Despite achievement gains over the past decade, particularly among minority students, American high-school students display a “dismal’’ level of mathematics proficiency, the National Assessment of Educational Progress reported last week.
About half of all 17-year-olds tested in 1986 were unable to perform “moderately complex’’ procedures usually taught in junior high school, such as finding averages and interpreting graphs, the assessment found. Only 6 percent were able to solve multi-step problems.
In addition, NAEP’s report says, an “alarming’’ number of 13-year-olds lack the skills in whole-number computation needed for everyday tasks, and approximately 700,000 of the 3rd and 4th graders who took the test “have not yet acquired an understanding of rudimentary mathematical skills and concepts.’'
These results, which federal officials last week called “tragic’’ and “sobering,’' are consistent with those of a 1982 international mathematics assessment, which found that U.S. students lagged far behind those of other industrialized nations.
The data suggest, according to the report, that students'--and the nation’s--economic future may be in jeopardy.
“Too many students leave high school without the mathematical understanding that will allow them to participate fully as workers and citizens in contemporary society,’' concludes the NAEP study, “Mathematics: Are We Measuring Up?’'
“As long as the supply of adequately prepared precollegiate students remains substandard,’' it says, “it will be difficult for [universities and businesses] to assume the dual responsibility of remedial and specialized training; without highly trained personnel, the United States risks forfeiting its competitive edge in world and domestic markets.’'
The report notes several “encouraging’’ trends, including significant gains among black and Hispanic students since 1978 and an increase in the number of students who took advanced-level math courses.
But Assistant Secretary of Education Chester E. Finn Jr. said at a press conference here that it would take some “reaching to find a silver lining in this particular cloud.’'
“We are climbing the cellar steps to get up to the ground floor,’' he said.
Other observers, echoing researchers who had analyzed the results of the international assessment, said the NAEP findings reflect the poor quality of American math curricula.
Noting that students performed well only on simple arithmetical topics, Ann P. Kahn, former president of the National PTA, suggested that schools’ emphasis on basic skills has become “a ceiling rather than a floor’’ for many children.
John A. Dossey, past president of the National Council of Teachers of Mathematics, urged states and districts to overhaul their curricula, undertake “massive’’ teacher-training efforts, and strengthen the use of computers and calculators, to enable more students to move more rapidly from simple computation to more advanced problem-solving skills.
But reform will not be possible, he said, until students and parents shed the mistaken notion that math is a subject only an elite can master, and until math is no longer a “fiscal stepchild’’ in the education system.
“Unless society values math, and expects a high level of performance among children, we have a long road to travel,’' Mr. Dossey said.
Steady Gains
The new report is based on a 1986 assessment of 10,945 students in grade 3; 12,185 students in grade 7; and 11,850 students in grade 11.
NAEP is a Congressionally mandated project that tests student achievement in reading, math, science, and other subjects every two years. It is administered by the Educational Testing Service under a contract with the Education Department.
The assessment, the fourth math test NAEP has conducted since 1973, showed that student achievement has improved over the past decade, and has in most cases recovered from the declines of the mid-1970’s.
“Although not particularly eye-catching or dramatic,’' the report states, “the national trends indicate recent improvements for all three age groups.’'
The average score for 9-year-olds, on a 0-to-500 scale, rose from 219 to 221.7 between 1982 and 1986, the study found, continuing a pattern that began in 1978. Among the 13-year-olds, scores improved between 1978 and 1982--after a decline from 1973 to 1978--and remained steady between 1982 and 1986, with an average score of about 269.
Seventeen-year-olds registered a significant increase over the four years, raising their scores from an average of 298.5 to 302, the study found. That gain reversed a decline from an average of 300.4 in 1978.
These increases were not uniform across all ethnic and geographic groups, the report notes. Black students’ scores, though lower than those of their white peers, improved substantially at every age level, and Hispanic students showed gradual gains.
But white 9- and 13-year-olds’ performance remained relatively level from 1973 to 1986. The scores for 17-year-old white students declined from 1973 to 1982, but increased between 1982 and 1986 to about their previous levels.
The only region of the country to show improvement at every age level between 1982 and 1986 was the Southeast, the report found. According to Pat Frank, a state senator from Florida and the chairman of NAEP’s assessment-policy committee, the improvement reflects the impact of the stiffer graduation requirements and other reforms enacted in those states in recent years.
Encouragement ‘Tempered’
But while NAEP officials said they were encouraged by such trends, the report notes that the gains are “tempered’’ by the fact that “most of the progress has occurred in the domain of lower-order skills.’'
“As operations grew more involved and moved out of the realm of whole numbers, performance levels decreased,’' the report says. “Similarly, students had more difficulty with questions requiring the application of concepts and with those requiring problem-solving strategies, particularly in less frequently encountered situations.’'
Moreover, the gap between what students are expected to know and what they can demonstrate they know widens over time, it notes.
While three-fourths of the 9-year-olds--most of whom were in 4th grade--could perform at the beginning level, only 21 percent appeared to have mastered the basic operations and problem-solving skills usually taught in elementary school.
At age 13, only 16 percent of students demonstrated a grasp of the more advanced arithmetical and geometrical procedures usually taught in junior high school.
The discrepancy between expectations and achievement was even more pronounced at age 17, where half the students had not mastered junior-high-school-level skills.
“Translated into population figures,’' the report says, “nearly 1.5 million 17-year-old students across the nation appear scarcely able to perform the kind of numerical applications that will likely be required of them in future life and work settings.’'
The actual achievement level of high-school students could in fact be worse, the document adds, since the sample of those tested did not include the estimated 14 percent of students who had dropped out of school before the junior year.
Drill and Practice
Data on instructional practices may help explain the low achievement levels, according to the report.
Despite research on the effectiveness of innovative techniques, it says, most math instruction still resembles instruction in years past.
“Teacher explanation, textbooks, board work, and a lot of practice seem to characterize American classrooms,’' said Archie E. Lapointe, NAEP’s executive director.
Moreover, the study found that though greater use of computers and hand-held calculators could replace the paper-and-pencil computation that tends to dominate classroom instruction, these tools have yet to find their way into most math classrooms.
Other findings suggest that some instructional practices have changed over the past decade, perhaps as a result of the school-reform movement.
For example, the amount of homework and testing has increased dramatically over the past few years, according to study findings. In 1986, 96 percent of 13-year-olds said homework was assigned daily, compared with 73 percent in 1982.
And some 82 percent of 17-year-olds in 1986 said they took math tests “often’'; in 1982, 70 percent did.
But these kinds of changes may in fact be detrimental to math instruction, noted Ms. Kahn of the PTA. Multiple-choice testing, she said, “works against the kind of higher-order skills we need to teach.’'
The report also found that the proportion of high-school students who said they took advanced-level math classes--including algebra 2, pre-calculus, and calculus--increased from 1982 to 1986. Nevertheless, it notes, a majority of 17-year-olds said they had taken no advanced courses.
Copies of the report are available for $14 each from The Nation’s Report Card, P.O. Box 6710, Princeton, N.J. 08541-6710. A 50 percent discount will be applied to orders of three or more copies.
