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From kindergarten to 5th grade, he found, the achievement gaps grew twice as fast among the students who started out performing above the mean than they did among lower-performing children.

"The long-term implication of this is that, if these gaps continue to grow throughout their schooling career, even kids who enter kindergarten with high levels of readiness are going to end up falling below where they started," said Mr. Reardon.

White students, however, had higher scores than Black students, on average, on all assessments.

While the nationwide gaps in 2007 were narrower than in previous assessments at both grades 4 and 8 in mathematics and at grade 4 in reading, White students had average scores at least 26 points higher than Black students in each subject, on a 0-500 scale

At the state level, gaps in grade 4 reading existed in 2007 in the 44 states for which results were available. Gaps narrowed from 1992 to 2007 in Delaware, Florida, and New Jersey, due to larger increases in Black students’ scores.