Curriculum, Methods Held Responsible for Math 'Crisis'
Washington--All fifty states faced a shortage of mathematics teachers last year, and the problem will get worse before it gets better, according to a group of mathematicians and educators who met here last week.
The shortage of qualified mathematics teachers and "quantitative thinkers" will grow more pronounced over the next 12 years, according to Richard D. Anderson, a mathematician at Louisiana State University. Mr. Anderson chaired a special session called "The Developing Crisis in the Mathematics Classroom: Some Causes and Cures" at the American Association for the Advancement of Science's (aaas) annual meeting.
The situation will become worse, Mr. Anderson said, not only because fewer students are electing to enter mathematics-related careers, but also because the number of 20-year-olds in the population--future mathematicians, teachers, and technicians--will drop by 25 percent over the next dozen years. Hence, he said, 25 percent more of the population of young people must choose such careers in order to maintain the numbers of the current work force--which, he added, are already inadequate.
"It's going to get a lot worse," he said. "We're going to need many more people who think quantitatively."
The situation in secondary-school mathematics is already grim, according to Zalman Usiskin, an associate professor of education at the University of Chicago. Last year, mathematics was the only subject area in which all 50 states reported teacher shortages, he said.
Moreover, Mr. Usiskin said, the shortages are likely to continue. In 1971, Illinois colleges and universities graduated 653 students certified to teach mathematics. In 1981, Mr. Usiskin said, the corresponding number was fewer than 100. In Maryland, 180 certified mathematics teachers graduated in 1971. A decade later, the number was down to 36.
Why this is so, however, remains a matter of speculation among experts. Several cited the phenomenon of low-salaried teachers being lured away from the profession by the high salaries paid by industry. Others pointed out that teaching is perceived by some people as a low-status occupation; one participant, a high-school mathematics teacher, said that even her students told her, "You must not be a very good mathematician since you're teaching high school."
Other participants, however, offered more subtle reasons for the shortage.
The secondary-school mathematics curriculum is one seldom-considered culprit, argued Mr. Usiskin. "The decision to teach mathematics in the first place is based more upon a person's experiences with high-school mathematics than with the job market," Mr. Usiskin said. The prospective teacher must not only enjoy mathematics, but must believe that he or she will enjoy teaching it and that it is a worthwhile subject for others to study.
"These feelings can only be based upon one's own high-school experiences," Mr. Usiskin said, "and thus, we are led to conclude that the high-school experiences of too many students in the recent past have not been positive enough to make them want to teach mathematics."
In an analysis that he acknowledged was somewhat speculative, Mr. Usiskin argued that the curriculum taught during a particular era can be linked to the supply of mathematics teachers four to eight years later. That time frame allows for a lag between "what goes on in high school and its effect on the number of college graduates ready to teach mathematics," he said.
Recent history offers support for the theory, he suggested.
Since World War II, he said, there have been two eras in which there were severe shortages of math teachers--1955-59 and 1977-81--and one, 1969-71, during which enrollment in math education programs peaked. Allowing for the four- to eight- year time lag, these three eras correspond with three distinct fashions in high-school mathematics curriculum.
The curriculum in the 1960's--the only era of plenty in the supply of mathematics teachers--was marked by innovation, modernization, an emphasis on "discovery" methods of teaching, and a focus on brighter students.
During the other two eras, which--according to Mr. Usiskin's analysis--correspond with later shortages of mathematics teachers, the curriculum was out-of-date with respect to mathematics and its applications; teachers relied more on classroom drill; and the focus was on improving the performance of slower students.
These practices made mathematics unattractive as a career, Mr. Usiskin believes. During the 1960's, in contrast, high-school students found mathematics exciting, and were attracted to it as a career, he said.
An Ohio mathematician offered a different set of reasons for students' apparent reluctance to choose careers in mathematics and science. By the time they get to college, argued Joan R. Leitzel, an associate professor of mathematics at Ohio State University, students' math skills are so poor, that for most of them, a career that requires further math simply is not an option.
Students entering Ohio State take a math placement test, Ms. Leitzel said, and are placed at one of five levels for college mathematics. During the late 1970's, 27 percent of the students were placed in the lowest level, which presupposed no knowledge of algebra.
Increase in Students
And between 1974 and 1980, Ohio State experienced a 72-percent increase in the number of students taking remedial mathematics. Those freshman who must take remedial math courses during their first year cannot take college-level math or science courses until their sophomore year. As a result, Ms. Leitzel said, they seldom elect math or science as majors.
In the past several years, Ohio State has made a major effort to reach high-school students and teachers. University officials began sending "performance data" on freshmen back to the high schools from which they graduated, so that high-school officials could see that many of their students were not adequately prepared for college math and, possibly, could make changes that would improve math preparation in the future.
As an experiment, university staff also administered mathematics tests to high-school juniors from one school. Forty percent of them scored in the lowest category. This year, at the request of high-school officials, the university will test juniors from 230 high schools.
Mathematicians from the university have also worked with teachers from two high schools to develop a math course for seniors whose skills are inadequate. After taking this course, high-school students in all but the lowest levels have gone on to succeed in college math courses.
Ms. Leitzel said that the university hopes to expand this program to 24 high schools next year although, she said, "We know that a last-chance remedial program in high school is not the answer."
The problem could be partially solved if high-school students were aware that the math courses that meet minimum requirements for college admissions--generally two years of high-school math--are often not adequate preparation for college math.
Ohio State and other universities are making efforts to alert students and their advisers to the problems a minimally-prepared student might face in college-level math courses, Ms. Leitzel said. Ohio State, for example, has published a heavily demanded booklet that describes the math courses high-school students should take if they plan to continue their study of math or science in college.
The present state of math education, the speakers agreed, is encumbered with closely related problems of curriculum, teaching methods, and teacher shortages. And, they said, there appear to be no quick remedies to break this cycle. However, they suggested, raising teachers' salaries to a level competitive with industry, making sure students take enough math in high school to allow them to continue in math or science in college, and taking a close look at how mathematics and science are taught would begin to ease the problems.