Federal and state policymakers continually call on U.S. schools to improve student achievement in mathematics so that students will be better prepared for the demands of today's workplace. Are schools making progress toward that goal? How can we tell?
The results of standardized state accountability tests are one indicator that might be expected to yield information on mathematics achievement. No Child Left Behind mandates that all states test students annually in math and reading through grade 8. If increasing numbers of students are passing the mathematics portion of these tests, we might assume that students' math proficiency has improved. And a recent report from the Center on Education Policy,Answering the Question That Matters Most: Has Student Achievement Increased Since No Child Left Behind?shows that student scores in math and reading have generally gone up since 2002. Elementary school math was the area in which most states showed improvement, with 37 of the 41 states with available trend data demonstrating moderate to large gains in the percentages of students deemed proficient.
Does this finding mean that efforts to boost mathematics performance through higher standards and increased accountability are working? Unfortunately, two recent studies have concluded that the results of state accountability tests don't tell us much.
In Mapping 2005 State Proficiency Standards onto the NAEP Scales, the National Center for Education Statistics (NCES) observed large discrepancies between the percentages of students achieving proficiency in both mathematics and reading on state accountability tests and those judged proficient on the National Assessment of Educational Progress (NAEP). The NCES compared the level of achievement required for proficiency in each state with the proficiency cutoff on the NAEP. Not surprisingly, states that had established low proficiency cutoffs relative to this common standard tended to report much larger percentages of students achieving proficiency on their state assessments.
- The level of performance rated as “proficient” varies wildly from state to state. Among the states studied, Colorado, Illinois, Michigan, and Wisconsin generally have the lowest proficiency standards in mathematics; South Carolina, Massachusetts, California, and New Mexico have the highest.
- Many states are internally inconsistent, with higher expectations in mathematics than in reading. “Such a discrepancy in expectations can yield the impression that students are performing better in reading than in math when that isn't necessarily the case,” the report states.
- In the past few years, twice as many states made their tests easier as made their tests more difficult.
- Improvements in passing rates on state tests can largely be explained by declines in the difficulty of these tests. “These declines,” states the report, “raise questions about whether the NCLB-era achievement gains reported by many states represent true growth in student learning.” In fact, conclusions about rising student achievement made on the basis of state test scores “may be smoke and mirrors.”
If state accountability tests can't tell us whether student mathematics achievement has improved, what is the most reliable indicator to shed light on this question? The National Assessment of Educational Progress has measured trends in mathematics achievement over time, and its most recent report shows a steady, long-term rise in achievement for 4th and 8th graders.
According to The Nation's Report Card: Mathematics 2007, the average score on the NAEP assessment for 4th graders has increased 27 points and the average score for 8th graders has increased 19 points since the first assessment year in 1991. Between 2005 and 2007, the average score for 4th graders rose 2 points, and the average score for 8th graders rose 3 points.
These gains in NAEP math scores in grades 4 and 8 have been broad and consistent. They have occurred at all levels of performance, resulting in more students scoring at or above the Basic and Proficient levels. They have occurred in each of the content areas tested—number properties and operations, measurement, geometry, data analysis and probability, and algebra—and across all 42 states participating in state-level analysis. Scores have risen regardless of students' poverty level (as determined by their eligibility for free and reduced-price lunch). And the gains have also been apparent across almost all racial/ethnic groups.
Among all this good news, a major concern remains: Achievement gaps between white students and minority students have generally not narrowed. For 8th graders, the white-black gap remains at 32 points—smaller than it was in 2005, but not significantly different from 1990. The only significant narrowing of the white-black gap over time occurred for 4th grade students, where it fell from 32 points in 1990 to 26 points in 2007. This gap has remained static, however, for the last two years.
Still, despite the remaining challenge of achieving equity across racial/ethnic and economic groups, the NAEP results suggest that schools are making progress over the long term in improving students' mathematics achievement.
