Public acceptance of deficient standards contributes significantly to poor performance in mathematics education.
—Everybody Counts, 1989
Mathematics education cannot be effective without strong support from society. Unfortunately, misconceptions about mathematics are deeply rooted in school and society, in home and family. From students' early years colleges inherit an enormous deficit of scholarly maturity. Interest payments on this deficit balloon college enrollments in remedial and school-level mathematics courses. Indeed, about two-thirds of all college mathematics enrollments are in school-level courses (below the level of calculus). In America today, the profile of mathematics in higher education is not much different from that of mathematics in high school.
The source of many of these difficulties can be found in public (and parental) attitudes about mathematics that are rooted more in myth than in reality:
At Spelman College in Atlanta, 8 percent of the graduates major in mathematics—a rate far greater than the national average of 1.6 percent.
The success of the mathematics and natural science program at Spelman is due to the special attention given to students that builds their confidence in their own ability to master mathematics. All natural science students participate in an eight-week summer program prior to the beginning of their first year, during which study skills are developed and role models are established. This careful mentoring is continued throughout the undergraduate program and develops into opportunities for research experiences and special honors sections. The faculty devotes a great deal of energy to advising, since student motivation is the most powerful factor in learning.
Not only does Spelman produce a large number of minority mathematicians and scientists, but its NASA Program for Women in Science and Engineering graduates a higher-than-average percentage of women mathematics majors who go on to pursue graduate studies in mathematics.
Myth: Success in mathematics depends more on innate ability than on hard work.
Reality: Sustained effort can carry most students to a satisfactory level of achievement in mathematics. Compare music and mathematics: although in both areas genetic factors clearly play a role at the very highest levels of creative achievement, parents and teachers generally believe that children can learn to play music at a reasonable level if only they exert sufficient effort. As a consequence, many
students achieve success and personal satisfaction from their study of music. Whenever parents or teachers believe that genetic ability is the primary factor contributing to success in mathematics, students are likely to fail before they begin; when expectations of success are high, so is the resulting performance.
Myth: Women and members of certain ethnic groups are less capable in mathematics.
Reality: The popular notion that women, Blacks, and Hispanics "can't do math" is just an expression of ignorance or prejudice. Ample evidence shows such beliefs to be false. Experiences of countries such as Holland and Japan belie this myth, as do results from numerous innovative programs in the United States. Such examples demonstrate unequivocally that most college students can succeed in mathematics when learning takes place in an appropriate structure and context.
Myth: Most jobs require little mathematics.
Reality: The truth is just the opposite: more and more jobs—especially those involving the use of computers—require the capability to employ sophisticated quantitative skills. Although a working knowledge of arithmetic may have sufficed for jobs of the past, it is clearly not enough for today, for the next decade, or for the next century.
Myth: All useful mathematics was discovered long ago.
Reality: Mathematical discoveries are essential for industrial competitiveness. Without advances in mathematics we would have neither telephones nor computers, neither jet airplanes nor international banking. Technology depends on both old and new mathematics for innovation and power. Indeed, more new mathematics is being created and used each year than ever before in history.
Mathematics in Action
One way to link undergraduate mathematics to industrial research and development is through student projects in mathematical modelling. Many such programs are patterned after the Mathematics Clinic, which began at Harvey Mudd College nearly twenty years ago. In these programs, which now operate in dozens of institutions, a team consisting of one or more faculty and several students works on an unsolved mathematically oriented problem that comes from a company or government agency.
The problems are usually open-ended and must first be cut down to a manageable size. Faculty leaders assist with the mathematical model and give "short courses" on the mathematics that seems to be needed. Different students work on different parts of the problem, parts that suit their interests and expertise, but teamwork is the mode of operation. Students must make formal oral presentations in terms understandable to the client; as a result, they develop strong expository skills. Written reports are submitted to the client at the end of the project, and so the writing involved in these reports is also a part of the students' education.
Texas Prefreshman Engineering Program
The Texas Prefreshman Engineering Program (TexPREP) was started in 1986 as a statewide expansion of the successful San Antonio PREP program begun in 1979 by Manuel P. Berriozabal, Professor of Mathematics at the University of Texas at San Antonio. The purposes of TexPREP are to recruit potential future scientists and engineers by identifying high-achieving middle school and high school students and by providing these students with academic reenforcement to pursue science and engineering fields. The program operates in 14 Texas cities on 19 college campuses.
Of the 4500 students who have participated in TexPREP, more than three-quarters have been minority students and half have been women. Of the college-age participants, nearly 90 percent either are attending college, plan to attend, or have graduated from college. Sixty percent of TexPREP graduates major in science or engineering fields. TexPREP features a strong academic component, with courses in logic, algebra, probability and statistics, problem solving, engineering, computer science, physics, and technical writing. Other activities include field trips, guest speakers, and practice SAT examinations.
Myth: To do mathematics is to calculate answers.
Reality: Rarely do workers or researchers confront mathematical problems requiring primarily calculation. Authentic problems are often ambiguous, admitting many forms and several answers. Mathematical power is revealed as much by the act of identifying and properly posing problems as by application of specific techniques and algorithms.
Myth: Only scientists and engineers need to study mathematics.
Reality: Mathematics is a science of patterns that is useful in many areas. Indeed, the most rapid areas of growth in applications of mathematics have been in the social, biological, and behavioral sciences. Financial analysts, legal scholars, political pollsters, and sales managers all rely on sophisticated mathematical models to analyze data and make projections. Even artists and musicians use mathematically based computer programs to aid in their work. No longer just a tool for the physical sciences, mathematics is a language for all disciplines.
If these myths were benign, with effects limited to the ignorance of those who believe them, they might be safely ignored. But ignorance in parents and teachers begets ignorance in students. Harmful myths about mathematics metastasize to the body politic, spreading ignorance and excusing underachievement throughout society. Efforts to eradicate these pernicious myths will require sustained support at all educational levels, but especially in colleges and universities where society's leaders are educated.