It's not just multiplying two times two, or subtracting five from 100. Students were graded on their skills in measurement, geometry, statistics and algebra. Some questions were multiple choice; in others, students had to formulate their own responses.
The National Assessment of Educational Progress, known as the nation's report card, said 25 percent of public-school fourth-graders performed at or above the proficient level in 2000. In 1992, 17 percent did.
Eighth-graders' performance increased as well, rising to 26 percent from 20 percent in 1992.
The figures in both grades rose about one point when private-school students' scores were added.
American students have consistently performed at lower levels in math than their counterparts in Asia and elsewhere. Calling the achievement gap unacceptable, U.S. education officials have long searched for ways to close it.
"States and districts around the country have paid closer attention to math instruction than reading over the past decade, and these results give us reason to believe that we're on the right track," Education Secretary Rod Paige said Thursday. "Yet they also make it clear that we have more work to do to make sure our children have enough math skills to lead their communities and expand our economy throughout the 21st century."
Students judged proficient are those who show solid academic performance on challenging problems, are able to think them through and apply their knowledge to word problems. Students working at the lower basic level have only partially mastered material and skills needed for math work at their grade levels.
The assessment test is administered every four years to more than 113,000 students. Currently, 40 states participate.
The results released Thursday also showed that:
Only 17 percent of high school seniors scored proficient or better in 2000, a decline from 1996. Researchers tend to be more cautious about interpreting the 12th-grade data, since older students may not take the test as seriously as younger ones.
Students who used calculators every day had lower scores in fourth grade, but by eighth grade they were the highest scorers; they continued to be the highest scorers in 12th grade.
At each grade, the percentage of pupils who reported they have computers available at all times in classrooms grew by at least 20 percent over 1996.
Students whose teachers reported being better prepared or who were certified to teach their subjects had higher scores.
Fourth-graders who spent only 15 to 30 minutes on homework each day scored higher than pupils who spent more time on homework, while 12th-graders who spent only 15 to 30 minutes on homework scored nearly as well as those who spent an hour or more.
Low-income students had scores 26 to 30 point lower than those of others.
NAEP reading scores, released last April, showed that 32 percent of fourth-graders read proficiently or better, up slightly from 1992, when 29 percent were proficient.
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