The differentiated curriculum, on the other hand, is a single-sequence curriculum in which the first three years constitute the core of learning that all students are expected to experience.
To compete successfully in the publishing marketplace of the 1990’s, educational publishers must begin producing a new generation of mathematics materials that reflects both a new emphasis on electronic learning aids and a changing understanding of how math should be taught, according to leading math educators.
The idea that the math classrooms of the decade will be technologically oriented “mathematics communities’’ that operate in harmony with the teaching and curriculum standards developed by the National Council of Teachers of Mathematics was sounded repeatedly here last week at a conference entitled “N.C.T.M. Standards: Implications for Instructional Materials.’'
The meeting--which was jointly sponsored by the N.C.T.M. and the School Division of the Association of American Publishers--was one in a series of regular conferences that the publishers’ group schedules to keep materials developers current on trends in education.
Noting that the N.C.T.M. standards describe a world in which all students perform “meaningful mathematics’’ using “appropriate’’ tools, Cathy Lynn Seeley, a former math coordinator for the Texas Education Agency, told attendees that many math educators agree that the document “absolutely, positively means technological tools.’'
And, added Diane Briars, the math coordinator for the Pittsburgh school district, publishers should not be wary of branching out into electronic media.
Indeed, she said, they should act as catalysts for change.
“Technology will be purchased for the public schools if [instructional] materials require [it],’' she said.
Changing Dispositions
Donald A. Eklund, the A.A.P.'s vice president, noted that the meeting was particularly timely in light of the national push, articulated by President Bush and the nation’s governors, for excellence in math instruction.
The standards, which have been widely hailed as exemplary and are influencing the development of similar standards for science education, place a strong emphasis on conceptual learning over computational skills and on real-world applications over abstract teaching.
“The standards are about changing kids’ disposition toward being involved in math,’' said Glenda Lappan, a mathematics professor at Michigan State University.
But, unless texts and other materials change dramatically to reflect the standards’ philosophical underpinnings, she said, there will be little, if any, change in the way that math is taught.
“If we don’t put our focus on writing better materials for teachers, we will have missed the boat,’' she said. “We will not serve the needs of teachers until we write better materials from which teachers can learn.’'
And presenters noted that machines used in isolation, as is generally the case in today’s classrooms, will not effect meaningful change.
“The computer has got to be used to radically change instruction,’' said John Olive, a professor of mathematics education at the University of Georgia.
As an example, Mr. Olive demonstrated several computer-generated “microworlds’’ that he and his colleagues have developed that allow young children to manipulate computer graphics in order to learn about counting and number theory and the properties of fractions and ratios.
A Common Curriculum
Mr. Eklund, however, said he is leery of predictions that textbooks have essentially been made obsolete.
“It’s not going to be “either-or,’ '' he said. “But textbooks are going to be much smaller.’'
Even so, other speakers emphatically warned that publishers cannot afford to ignore the new trends.
“This is a fundamental change that you as publishers will have to respond to,’' said John Kenelly, the alumni professor of mathematics at Clemson University. “This is not ‘Son of New Math.’ ''
But not all presenters focused on such electronic aids as computers, videodisks, and calculators as the source of meaningful change.
Christian Hirsch, a professor of mathematics and math education at Western Michigan University, unveiled a proposed “common-core curriculum’’ for secondary schools that the N.C.T.M. will publish as one of a series of addenda to its standards documents.
Mr. Hirsch, who edits the addenda series, said the new document proposes, for purposes of discussion and further refinement, a “two-sequence course of study’’ in which three years of instruction constitute a “common core’’ of mathematical learning.
“This is ‘mathematics for all’,’' he said. “It’s an attempt to give curriculum developers a new way of thinking.’'
The excerpts from the document, “A Core Curriculum: Making Mathematics Count for Everyone,’' contain two alternative methods for revising the existing curriculum--based on preparing students for the next course--that is used in most secondary schools.
The “crossover model,’' which is intended to be a transition to a core curriculum, uses current texts, but focuses in its early stages on more concrete topics.
The curriculum is designed to give more prominence to actual applications of the mathematics taught and to “lighten the calculation and symbol manipulation load by integrating calculator and computer software use into all work.’'
The differentiated curriculum, on the other hand, is a single-sequence curriculum in which the first three years constitute the core of learning that all students are expected to experience.
The fourth year of instruction would consist of courses designated “mathematics for college-intending students.’'
