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The level of skill required to solve many of the math questions posed to 4th and 8th graders on the nation鈥檚 benchmark of academic progress is 鈥渆xtraordinarily easy,鈥� asserts an analysis unveiled last week.

The report, , is available online from the . ()

Conducted by the Brown Center on Education Policy, the study also concludes that middle school teachers of mathematics lack academic preparation in the subject and have too few professional-development options available that could help them improve their capabilities.

The report, 鈥淗ow Well Are American Students Learning?,鈥� examines more than 500 questions from the math section of the National Assessment of Educational Progress.

A central finding is that items on the 4th and 8th grade NAEP鈥攁 test states must take part in to receive certain federal funds鈥攄o not adequately gauge students鈥� arithmetic ability that is needed to conduct problem-solving on the assessment. The exam puts too much emphasis on testing students鈥� adeptness to work with whole numbers, the study says, at the expense of fractions, decimals, and percentages that would reflect broader capabilities.

National test scores on NAEP rose in mathematics for both grade levels in 2003, as they have over the past decade. But the study by the Brown Center, a research institute located within the Brookings Institution, a Washington think tank, questions the significance of those gains.

鈥淓ven if American students are making progress in mathematics, the arithmetic on which the gains are being registered is not very challenging,鈥� the report contends. 鈥淪tudents know more math than in 1990, but the increase is probably far short of the two years鈥� worth of knowledge suggested by the NAEP scales.鈥�

Whole Numbers vs. Fractions

The study鈥檚 author, Brown Center Director Tom Loveless, focused on 512 NAEP math items that have been made public. He then analyzed the level of arithmetic required to answer correctly questions that test problem-solving skills. Mr. Loveless said he focused on arithmetic because of its importance as both a springboard for learning more complex math and its relevance to real-world problem-solving. Arithmetic is broadly defined as computational skills.

On the 4th grade NAEP, six of 39 questions Mr. Loveless examined required knowledge of 1st-grade-level arithmetic. Overall, those 4th grade questions tested students鈥� knowledge of arithmetic at a level only slightly above 3rd grade, the analysis found. Yet only 36 percent of the students correctly answered questions at the average level of difficulty, according to the study.

The 8th grade NAEP questions tested students鈥� arithmetic skills, on average, at only slightly higher than the 3rd grade level, the study found. Almost 40 percent of the questions tested arithmetic skills taught in 1st or 2nd grade, it concludes.

鈥淲e dress up these items as problem-solving,鈥� Mr. Loveless said. 鈥淏ut the fact is that to solve these items, you don鈥檛 have to know arithmetic beyond a 3rd grade level.鈥�

But Sharif M. Shakrani, the deputy executive director of the National Assessment Governing Board, which sets policy for NAEP, said the study defines the skills needed in problem-solving in a restrictive way.

Students needed to 鈥渋dentify the appropriate math to use, then use it correctly,鈥� in test questions, he said. 鈥淢r. Loveless does not think [the test measures] arithmetic skills because it measures something in addition to arithmetic skills.鈥�

The Brown Center report recommends that NAEP break out students鈥� arithmetic skills in its reporting, and that the test-makers reduce the proportion of whole-number items and increase the proportion of fractions, decimals, and percentages. Mr. Shakrani said officials, however, should be cautious about overemphasizing arithmetic at the expense of such subjects as geometry.

Middle School Deficiencies

The Brown Center study also examined the academic skills of middle school mathematics teachers, based on a survey of 252 teachers nationwide.

Of those polled, only 22 percent said they had majored in math in college, and just 41 percent said they had teaching certificates in the subject. The survey has a 6-percentage-point margin of error.

When it came to teacher efforts to improve their skills, only 32 percent of those polled had taken more than five hours of training in algebra, and 17 percent had undertaken that level of work in geometry. More teachers reported seeking some combination of professional development in a variety of classroom-teaching strategies.

The report describes a 鈥渓ack of focus鈥� in professional-development activities for teachers, with insufficient emphasis on content. Having teachers seek help in two or three well-defined content areas, it says, 鈥渨ould focus resources most effectively.鈥� At least 80 percent of teachers surveyed said that salary increases or stipends would be effective in persuading them to seek such training.

James M. Rubillo, the executive director of the National Council of Teachers of Mathematics, in Reston, Va., said that middle school teachers were more likely than teachers at other grade levels to be bounced among subjects, including mathematics, producing a need for more training. At the same time, he said, providing students with effective middle-grades math instruction is crucial.

鈥淚n middle school, the teacher has to build algebraic and geometric thinking,鈥� Mr. Rubillo said. 鈥淲hat [the report] is saying is that people can鈥檛 teach what they don鈥檛 know.鈥�