Math Group Issues 'Standards' To Update Curricula
In a document scheduled for release this week, the National Council of Teachers of Mathematics underscores recently raised concerns that the math curriculum has failed to keep pace with contemporary needs and offers a new direction stressing the subject's real-world applications.
The council's "Curriculum and Evaluation Standards for School Mathematics" is expected to have a strong influence on state and local curriculum developers, textbook publishers, and test makers.
It is aimed, officials said, at outlining learning goals and teaching strategies that will develop all students' "mathematical power."
"Mathematics now offers unprecedented potential for helping people understand the world," the document says. "Yet in the midst of change, the teaching of mathematics has remained essentially unchanged."
"To equip students for productive, fulfilling lives in the Information Age," it continues, "the definition of success in mathematics—the objectives of mathematics—must be transformed."
Reflecting a growing consensus among math educators, the council recommends that schools shift from an emphasis on paper-and-pencil drill and instead use technologies—including calculators and computers in all grades—to focus on problem solving, communication, and reasoning.
It also proposes that math courses employ actual problems, rather than those contrived for a textbook, to emphasize the subject's real-world applications and its connections to other disciplines.
Shirley M. Frye, the nctm's president, stressed that the standards do not prescribe a curriculum or teaching method, but are intended to be a yardstick against which districts can measure their own programs.
"Some would like us to give a 'Good Housekeeping' seal of approval,'' said Ms. Frye, who is director of curriculum and instruction for the Scottsdale (Ariz.) School District. "That's not our job."
"There is not one way to do this," she pointed out.
'Direction for Reformation'
The 258-page standards are the result of a three-year effort by the organization to set a "direction for the reformation" of the subject, according to Ms. Frye.
The effort began in 1986, when the council appointed a 26-member commission charged with creating "a coherent vision of what it means to be mathematically literate in a world that relies on calculators and computers to carry out mathematical procedures, and in a world where mathematics is rapidly growing and is extensively being applied in diverse fields."
The panel released a draft document in 1987, which was distributed to some 10,000 teachers, curriculum specialists, and test and textbook publishers. Although the final version reflects changes these reviewers proposed, the draft standards have influenced the development of curriculum frameworks in several states, as well as the 1990 National Assessment of Educational Progress.
The new document states that high-quality mathematics instruction is essential to the development of an informed electorate, a mathematically literate workforce, and a generation of lifelong learners.
Moreover, it says, math programs should create opportunity for all students, not just those who intend to study math or science in college.
"Women and most minorities study less mathematics and are seriously underrepresented in careers using science and technology," the document states. "We cannot afford to have the majority of our population mathematically illiterate: Equity has become an economic necessity."
'More Than Concepts and Skills'
Creating such a society, the council argues, demands a new "vision" of the subject.
Mathematics, it says, is "more than a collection of concepts and skills to be mastered; it includes methods of investigating and reasoning, means of communication, notions of context ... [and] the development of personal self-confidence."
"Toward this end, we see classrooms as places where interesting problems are explored using important mathematical ideas," it adds. "Our premise is that what a student learns depends to a great degree on how he or she has learned it."
To "frame" this vision, the nctm developed 40 curriculum standards and 14 evaluation standards schools can use to judge the quality of their programs. Rather than a list of topics or a scope-and-sequence chart, the standards outline models for instruction in grades K-4, 5-8, and 9-12.
Many schools around the country already employ elements of the recommended standards, according to Ms. Frye.
"It isn't as if we're starting with a program that's never been tried," she said.
All the standards, the council states, emphasize "doing," rather than "knowing" math, and stress the way mathematical models apply to other disciplines.
In addition, they encourage the use of technology, particularly calculators and computers. To underscore this emphasis, the council recommends that calculators be available to all students at all times, and that every student have access to a computer.
"Calculators and computers for users of mathematics, like word processors for writers, are tools that simplify, but do not accomplish, the work at hand," the document states.
Copies of "Curriculum and Evaluation Standards for School Mathematics" (Stock Number 396) are available for $25 each from the National Council of Teachers of Mathematics, 1906 Association Drive, Reston, Va. 22091.