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Assessment

A National Yardstick for Gauging Math Progress

By Christopher B. Swanson — January 07, 2010 5 min read
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To complement Quality Counts 2010’s exploration of reinvigorated interest in common standards and assessments on the national stage, the Editorial Projects in Education Research Center conducted an original analysis intended to help ground these dynamic debates in a firm understanding of state performance in one core academic area.

Built around the dimensions of performance, improvement, and opportunity, the Math Progress Index investigates: the state of academic performance in mathematics nationwide, trajectories of change over time, and student access to educational supports that promote greater learning and successful school careers. Woven throughout this framework is a thread concerned with equitable outcomes and opportunities, specifically as they relate to the experiences of economically disadvantaged students. The analysis also offers an in-depth perspective on state-to-state differences.

The index comprises a dozen indicators drawn largely from the National Assessment of Educational Progress, which is widely recognized as the most authoritative source of ongoing national and state data on student performance and educational context. The index also incorporates data on Advanced Placement testing from the College Board.

The analysis takes a “best in class” approach to generating summative scores, by which states are evaluated relative to the top-performing state on each individual indicator. By this standard, a state that (hypothetically) ranked at the top of the nation on every measure would earn 100 points, a perfect score. More-detailed information on indicators and scoring can be found in Quality CountsMethodology section.

States Lag

The overall results from the analysis underscore two general, but very important, findings. First, in reality, not even the top-ranking states come within striking distance of the 100-point ideal. The national leaders—Maryland, Massachusetts, and New Hampshire—fall just shy of 80 points.

Second, a considerable divide separates the highest- and lowest-performing states. If the 27-point gap between Massachusetts and Louisiana were placed on a metric more akin to Quality Counts’ traditional grading scale, it would translate to a difference on the order of two to three full letter grades.

Data Download
Math Progress Index PDF

Summative scores can provide one useful touchpoint for grappling with complex issues, such as gauging the headway that states have made in advancing levels of academic performance. But they can tell only one part—and perhaps not even the most important part—of the story. Gaining deeper insight requires a look beyond the surface.

Generally speaking, for example, states that score well (or poorly) on one dimension of the index tend to post similar results for the others. However, state math patterns are more often characterized by variability than by consistency with respect to performance, improvement, and opportunity.

Thirty-eight states, a tally that includes the District of Columbia, rank in either the top or bottom 10 for at least one component of the index. In fact, only two states (Maryland and Massachusetts) post top-tier scores across the board, while two others (Arizona and Mississippi) rank among the last 10 on all three index elements.

The release of NAEP scores has become an eagerly awaited event on the education calendar, with the test’s results soon thoroughly scrutinized by policy analysts and the public alike. So it should come as no surprise that the Math Progress Index finds that “proficiency” in math, as defined by the national assessment, is the norm in only a handful of states. Many leading voices have raised concerns that such performance falls well short of national aspirations, not to mention the educational foundations the United States needs to remain competitive in a 21st-century global economy.

Some Improvement Seen

Among the more hopeful signs that emerge from the Math Progress Index is the finding that all but two states improved their average levels of math achievement in both 4th and 8th grades from 2003 to 2009. Likewise, although relatively few students currently reach the highest levels of math competency by the end of their K-12 school careers, all states are on an upward trajectory. In fact, the share of students earning high scores on Advanced Placement math tests has doubled in a dozen states during the past decade.

Nevertheless, the nation as a whole and all states, to a greater or lesser degree, continue to struggle with the challenge of improving performance and opportunities while at the same time narrowing the historical gaps between educational haves and have-nots.

In the 8th grade, for example, economically disadvantaged students lag behind their more affluent classmates by anywhere from 1.5 to more than three grade levels, depending on the state. (Experts typically peg a grade level at about 10 points on the NAEP scale.)

Such poverty-based disparities have also proven extremely intractable. Although math achievement among poor students has improved in every state, test scores for nonpoor students have improved faster for nearly half the nation. As a result, the nation’s poverty gap has shown little movement over the past decade.

Geography matters. Where a student lives affects his or her chances of benefiting from known correlates of achievement and attainment. Those would include exposure to a middle school curriculum that places students on track for advanced coursetaking during high school, as well as the opportunity to learn from experienced and well-qualified math teachers.

For example, only one out of five students nationally attends a school where taking algebra by the 8th grade is the norm. However, the index shows tremendous cross-state variability in this opportunity indicator, with virtually no 8th graders attending such schools in some states, compared with more than half in California.

In almost all cases, economically disadvantaged students are less likely to have access to an experienced math teacher, although this teacher gap differs markedly from state to state.

A closer investigation of Math Progress Index data reveals that states where poor students have more-equal access to experienced math teachers also tend to post significantly smaller math-achievement gaps. This is, just to be clear, correlation and not causation. But it can offer a useful perspective on current debates over state efforts to more effectively allocate teaching talent to students with the greatest academic need.

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