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Many Factors Make Up Effective Math Teaching, Report Concludes

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Effective mathematics instruction is the result of a complex web of factors, many of which can be controlled by educational policymakers and are independent of socioeconomic and other conditions, according to a new analysis of data collected by the National Assessment of Educational Progress.

The report, "Effective Schools in Mathematics," was prepared by researchers from the Educational Testing Service for the U.S. Education Department's National Center for Education Statistics.

It argues that when such factors as race and wealth are controlled for, characteristics of the instructional program can accurately predict whether the program will be effective.

The findings are based on questionnaires completed by teachers, students, and administrators as part of the NAEP assessments from 1990 and 1992.

"Our most salient finding is that there is not one single variable that, if manipulated, will bring about effective schooling," said Sharif Shakrani, the chief of design and analysis at the N.C.E.S. "There is no silver bullet."

Groundbreaking Study

The findings were discussed publicly for the first time last week at a seminar in Washington for researchers and NAEP participants held by the department's office of educational research and improvement.

The report compares the characteristics of the top-performing schools with those performing at the bottom on the assessment.

It found that variables such as curriculum, instructional strategies, school climate, and how testing is related to instruction have an impact on whether an instructional program is effective.

But no single factor in isolation can insure effective instruction, Mr. Shakrani said.

"These are things that schools can do that are within their power to bring about a change," he said. "But if we simply say that all students should take algebra from now on, it's not going to do it."

The study breaks new ground, Mr. Shakrani added, by examining the conditions necessary within schools to foster academic success.

"We always look at the [performance of] individual students; we never look at what is available to them," he said. "What is important here is that for the first time we are looking are what the schools offer that allows students to succeed."

Factors of Success

The study examines factors that contribute to academic success in math in grades 4, 8, and 12.

For example, the researchers found that at the 4th-grade level, transience and a "school culture" centered on academic achievement have important consequences for student success.

Schools in which students move every two years or do not have a positive attitude toward school tend to be far less effective, Mr. Shakrani said.

"At the 8th grade we found something more interesting," he added. In effective schools, 8th graders were enrolled in algebra rather than general math and planned to take geometry classes.

Students in effective 8th-grade programs tended to watch less television than students in weaker programs, he said.

Effective schools at the 12th-grade level shared such characteristics as a "very well-defined mathematics curriculum for all students," he said.

"In other words, they do not track students," he added. "They have high standards for all of their students."

The report notes that while two years' worth of data is insufficient to establish the existence of trends, there were signs in the NAEP data of movement toward effective reform of math education.

Indicators of Reform

Some of those indicators include:

  • Students indicated that they were taking more advanced courses. At the 8th-grade level, for example, 28 percent of students reported taking pre-algebra in 1992, compared with 20 percent in 1990. At the same time, the percentage of students enrolled in "general" math classes dropped from 61 percent to 49 percent.
  • Students and teachers also reported increased access to calculators and computers. According to the NAEP data, 59 percent of 4th graders had access to school-owned computers in 1992, compared with 44 percent in 1990.
  • Students and teachers also reported increased emphasis on daily problem-solving exercises.

More students over all, meanwhile, reported "more positive attitudes about the value of math."

Copies of "Effective Schools in Mathematics" are available for $7 each from the N.C.E.S.'s education-information branch at the U.S. Education Department, 555 New Jersey Ave., N.W., 20208-5641; (800) 424-1616. The document-order number is 065-000-00706-1.

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