Math Group Sets New 'Vision' for Curriculum
The National Council of Teachers of Mathematics last week unveiled proposed standards for the K-12 math curriculum that set forth a new "vision" of the way the subject should be taught and tested.
The 179-page document, which could be revised before it is released in final form next year, is intended by its authors to serve as a "yardstick" against which states and school districts can measure their own mathematics programs.
"This will get before the teaching community, for the first time, a relatively clear statement of expectations concerning what should be accomplished in school mathematics," said Lynn A. Steen, professor of mathematics at St. Olaf College and a member of the commission that drew up the document.
The standards call for a shift away from math classrooms in which students chiefly work at their desks at pre-assigned exercises.
Instead, the statement proposes, students should be encouraged to explore problems using mathematical concepts, make conjectures, and discuss ideas.
In addition, it urges:
A greater reliance on computers and hand-held calculators in all grades to help improve students' problem-solving skills;
An increase in the use of mathematical models across the curriculum;
A complete overhaul of high-school math to provide a new core curriculum for all students; and
New forms of assessment that would enable teachers to better understand the level of students' mathematical skills.
Unlike past efforts to reshape the mathematics curriculum, such as the "new math" approach of the 1960's, the proposed standards are not intended to be implemented "from the top down," said Iris M. Carl, supervisor of elementary math for the Houston Independent School District #14 and a member of the standards commission.
"In many school districts," she noted, "teachers are now involved in looking at recommendations of national organizations and making decisions about where they should be going."
Some states and districts have already moved in the direction the nctm recommends. But most have not, according to the council, and its statement anticipates that the proposals will encounter resistance from teachers and administrators accustomed to traditional practices.
"A teacher who believes that the speed of paper-and-pencil calculation to find answers to arithmetic problems is important is going to be reluctant to let children use calculators," the statement acknowledges. "The administrator who has charted group scores on the standardized test that has been given in the district for years is going to be reluctant to replace it."
"Our hope and expectation," it says, "is that there are a sufficient number of persons willing to work so that reform is accomplished."
The nctm study is one of three major projects under way that are attempting to redefine the content of mathematics instruction in elementary and secondary schools.
The Mathematical Sciences Education Board, a branch of the National Academy of Sciences, is developing a set of curriculum guidelines for the subject, and the American Association for the Advancement of Science, through its Project 2061, is working to define what math students in the middle of the next century should know.
The three projects are "complementary and consistent," said Shirley A. Hill, chairman of the math-education board.
The nctm project was designed to set a target that school systems could aim for in the next five years, she explained, while the other projects are intended to set long-term goals for math education.
Plans for Early Grades
Four working groups, composed of teachers, supervisors, researchers, teacher educators, and mathematicians, collaborated on the nctm document. One group proposed standards for student assessment, while the other three examined math curricula for grades K-4, 5-8, and 9-12.
Specifically, the document proposes a stronger, more conceptually oriented curriculum for the early grades. Such a curriculum, it argues, would build on math skills children have when they enter school, help prepare them for more advanced study, and help shapeel10ltheir understanding of what math is and how it can be used.
The K-4 curriculum, it recommends, should actively involve students in "doing" math, include a broad range of content, and emphasize applied math.
In grades 5-8, the proposal says, the curriculum should cover a broader range of mathematical topics--including statistics, probability, geometry, and measurement--than has been typical in the past.
Such an approach, it says, would offer students in the middle grades "the intellectual stimulation appropriate to the students' capabilities and important to their future."
Overhaul of High-School Math
At the high-school level, the statement argues, a complete overhaul of the math curriculum is needed.
In contrast to the current curriculum, which commonly offers a wide range of courses geared to differing interests and abilities, it proposes a core curriculum "that will reflect the needs of all students, who will spend their adult lives in a society increasingly dominated by technology and quantitative methods."
The document recommends that all high-school students study at least three years of math through courses that integrate topics traditionally taught under discrete subjects, such as algebra and geometry.
The curriculum, it says, should be changed to place less emphasis on "memorization of isolated facts and procedures" and greater emphasis on conceptual understanding and problem-solving.
New approaches to student assessment at all grade levels must accompany the curricular reforms, the document says.
Contending that tests made up of questions that call for a single correct answer "no longer suffice," it suggests using other methods of evaluation, such as observing students as they work on math problems alone or in groups.
The draft document will be presented to a broad range of educators and policymakers over the coming year. While they are likely to suggest changes, said Mr. Steen of St. Olaf College, the basic structure will probably remain intact.
"There is going to be a lot of dissent on particular things," he said. "There are issues that people will say are impractical. But I don't think there will be any change in the philosophical stance."
When complete, the standards, because they carry the imprimatur of the nctm, will bolster state and local efforts to reform the math curriculum, predicted Joan Akers, chairman of the math committee of the state curriculum commission in California.
"This represents a national consensus of what a good math program should be," she said. "That gives strength to documents like the California curriculum framework."
Dorothy S. Strong, director of the bureau of mathematics for the Chicago Public Schools, agreed.
"Nobody knew how to get to the moon," she said. "We needed somebody to say, 'We are going to the moon,' and then we figured out steps to get there. That's what's happening in math education."