Should 4th graders master addition, subtraction, and other simple arithmetic?
Should 8th graders be tested on the basics of algebra even though the subject still isn’t usually taught until high school?
Should any student taking a math test have the aid of an electronic calculator?
The debates over such questions have been centered on state and local decisions—until now.
The National Assessment Governing Board, which oversees the only federal testing program, is proposing to change the guidelines that define the content on its mathematics exams. In doing so, the board has spawned a debate over what should be tested on the flagship National Assessment of Educational Progress, and what help students should receive in taking the tests.
A committee of mathematicians and educators impaneled by the board has recommended slight changes to the existing frameworks that spell out what will be on the math tests that are given every four years.
The tests produce national results and scores for individual states that participate in the program. Results of the math tests administered last year showed 4th and 8th graders posting steady increases over the decade since NAEP began using the current form of the tests. (“Math NAEP Delivers Some Good News,” Aug. 8, 2001.)
At a public hearing in Washington last week on the proposed changes, different sides in the controversies over how to teach mathematics and what student knowledge to assess aired familiar arguments.
The proposed changes would continue a pattern of reducing the emphasis on basic arithmetic skills, according to Tom Loveless, the director of the Brown Center on Education Policy at the Brookings Institution, a Washington think tank.
The proposal would shrink the proportion of NAEP questions that gauge 8th graders’ skills in “numbers and operations” to 20 percent of the test. That would be 5 percentage points lower than on the current test. About 40 percent of the 4th grade exam would be made up of such arithmetic functions.
“That’s far too low,” argued Mr. Loveless, especially because NAEP’s survey of teachers finds that 87 percent of 4th grade teachers and 72 percent of 8th grade teachers place a “heavy emphasis” on such skills.
“It creates a test that does not reflect what teachers are currently doing, and it doesn’t reflect what teachers should be doing,” said Mr. Loveless.
By contrast, the leader of the nation’s largest group of math educators supports the current frameworks and the proposed changes for the most part.
But by raising the proportion of 8th grade questions that incorporate algebraic principles to 30 percent, NAEP may not get a fair measure of students’ skills, said Lee V. Stiff, the president of the 100,000-member National Council of Teachers of Mathematics.
“Algebra as an 8th grade course does not exist for a lot of students,” said Mr. Stiff, a professor of mathematics education at North Carolina State University in Raleigh. “When we evaluate young people, we should evaluate them on what they have had an opportunity to learn.”
The process of revising the frameworks included voices from across the spectrum of mathematics education. The committee included many representatives of the NCTM and other advocates of teaching both the concepts of math and its functions.
It also had members who say math education must stress the basic skills. “They’ve cured some of the defects,” said Frank Y. Wang, the chairman of Saxon Publishers Inc., a privately held Norman, Okla., textbook company noted for emphasizing skills, and a member of the planning committee that produced the proposed frameworks.
“But I still have some nuts-and-bolts reservations with some of the aspects of the frameworks.”
For example, NAEP would continue to allow the use of calculators on about a third of the exam questions—a decision that runs contrary to those who believe students need to master arithmetic.
Mr. Stiff, however, said students should continue to be allowed to use calculators on portions of the exam. “Calculators and technology are important tools in learning mathematics, so they should not be ignored,” he said. “They should be included in some way because they reflect what’s happening in the schools and what’s happening in the real world.”
The governing board is scheduled to decide on the mathematics frameworks at its November meeting, according to Lawrence Feinberg, the board’s assistant director of reporting and analysis.