kinesthetic ability will completely fail to do a somersault with a full twist."

Real Education
Charles Murray (2008)