The latest round of the federal government’s grade-school tests is showing improvement in both reading and mathematics, giving a boost to advocates of the No Child Left Behind law.

The results, issued this morning, show that fourth graders and eighth graders did better in both subjects on this year’s National Assessment of Educational Progress tests, as compared to the previous round of NAEP testing two years ago.

The gains were especially pronounced in math, with the proportion of eighth-grade students scoring “proficient” now at 32 percent, more than double the figure from 1990.

“To those who would suggest that No Child Left Behind is not working, our nation’s fourth and eighth graders and their teachers just proved the naysayers wrong,” the education secretary, Margaret Spellings, said in a statement.

Yet the figures also reveal continued shortcomings. The average eighth-grade reading score remained below the 2002 level, and performance gaps on the basis of race and family income persisted.

Such findings “directly contradict the argument that NCLB, which went into effect in the 2002-3 school year, has produced marked improvements in educational performance,” said Robert Schaeffer, public-education director at FairTest, a nonprofit advocacy group. —Paul Basken