Report Offers Glimpse of Mathematics Assessment of the Future

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WASHINGTON--Providing a glimpse of the future of mathematics assessment, the Mathematical Sciences Education Board last week released a report describing 13 "prototype'' math-assessment tasks for 4th graders.

While not exhaustive, the tasks are aimed at showing different ways of measuring the type of learning called for by the standards for the field developed by the National Council of Teachers of Mathematics, according to Nancy S. Cole, the report's author.

"The N.C.T.M. standards, and other math-reform efforts, are directed toward new kinds of learning for students in mathematics,'' said Ms. Cole, the executive vice president of the Educational Testing Service. "For those new goals, we have to have very different kinds of assessments.''

Although several schools have begun to revamp their assessment systems to match the reforms, Ms. Cole noted, a recent study funded by the National Science Foundation found that most tests do not reflect those goals.

In contrast to traditional tests, the prototype tasks included in the new report ask students to solve problems using reasoning skills, and to communicate their answers in writing or some other form, rather than simply to choose the correct answer.

Taking from one to three class periods to complete, they include a range of activities that involve both pencil-and-paper work and manipulative materials. One involves the use of a computer-graphics program.

In addition to the tasks themselves, the report also includes background activities to prepare students for the tasks, rationales that indicate the skills and knowledge they attempt to tap, and characteristics of high, medium, and low performance.

But while teachers can use the tasks in classrooms--in fact, they were all tested in elementary schools in four states--they are intended primarily for a "hypothetical audience'': students who have been through a revamped math program. For current students, it says, the tasks may be "daunting.''

"Teachers should look at the prototypes,'' the report states, "not as current expectations, but rather as goals to aim for.''

Not a Ready-Made Assessment

The report issued last week, "Measuring Up,'' is a direct follow-up to a national mathematics assessment "summit meeting'' held in Washington in April 1991.

At that meeting, the report notes, Gov. Roy Romer of Colorado, then the chairman of the National Education Goals Panel, "challenged the mathematical community to show the nation what mathematics edu cx12p4 el-95lcators mean by mathematical power and what new and more demanding standards will mean for our young people.''

In response, the M.S.E.B., an arm of the National Academy of Sciences, agreed to develop a set of prototypical assessment tasks, and convened a writing group consisting of math educators from universities, schools, and research centers.

The report cautions that the document--which it calls a "work in progress''--is not intended to present an assessment that could be administered immediately.

For one thing, it notes, the panel was not asked to consider issues of cost, efficiency, and feasibility.

In addition, the report, by focusing on tasks, does not include other forms of assessment, such as projects and portfolios, and does not represent the full range of topics that 4th graders should know and be able to do, it states.

"Much that is important in the curriculum is not covered adequately in the particular examples chosen for this volume,'' the report states.

Variety of Formats

In presenting the tasks, the report notes, the authors set out to show that assessments can be introduced in a variety of formats: by videotapes or by teachers, with manipulative materials or computers. The report also includes two tasks that are presented in Spanish as well as in English.

"Too often,'' it says, "test questions and assessment tasks are presented solely in written form, which may be a burden for poor readers and for children whose first language is not English.''

It also notes that the tasks allow students to respond in different ways, including constructing an object and creating a pattern on a computer screen.

In keeping with the N.C.T.M. standards, the tasks differ sharply from traditional math tests.

Their content, for example, incorporates a variety of mathematics, particularly topics--such as statistics, geometry, and probability--that are seldom emphasized at the K-4 level, the report notes.

One task, for example--which asks students to analyze a graph network related to a checkers tournament--was included partly to show that some mathematics does not involve computation, the centerpiece of the traditional elementary curriculum.

Allowing Students To Decide

In addition, all of the tasks offer students the ability to decide how to solve problems and to explain how they went about solving them.

In fact, the scoring rubrics indicate that students who provide well-reasoned explanations for their responses earn higher scores than those who simply provide the correct answer.

Moreover, in some cases, the report points out, there is no "right'' answer.

"A question is not very good if the right answer is a single number,'' Ms. Cole said. "There are better answers and less-good answers.''

Several of the tasks also allow students to decide how they will answer questions.

One task, which asks students to draw a new geometric figure called a "hexaright,'' deliberately leaves too little space to answer the question.

"The purpose of this is to force the child to decide what kind of paper to use,'' the report states. "Centimeter graph paper will be helpful to some students and a distraction for others.''

In another task, which asks students to generate equations to solve an arithmetic game called "bowl-a-fact,'' the questions leave unstated whether a calculator should be used. In the N.C.T.M. standards, the use of calculators is an important skill.

But while calculators should be available to students, the report notes, "it will soon become clear to them that calculators have very limited value in this situation. In fact, using a calculator to generate an equation to knock over pins is an extremely inefficient way to approach the task.''

"Thus,'' it says, "one reason for using these kinds of tasks is to sharpen students' perception of when calculators are useful and when they are not.''

Copies of the report, "Measuring Up: Prototypes for Mathematics Assessment,'' are available for $10.95 each, prepaid, plus $4 for shipping, from the National Academy Press, 2101 Constitution Ave., N.W., Washington, D.C. 20418.

Vol. 12, Issue 14

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