U.S. Reading and Math Scores Show Incremental Gains American fourth and eighth graders showed incremental gains in reading and math this year, but achievement gaps between whites and blacks, whites and Hispanics, and low-income and more affluent students stubbornly persist, data released by the Education Department on Thursday showed. The results of the tests - administered every two years as the National Assessment of Educational Progress, sometimes called the nation's report card - continued an upward trend in both areas over the past two decades. But still, far less than half of the nation's students are performing at a level deemed proficient in either math or reading. "There are some positive results here, which we were heartened to see," said Jack Buckley, the commissioner of the National Center for Education Statistics, which administers the exams. But places where we had hoped to see improvement, we didn't. Arne Duncan, the secretary of education, said in a telephone briefing that schools were having to expend too much energy to bring underprivileged students up to the level of more affluent peers. He urged more focus on the years before formal schooling begins, citing President Obama's proposal to help states fund preschool for all low- and moderate-income 4-year-olds. Why do we want to stay in the catch-up business? Mr. Duncan asked. The average fourth-grade math score this year was 242 on a scale of 500, up from 241 in 2011, the last time the federal assessment results were released. The average eighth-grade math score was 285, up from 284 two years ago. In reading, the average fourth-grade score edged up slightly to 222 from 221 two years ago, while the average eighth-grade score rose to 268 from 265. About 400,000 fourth graders and 350,000 eighth graders took the exams; the results represent students in both public and private schools. With reading gains trailing math gains over the long term, some educators said they hoped that new standards being introduced for students in kindergarten through high school, known as the Common Core, would help bolster reading skills. Susan Pimentel, one of the lead writers of the Common Core standards for English language and literacy, said the new guidelines asked students to read more demanding texts, including more nonfiction, and to cite evidence from their reading when answering complex questions. She said that such instruction could help both to improve reading skills generally and to close the gap between boys and girls, since boys seem to prefer nonfiction. A handful of states and jurisdictions showed more notable increases in average scores at certain grade levels on either reading or math. The District of Columbia, Hawaii, Tennessee, and Defense Department schools had gains in both subjects and both grade levels over the past two years. Kaya Henderson, the public schools chancellor in Washington, described the increases in the district as "breakthrough gains." Average scores for public and charter school students in fourth-grade reading increased by five points from 2011, and eighth-grade reading moved up six points, half the total gain in average scores since 1998. Average fourth-grade math scores among public school students increased by seven points, and eighth-grade scores by five points. New York, by contrast, had smaller gains, and scores in eighth-grade reading were flat compared with 2011. Although they came from a low base, Washington's African-American students, who represent about three-quarters of public school enrollment, raised their average scores in both subjects and grades to their highest levels on record, Ms. Henderson said. She attributed the improvement to changes in curriculum and the teaching population, and to a rigorous evaluation program for educators. "When you raise expectations for students and teachers, they rise to the challenge and produce," she said. The district's new policies, initiated by the former chancellor Michelle A. Rhee, have come under criticism from teachers" unions and others who say they put too much emphasis on test scores.