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The push to reform America鈥檚 failing schools dates to the Reagan administration鈥檚 1983 report, 鈥淎 Nation at Risk,鈥� which found that U.S. students鈥� test scores were plummeting. That news was so startling that Reagan鈥檚 energy secretary, Admiral James Watkins, commissioned the Sandia National Laboratory to find out why. What Sandia found (in a report not published until 1993) was even more startling: Although the overall average score had gone down, scores had gone up in each demographic group. How鈥檚 that work?

Across the board, scores had gone up.

For starters, it鈥檚 established that less-advantaged children, whether poorer, or members of a disfavored minority, or recent immigrants, score lower on standardized tests.

In the period of time covered by 鈥淎 Nation at Risk,鈥� the number of disadvantaged students had increased much faster than the number of more advantaged ones. During that time, scores for each group had gone up. Schools and teachers were succeeding.

Here鈥檚 an illustration of how the math works:

1,000 students take a standardized test. They are evenly split among income groups, and the richer students score better than the poorer ones. Later, 1,000 students take the same test. In between, the demographics have shifted. Across the board, scores have gone up. But because there are so many more low-income students than there used to be, the overall average goes down. This is exactly what the Sandia report said had happened in the United States.

鈥淎 Nation at Risk鈥� didn鈥檛 prove that schools were failing. It proved that the study鈥檚 authors failed math.