False Rigor: 8th-Grade Math Test Requires Only 3rd-Grade Skills

Published January 1, 2005

The dramatic gains in student test scores on a national math exam over the past decade are being called into question by an analysis from the Brookings Institution’s Brown Center, which found questions on fourth-grade and eighth-grade tests to be “extraordinarily easy” since they tested mainly third-grade skills.

The report also found a significant number of middle school math teachers did not major in math in college, do not hold a teaching certificate in the subject, and are not receiving adequate professional development to build subject mastery.

The National Assessment of Educational Progress (NAEP) is an exam given to a sample of students across the nation for the past 30 years to gauge the level of student proficiency over time. Since 1990, the NAEP math test has reflected the recommendations of the National Council of Teachers of Mathematics (NCTM).

“The good news is that NAEP scores have risen dramatically in mathematics over the past decade,” noted Tom Loveless, director of the Brown Center on Education Policy. NAEP test scores indicate today’s eighth-graders know about as much math as a typical tenth-grader in 1990, and today’s fourth-graders are about two years ahead of their 1990 counterparts, too.

However, Loveless questioned whether the gains were real, pointing out that most of today’s eighth-graders are not even enrolled in the higher math courses–Algebra I, Algebra II, and geometry–that many of the tenth-graders in 1990 had completed. To address this concern, he examined the publicly released questions posed in NAEP exams to determine the level of mathematical skill actually tested. His results are reported in the 2004 Brown Center Report on American Education: How Well Are American Students Learning?

Loveless discovered that most of the arithmetic required to solve the average question on the fourth-grade and eighth-grade NAEP math tests is taught by the end of third grade. Even though the mathematics required to answer many NAEP questions is “extraordinarily easy,” he found students at both grade levels had trouble getting the right answers.

For both the fourth- and eighth-grade tests, the accompanying chart shows the cumulative percentage of questions on the NAEP math test that require the math skills taught through a given grade level. Thus, 64.1 percent of the fourth-grade NAEP test questions require only third-grade skills or less. Remarkably, 58.1 percent of eighth-grade NAEP test questions also require only third-grade skills or less–and 90.7 percent of the eighth-grade NAEP test questions require only fifth-grade skills or less. A bare 9.3 percent of the questions on the eighth-grade test probe skills beyond those required for the fourth-grade test.

Few Correct Answers

Loveless’s analysis also broke down how well students scored on questions at each grade level:

  • About half of fourth-graders answered questions at a first- and second-grade level correctly.
  • About half of eighth-graders answered first- and second-grade level questions correctly.
  • Thirty-one percent or fewer of fourth-graders were able to answer questions at a third- through fifth-grade level correctly.
  • Less than one-third of eighth-graders answered questions requiring seventh-grade skills correctly.

The study found whole-number arithmetic predominated in the questions at fourth and eighth grade, with few problems requiring students to use fractions, decimals, and percentages. Failure to grasp these basic mathematical concepts has repercussions since proficiency in the use of non-whole numbers is needed to solve higher-level mathematics such as algebra.

“Really knowing algebra means being able to solve equations that contain more sophisticated forms of numbers than whole numbers,” noted Loveless. “Calling these items algebra is conveying a false sense of rigor, making very simple math seem more sophisticated than it actually is.”

Students will be able to solve only “mathematically trivial” problems if they cannot handle fractions, decimals, and percents, cautions the report.

The report recommends the following steps for improving the teaching and testing of U.S. students:

  • Raising the level of arithmetic skill required in NAEP exams by including more test questions involving the manipulation of non-whole numbers.
  • Assessing arithmetic skills of students in fourth and eighth grades, since computation is especially important for algebra readiness.
  • Replacing easy “algebra” questions with appropriate grade-level math problems.
  • Eliminating calculator use at fourth-grade level and restricting its use in eighth grade.

Teacher Qualifications

The report also examined the subject mastery of middle school math teachers. To do this, the Brown Center surveyed 252 middle school math teachers across the nation. Of those responding to the survey, only 22 percent majored in math in college, and only 41 percent held a teaching certificate in mathematics.

Most of the teachers surveyed indicated they had received professional development on four or more topics, while 44 percent received development on four to seven topics. Although most viewed the training they had received in the past two years as somewhat or very helpful, a majority also believed that they and their colleagues needed additional training.

“Professional development for middle school mathematics needs to be focused on the core knowledge and skills teachers must master in order to teach their students effectively,” Loveless recommended.

Blue Ribbon Schools

The new report also revisited the issue of the Department of Education’s Blue Ribbon Schools Program. The 2000 Brown Center Report had found roughly one-fourth of the schools honored with the Blue Ribbon distinction had scored below the 50th percentile on their states’ assessments of academic achievement.

While the proportion of lower performing designees was reduced to 9 percent in the 2003 program, the study suggests more could be done to raise the standard. For one thing, the report recommends, the U.S. Department of Education could standardize its definition of “dramatic” improvement.

Another recommendation for raising the standard is to remove the section of the application dealing with how a school is implementing trendy practices such as community partnerships and conflict resolution programs. Also recommended is making use of data from Just for the Kids and Standard and Poors to choose schools based on performance.

Krista Kafer ([email protected]) is senior policy analyst for education at The Heritage Foundation.

For more information …

The November 2004 publication, 2004 Brown Center Report on American Education: How Well Are American Students Learning? by Tom Loveless, is published by The Brookings Institution Press and available online at http://www.brookings.edu/gs/brown/bc_report/2004/2004report.htm.

Sample questions from the National Assessment of Educational Progress are available online at http://nces.ed.gov/nationsreportcard/itmrls.