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National math test

Discerning how

The test for fourthgraders also has "false rigor," Loveless said: More than 40 percent of questions gauge first and secondgrade skills, two levels below the students tested.
The central fault, Loveless contends, is that too many problemsolving questions rely on whole numbers, with too few challenges involving fractions, decimals and percentages. Such instruction sets students up for trouble in more advanced high school classes and in daily life, where tasks such as shopping and measuring rarely involve neat, round numbers, he said.
"If we want kids to be sophisticated problemsolvers, they've got to be able to think beyond whole numbers," Loveless said.
Known as the nation's report card, the National Assessment of Educational Progress is the most widely respected measure of the skill levels of U.S. students. Given to representative samples of students, it is offered periodically in many subjects, including math in 2003.
A leader of the National Assessment Governing Board, which sets the test content, strongly disagreed with the findings, saying the study is flawed because it is based on a questionable formula of what kids should know when.
The Hawaii state coordinator of the National Assessment of Education Progress echoed that opinion. "The scores were pretty dramatically higher in Hawaii as well as nationally," said Robert Hillier.
Hawaii's fourthgraders gained 11 points in the 2003 math testing, and eighthgraders gained four points. The results were compared with 2000 test results.
"I'd be surprised if people found the questions easy," Hillier said. "It is very doubtful to me that they were first and secondgrade level." He had not seen the study and would not comment further until he had studied the criticism.
Hawaii fourthgraders averaged 227 points total out of a perfect score of 500. The number ranked at or above proficient in math was 23 percent compared with 31 percent nationally. The Hawaii score was 14 percent in 2000.
Hawaii eighthgraders reached a 266point average. Only 17 percent were considered proficient in math, compared with 27 percent nationally. Hawaii scored 16 percent in 2000.
The study, being released today, analyzed questions from the 2003 math tests and then determined a grade level for those questions based on the Singapore math textbook program.
Loveless said he chose that program because of its clarity and strong international reputation, and he said it compared well with the mathclass sequences used in states such as California and North Carolina.
But using Singapore as a model presents skewed results, said Sharif Shakrani, deputy executive director of the assessment governing board. Math is taught differently in that country, with heavy concentration on computation early before other topics are introduced. U.S. schools go for breadth, he said, with more math skills to cover each year.
Overall, he said, the questions on the national in fourth grade and eighth grade are commensurate with what is being taught in those grades.
"I contend that if we do what he suggests, moving to much more complex skills, it would be akin to giving a test in Russian," Shakrani said. "We already are not doing well. If you increase the cognitive function of the math concepts and the way you test them, you will end up with scores so low you will not be able to make sense of the results."
Some questions  about 20 percent of them  are intentionally the same on the fourth and eighthgrade tests to help track growth in achievement over grades, Shakrani said.
Scale scores on the math tests have risen sharply for fourth and eighthgraders since 1990.
Answer to sample problem: E
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