There is a famous paradox, attributed to the Greek mathematician Zeno, in which there is a race between the great hero Achilles and a lowly tortoise. In view of their vastly different speeds, the tortoise was granted a substantial head start. The race began, and in a short time Achilles had reached the tortoise's starting spot. But in that time, the tortoise had moved slightly ahead. In the second stage of the race Achilles quickly covered that short distance, but the tortoise moved a little farther onward. And so it was that this continued -- Achilles would reach where the tortoise had been, but the tortoise would always inch ahead, just out of his reach. From this example, the great Aristotle, concluded that, "In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead."
The lesson that we should take from this paradox is that when we focus only on the differences between groups, we too easily lose track of the big picture. Nowhere is this more obvious than in the current public discussions of the size of the gap in test scores that is observed between racial groups. It has been noted that in New Jersey the gap between the average scores of white and black students on the well-developed scale of the National Assessment of Educational Progress (NAEP) has shrunk by only about 25 percent over the past two decades. The conclusion drawn was that even though the change is in the right direction, it is far too slow.
But focusing on the difference blinds us to what has been a remarkable success in education over the past 20 years. Although the direction and size of student improvements are considered across many subject areas and many age groups, I will describe just one -- 4th grade mathematics. In the figure, the dots represent the average scores for all states that are available for NAEP's 4th grade mathematics test (with New Jersey's dot labeled for emphasis). These are shown broken down by race (black and white students) as well as by year (1992 and 2011). We can see that there have been steep gains for both racial groups over this period (somewhat steeper gains for blacks than for whites). Of course we can also see the all-too-familiar gap between the performance of black and white students, but here comes Achilles. New Jersey's black students performed as well in 2011 as New Jersey's white students did in 1992. Given the consequential differences in wealth between these two groups, which has always been inextricably connected with student performance, reaching this mark is an accomplishment worthy of applause, not criticism.
The last thing that we see is that the performance of New Jersey's students was among the very best of all states in both years and for both ethnic groups.
If we couple our concerns about American education and the remarkable success shown in this data, it seems sensible to try to understand what was going on, so that we can do more of it. A detailed examination of this question is well beyond my goals, but let me make one observation. A little more than 20 years ago, several suits challenging the way that public schools were financed were working their way through the courts. In California it was Serrano v. Priest and in New Jersey it was Abbott v. Burke; there were others elsewhere. The courts decided that in order for the mandated "equal educational opportunity" to be true, per-pupil expenditures in all school districts should be about equal. In order for that to happen, given the vast differences in the tax base across different communities, the state had to step in and augment the school budgets of poorer districts. The fact that substantially increased funding has accompanied these substantial improvements in student performance must be considered as a prime candidate in any search for cause.
This conclusion, albeit with a broader purview, was expressed by the famous economist John Kenneth Galbraith, who I paraphrase as,"Money is not without its advantages and the case to the contrary, although it has often been made, has never proved widely persuasive."