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Students Fall Short on 'Extended' Math Questions, Study Finds

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WASHINGTON--Between one-third and two-thirds of students perform poorly on mathematics questions that require them to take time to reason and to explain their answers, a new analysis of data from the 1992 National Assessment of Educational Progress suggests.

The 1992 mathematics exams, which were given to nearly 250,000 students across the country in grades 4, 8, and 12, were the first to include what testing experts call "extended, constructed-response'' questions in addition to multiple-choice and short-answer questions.

Designed to reflect changes in math instruction being called for by education reformers, these questions required students to spend up to five minutes figuring out the problem and using words or pictures to explain their methods.

The analysis, which was released last week by the National Center for Education Statistics, shows that although most students made some attempt to answer such questions, their performance "left much to be desired.''

Answers given by one-third to two-thirds of the students, the report says, "showed little evidence of understanding the mathematics concepts involved or even the question being asked.''

As many as one-fifth of the students, when confronted with the new questions, left their papers blank.

By contrast, students appeared to have a much easier time with multiple-choice questions, correctly answering half or more of those items.

"These findings can certainly be viewed as pessimistic and even worrisome,'' said John A. Dossey, the math professor who led the study. "Many of these students are in classrooms where they have no opportunities to do this type of problem-solving activity.''

Much Variation

The analysis also indicates that:

  • The gap between white and black students' performance on the newer types of questions is substantially greater than that on multiple-choice and short-answer questions. (See Education Week, June 23, 1993.)
  • Even though by the 12th grade male students tend to outperform female students on the overall NAEP examination, the groups had comparable scores on the extended-response questions.
  • Students in advantaged urban areas performed significantly better than did students from disadvantaged urban areas on the new questions.
  • The questions appeared to be difficult even for students who took more advanced math courses. Those students, however, also tended to give better responses than their counterparts taking more basic courses.
  • More costly than traditional test items, the extended-response questions provide four times as much information about higher-performing students' math abilities.

"For what you get for the item, the cost is very reasonable,'' said Sharif Shakrani, chief of the design and analysis branch of the education assessment division of the N.C.E.S.

By comparison, multiple-choice items, which allow students to guess at some answers, may "camouflage'' students' weaknesses in math, Mr. Dossey said.

The 1992 NAEP math tests contained five extended-response questions on the 4th-grade examination and six each on the 8th- and 12th-grade tests.

One such item, for example, asked 4th graders: "JosÀe ate of a pizza. Ella ate of another pizza. Jose said that he ate more pizza than Ella, but Ella said they are both the same amount. Use words and pictures to show that JosÀe could be right.''

About 23 percent of the students were able to answer that question correctly to varying degrees. Almost half of all students taking that examination, however, gave wrong answers. Seven percent gave none at all.

In addition, 28 percent of white 4th graders gave satisfactory or better responses to the question, compared with only 9 percent of black students and 12 percent of Hispanic students.

The report also includes student-performance data for each of the states and territories.

Information on ordering the report, "Can Students Do Mathematical Problem Solving?,'' is available from the Education Information Branch, Office of Educational Research and Improvement, U.S. Education Department, 555 New Jersey Ave., N.W., Washington, D.C. 20208-5641.

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