Washington--With a dramatic plea for the nation to “wake up” to the need to address the impoverished mathematical abilities of its young, the National Academy of Sciences last week called for a sweeping overhaul of the way the subject is taught at all levels of education.
Among its recommendations for elementary and secondary schools is a controversial proposal that teachers make greater use of hand-held calculators as a way of helping their students keep pace with a “mathematical revolution” that favors the logic of problem-solving over purely computational skills.
The report by the academy’s National Research Council warns that failure to correct existing educational deficiencies will have social as well as economic consequences.
“We are at risk of becoming a divided nation in which knowledge of mathematics supports a productive, technologically powerful elite while a dependent, semiliterate majority, disproportionately Hispanic and black, find economic and political power beyond reach,” it says.
Although reform is needed in much of the education system, the report notes, math is particularly crucial because of its central role in preparing students for job opportunities and in developing their thinking skills.
Despite this importance, however, most Americans lack the mathematical literacy needed for the future, the report asserts. Three-fourths of all students stop studying the subject before completing prerequisites for college- or career-level work, it maintains, and international comparisons have shown that the achievement level of U.S. students lags far behind that of other countries.
These trends have developed in large part, the study contends, because schools have failed to adapt math instruction to current and future needs.
In addition, it says, “broad-brush” reform efforts, such as the push to increase graduation rates, have exacerbated the problems by failing to raise standards for achievement.
To bring about meaningful4changes, the academy report urges national leaders to wage a massive campaign to develop new curricular standards; enhance teacher professionalism; design new forms of assessment that meet instructional goals; and push for the creation of a “tradition’’ of elementary-school math specialists.
Above all, it says, leaders must generate political support, so that such changes can be implemented at the local level.
But while the need for reform is “urgent,” the report concludes, the prospects for success are good.
“Because of emerging general agreement within the mathematics, mathematics-education, and related professional communities on goals for mathematics education and the means for achieving them,” it states, “there is at this time a special opportunity for the nation to push ahead boldly in this area of education.”
“It is time to act,” the academy concludes.
‘A Special Role’
The report issued last week, “Everybody Counts,” is the “public preface” to the work of three academy committees charged with studying problems in mathematics education and working to bring about reforms.
“It is not the final report of a commission,” the academy’s president, Frank Press, notes in a foreword, “but the beginning of a process in which teachers, state and local authorities, and the varied constituencies of mathematics education can draw together in a sustained revitalization effort.”
The committees include the Mathematical Sciences Education8Board, a 34-member panel of mathematicians and educators focusing on math education at all levels; the Board on Mathematics Education, a 15-member committee studying math research; and the Committee on Mathematical Sciences in the Year 2000, a 21-member group addressing proposals for reforms in undergraduate math instruction.
Over the next few years, the groups expect to issue additional reports on curricular reforms, work with parents, and hold symposia on minority achievement, among other activities.
The report, written by Lynn A. Steen, professor of mathematics at St. Olaf College, notes that while all subjects are important to students’ educational and career prospects, math “plays a special role in school education.”
Because of the growing importance of science and technology in a technological society, the document argues, mathematical “habits of mind’’ are increasingly vital to youths’ career opportunities.
Moreover, it suggests, an understanding of the subject is an important element in developing general literacy, because of the growing mathematical content of written material, such as newspaper articles.
Properly taught, the report observes, math can inculcate the “power of thought,” rather than the “power of authority.”
‘Raise the Water Table’
These benefits notwithstanding, schools have failed, the study charges, to generate either a sufficient supply of mathematically trained personnel or an adequate level of general mathematical literacy.
Such problems will become more acute in the coming decades, it notes, as the proportion of women and minorities in schools grows. These groups, the report points out, have traditionally been underrepresented in math; yet, by the end of the century, only 15 percent of net new entrants to the labor force will be white males.
"[T]he United States is reasonably successful in tapping and channeling the highly visible talent springs which develop without speel10lcial support from formal schooling,” it states. “But these sources are inadequate to our national need. We must, in addition, raise the entire water table.”
Schools have been hampered in part, the report suggests, by the erroneous belief among many Americans that performance in the subject is based on innate ability, rather than effort, and by peer pressure that ''makes good performance in mathematics socially unacceptable.”
But perhaps more importantly, it states, school math has failed to keep pace with changes in mathematical sciences.
“The arithmetic, algebra, geometry, and calculus taught nowadays are mere shadow images of modern mathematics,” it states.
The growing use of computers and calculators, together with the increase in mathematical applications in a wide range of fields, the study says, have created a “revolution” in the mathematical sciences “that must be reflected in the schools if our students are to be prepared for tomorrow’s world.”
To incorporate such changes, teaching in the field must shift from an emphasis on rigid rules and procedures to an approach that encourages students to discover patterns and make conjectures based on observations, the study contends.
“We believe that the ‘lecture-and-listen’ format that currently predominates in most mathematics classrooms is one reason why so many students are turned off to mathematics early in their lives,” Shirley A. Hill, chairman of the academy’s math-education board, said at a press conference here.
“We recommend that teachers serve more as class facilitators, moderators, questioners, and coaches than as lecturers,” Ms. Hill said. “The basic goal should be to encourage students to think mathematically, rather than simply to memorize mathematical skills without understanding.”
In addition, the report states, the objectives for math instruction at all levels should shift to reflect present-day and future needs.
In particular, it says, elementary-school instruction should move beyond the traditional focus on “shopkeeper” arithmetic skills to an emphasis on the development of “number sense.”
Young people should not only know how to estimate and calculate, it advises, but also how to decide whether to estimate and calculate.
Developing such skills, the academy argues in a proposal likely to be controversial, would require greater use of hand-held calculators.
In addition to exposing young peo4ple to tools most adults use routinely, it notes, the use of calculators can also enable children to move beyond simple whole-number computations.
“Many adults fear that early introduction to calculators will prevent children from learning arithmetic ‘properly,’ as their parents learned it,” the report states. “The experiences of many schools during the last 15 years show that this fear is unfounded.”
“Students who use calculators,” it maintains, “learn traditional arithmetic as well as those who do not use calculators and emerge from elementary school with better problem-solving skills and much better attitudes about mathematics.”
High-school math, according to the report, should continue to focus on “the transition from concrete to conceptual mathematics.”
But the secondary curriculum should encompass greater breadth than it currently does, and should help students develop “symbol sense.”
“High-school graduates need to know enough about chance to understand health and environmental risks; enough about data and experiments to understand the grounds for scientific conclusions; enough about representation to interpret graphs; and enough about the nature of mathematics to be supportive parents to their children, who will learn aspects of mathematics that their parents never studied,” it concludes.
Reforms in the undergraduate curriculum are the “linchpin” for revitalization efforts, it adds, and should be aimed at producing a new generation of teachers exposed to the instructional styles and course content required for classroom improvements.
“It will no longer do for teachers to teach as they were taught in the paper-and-pencil era,” it asserts.
Copies of “Everybody Counts--A Report to the Nation on the Future of Mathematics Education,” are available for $7.95 each, with discounts for multiple orders, from the National Academy Press, 2101 Constitution Ave., N.W., Washington, D.C. 20418.
A version of this article appeared in the February 01, 1989 edition of Education Week as Academy Urges Nation To ‘Wake Up’ And Revamp Mathematics Education