Effective reform of precollegiate mathematics demands the development of more sophisticated and wider-ranging forms of student assessment than the simple “end of chapter” multiple-choice tests now commonly in use, according to a document released last week by the National Council of Teachers of Mathematics.
Assessment should be a continuous process, based on multiple sources of evidence of student ability, including class discussions, written presentations, and illustrations as well as traditional paper-and-pencil examinations, the document says.
The N.C.T.M. unveiled the 102-page framework, “Assessment Standards for School Mathematics,” during a news conference here.
“We know that math assessment should reflect what is important for students to learn, rather than what is easy to assess,” said Diane J. Briars, a math specialist with the Pittsburgh public schools and a member of one of three working groups that drafted the standards.
The publication of the assessment standards completes a trio of documents that embody the N.C.T.M.'s vision of what students should know and be able to do in precollegiate math. The other documents are “Curriculum and Evaluation Standards for School Mathematics,” which was released in 1989, and “Professional Standards for Teaching Mathematics,” published in 1991.
Because the previous documents outline a more challenging and comprehensive math curriculum than has been in place in most U.S. schools, they necessitate the use of assessments that break with tradition, officials of the math teachers’ group said.
“As math education broadens to give all students the opportunity to learn richer and deeper mathematics,” said Jack Price, the N.C.T.M.'s president, “we found ourselves asking, ‘Are we allowing students of varying backgrounds to demonstrate their knowledge, or are we merely relying on forms of assessment that are convenient and cost-effective?’”
The assessment document emphasizes a shift toward more comprehensive exams that “present a more balanced, equitable means on which decisions about students’ performance can be based,” Mr. Price added.
Six Basic Tenets
The assessment standards emphasize six tenets about valid assessments. These tenets say that assessments should:
- Reflect the mathematics that all students need to know and be able to do;
- Enhance mathematics learning;
- Promote equity;
- Be an open process;
- Promote valid inferences about mathematics learning; and
- Be a coherent process.
Under the rubric of equity, for example, the document asserts that traditional assessments have too long ignored differences in students’ experiences, physical condition, gender, and ethnic, cultural, and social backgrounds “in an effort to be fair.”
Because of those differences, “students may need to specify the assumptions that they are making when they communicate the results of their work,” the document adds. “Assessors need to be open to alternative solutions.”
Officials of the council said the assessment standards are firmly grounded in research, particularly in the findings contained in “Measuring What Counts: Prototypes for Mathematics Assessment,” which the Mathematical Sciences Education Board published in 1993.
They also said the assessment standards should help educators create measurements that offer more than just a simple means to rank individual students, districts, or states.
Anticipating Critics
Unlike the previous math-standards documents, which were published to little public fanfare, the assessment standards were released in a climate of public skepticism about national education standards in general, and resistance in some school districts to the math standards in particular.
In Palo Alto, Calif., for example, a parents’ group called Honest, Open, and Logical Debate on mathematics reform, or HOLD, has challenged efforts to implement a program based on the state math curriculum framework, which the group has dubbed “the new ‘new math.’” (See Education Week, 5/10/95.)
The California framework, which is similar to the N.C.T.M. achievement standards, downplays rote drill and encourages “authentic assessment” of student performance.
Perhaps in response to the criticism, N.C.T.M. officials last week noted that more than 2,000 people, not all of them math educators, reviewed and commented on the assessment standards over the past three years.
The standards, officials added, make more demands of all students.
“Of course we expect students to learn basic skills such as addition, subtraction, multiplication, and division of whole numbers and fractions,” said Thomas J. Romberg, the director of the assessment-standards project. “But, teaching those skills only through rote drill is a recipe for frustration, forgetting, and eventual failure.”
“Students are not going to live in a textbook,” Mr. Romberg added. “They are going to live in a world awash with numbers, where problem-solving, decisionmaking, and the accurate uses of technology are essential to everyday life.”
