The first-ever state-by-state assessment of student achievement has found that student performance in mathematics varies widely among states, but that performance in all states remains low.
The much-anticipated 1990 assessment, conducted by the National Assessment of Educational Progress, tested a national sample of students in grades 4, 8, and 12, and samples of 8th-grade public-school students in 37 states, the District of Columbia, and two territories.
It found that, nationwide, more than a quarter of the 4th graders failed to demonstrate the ability to perform simple arithmetic reasoning with whole numbers, and that, at later grades, the proportion of students showing the skills to perform more complex mathematical tasks declines sharply.
Only 5 percent of the high-school seniors demonstrated the skills needed for high-technology or college-level work, officials noted.
And the state-level data show that there are large differences in performance among states. The gap between the highest-performing states and the lowest-performing ones—35 points on a 500-point scale—is larger than the gap between the national average scores for 8th graders and 12th graders, the report notes.
In examining possible explanations for performance, the study found that students who watch a great deal of television, who are absent often from school, and who come from single-parent families tend to do relatively poorly on the assessment.
It also found that, despite calls for reforming math instruction, most classrooms, particularly those with low-performing students, tend to rely on textbooks, worksheets, and frequent tests.
In addition, it states, there are wide differences in the content of math instruction, particularly in the 8th grade. At that level, high-performing students tend to receive instruction in algebra and functions, it found, while low-performers tend to be taught arithmetic operations.
Secretary of Education Lamar Alexander called the report the most comprehensive assessment ever conducted, and said it should sound an “alarm bell that should ring all night throughout this country.”
“America is the country that grew up reading The Little Engine That Could,” he said at a press conference here. “We believe we can do almost anything, and usually we can.”
“But if our aim is to be first in the world in math by the year 2000,” he continued, “we had better fire up our engines, because we have an enormous challenge ahead of us.”
‘A Better Way’
The massive volume of data issued last week—a 532-page overview report and separate reports for each of the 40 participating state-level jurisdictions—represents the most significant source of information on education the federal government has released since it published the so-called “Coleman report” in the 1960’s, according to Emerson J. Elliott, acting commissioner of the National Center for Education Statistics.
“This is the first time in the history of the nation,” he said, “that we have data on a common assessment conducted in a uniform manner, with representative samples of students state by state.”
A Congressionally mandated project, NAEP has for more than 20 years tested national samples of students in reading, math, science, and other subjects. It is currently operated by the Educational Testing Service under contract to the Education Department.
The pilot state-level assessment came about, in part, because chief state school officers agreed in 1984, after long resistance, to permit state-by-state comparisons of student achievement, according to Richard A. Boyd, former state superintendent of education in Mississippi.
“That decision in November of 1984 was revolutionary,” recalled Mr. Boyd, currently the chairman of NAEP’s governing board, “because the prevailing sentiment at the time was not to display in public the strengths or weaknesses of schools in the various states.”
The officials changed their minds, however, because “a majority of chiefs felt that their states were already being ranked by various people, usually in unfair ways, and that a better way had to be found,” Mr. Boyd said. “I think a better way has been found.”
Mr. Boyd noted, though, that Mississippi was among the 13 states that did not participate in the trial assessment. He said that the state had already planned to conduct an 8th-grade test in 1990, but that it could not use the NAEP assessment in its place because the law authorizing the assessment prohibits the use of NAEP data at the school or school-district level.
In addition to permitting the 1990 trial, the Congress also authorized a state-level assessment in 1992, in 4th- and 8th-grade math and in 4th-grade reading. Some 43 states, the District of Columbia, and one territory have agreed to participate in that project, according to Mr. Elliott.
Far From Reform Vision
To conduct the 1990 assessment, NAEP officials administered tests to 26,000 students in 1,300 public and private schools nationally and about 2,500 students in 100 public schools in each of the 40 participating states and territories.
The test was based, in part, on the math-reform proposals advocated by the National Council of Teachers of Mathematics, and it represents a substantial departure from past NAEP math tests.
As a result, Mr. Elliott said, the reports issued last week did not show any trends in performance over time. But he said the Education Department this fall would release a study, based on a smaller sample, that compares student performance with that in prior NAEP studies.
The results of the assessment, according to the report, show “quite clearly and in some detail that mathematics education in our nation and in our states is far from the vision described in the recommendations for reform of what mathematics education could be.”
Specifically, it notes, 72 percent of the 4th graders tested could solve simple addition and subtraction problems with whole numbers, concepts typically taught in the 3rd grade.
Although nearly all older students demonstrated competence on such problems, the report notes, fewer could perform more complex problems. For example, it states, two-thirds of the 8th graders could consistently multiply and divide whole numbers—usually 5th-grade math—and less than half the 12th-grade students demonstrated a “consistent grasp of decimals, percents, fractions, and simple algebra.”
Moreover, it notes, only 5 percent of the high-school seniors showed an understanding of more advanced algebra and geometry that would prepare them for college-level work.
“We see diminishing returns in our educational efforts,” said Gary W. Phillips, acting associate commissioner of the NCES.
Gender Gap in States
But while the overall results are relatively low, the report notes, there are considerable variations among groups of students and among states.
As in previous studies, Asians and Pacific Islanders and white students, those attending schools in advantaged urban areas, and those with well-educated parents were in the higher-performing groups, the study notes. Nevertheless, it states, even in the high-performing groups, only 10 percent to 12 percent of the high-school seniors demonstrated a readiness for advanced work.
The report also notes that the highest-performing states—North Dakota, Montana, Iowa, Nebraska, Minnesota, and Wisconsin—considerably outperformed the lowest-performers—Alabama, Hawaii, North Carolina, Louisiana, Guam, and the District of Columbia.
However, it points out, the differences from state to state were small, in many cases smaller than the margin of error. As a result, NAEP officials cautioned against ranking the states according to overall performance.
The high-performing states tended to have fewer students in large-city schools, fewer receiving free lunches, smaller percentages of blacks and Hispanics, and larger percentages of two-parent families, the study found.
While most of the 8th graders in all states demonstrated the ability to perform simple arithmetic operations, there were wide gaps in the proportions who could solve more complex problems. From 0 percent to 24 percent of 8th graders, for example, could solve problems involving fractions and decimals, material introduced in the 7th grade, the study found.
The study also found essentially no gender gap in math performance in the 4th and 8th grades, but it found a slight advantage for males in the 12th grade, particularly in higher levels of performance.
At the state level, however, males outperformed females in all content areas except algebra and functions in eight states. In one state—Hawaii—girls had higher average scores than boys, however.
Three 8th-Grade Courses
In analyzing the separate content areas tested, the study found that the school curriculum emphasizes arithmetic facts and procedures, and the results reflect that emphasis.
Among 4th graders, it found, students’ proficiency was highest in measurement, while 8th graders tended to perform best on numbers and operations.
But, it notes, in each content area, 12th graders’ performance was more similar to that of 8th graders than 8th graders’ was of 4th graders. Such results suggest that, “as presently configured, the mathematics curriculum facilitates more learning in the lower grades,” the report states.
In surveying teachers and students, the study also notes that there were significant differences in curricular content at the 8th-grade level.
Some 58 percent of the 8th graders were enrolled in 8th-grade mathematics, which tended to focus on numbers and operations, 22 percent were in pre-algebra, and 16 percent were taking algebra. Those in the more advanced classes tended to have higher levels of proficiency on the assessment, the report notes.
However, the study also found considerable variability among states. For example, the District of Columbia, which had the highest proportion of 8th graders enrolled in algebra—32 percent—had among the lowest overall performance among the states, while North Dakota, one of the highest-performing states, had one of the lowest proportions—8 percent—of students in algebra.
The overall findings suggest that schools may be denying lower-ability students the opportunity to learn more challenging material, said John A. Dossey, a professor of mathematics at Illinois State University and a former president of the NCTM.
“You might think low-ability students need more work on numbers,” he said. “But the math curriculum in the middle grades should provide a bridge between arithmetic thinking and algebraic thinking.”
Schools provide “an opportunity to cross that bridge differentially,” he said.
Traditional Teaching
Mr. Dossey also noted that, while only a fourth of 4th graders are assigned to classes on the basis of their ability, two-thirds of the 8th graders are in such classes, and those who are achieved at a “significantly higher level.”
Differences in instructional practices also favor high-achieving students, noted Ina V.S. Mullis, deputy director of NAEP.
High-ability students were more likely than low-ability students to use calculators, she noted, while poorer performers tended more than higher achievers to use worksheets.
Nevertheless, she pointed out, the use of innovative strategies—such as group work, reports and projects, and calculators and computers—are relatively rare. Three-fifths of the 4th graders, three-fourths of the 8th graders, and four-fifths of the 12th graders, for example, said they used a textbook daily in math class, the study notes.
“Many teachers are still using the same instructional procedures their teachers did, and their teachers before them,” Ms. Mullis said.
However, the report found that math teachers are generally well qualified. On average, teachers had some 14 years’ experience teaching math, it found, and two-thirds had the highest level of certification. Two-fifths of the 8th graders, moreover, were taught by teachers who had majored in math in college, and those students outperformed those taught by teachers who majored in education or another subject.
The study also found that:
- In all states, no more than a third of students were in classrooms where teachers reported receiving all the necessary resources. Those who were in such classrooms outperformed those in less-well-stocked schools, it found.
- Students in most states generally liked math, and those who reported more interest in the subject tended to perform better.
However, the study notes that the District of Columbia, one of the lowest performers, had the highest proportion—32 percent—of students who strongly agreed that they liked the subject, as well as the most students who said they were good at it.
To order a copy of the overview report, “The State of Mathematics Achievement,” write: Education Information Branch, Office of Educational Research and Improvement, U.S. Education Department, 555 New Jersey Ave., N.W., Washington, D.C. 20208-5641; telephone, (800) 424-1616.
Copies of state reports are available from the state departments of education in participating states.
