Time To Solve the Math Education Equation
The Third International Mathematics and Science Study, one of the most ambitious studies of school achievement in math and science ever undertaken, reports that American 12th graders placed last in comparison with the rest of the world. ("U.S. Seniors Near Bottom in World Test," March 4, 1998.) What kind of indifference to America's public good has allowed such a thing to happen?
On the record, the country's political leaders have been anything but indifferent. Consider the Goals 2000: Educate America Act, passed by Congress with much fanfare in 1994. The act called on our educational system to solidify American leadership of this "age of technology" by raising student achievement in science and math into first place in the world by the year 2000. The U.S. Department of Education and the National Science Foundation were directed to target projects in the hundreds of millions of dollars in pursuit of this goal. The educational battle cry was to "Rethink! Reform!" Standards for science and math were revised; conferences disseminated information on newly developed curricula, materials, and methods of instruction; enhanced training for preservice and in-service teachers was supported. At the same time, most states were implementing their own standards for a variety of subjects and rewarding teachers for strengthening their professional training.
Thus, the 12th grade TIMSS result, placing the United States in the world cellar for math and science, comes as a rude shock. Just what has been going on here between the K and the 12? Shock is still being felt, while constructive suggestions remain largely absent.
There had already been a good deal of unhappiness at the time of the first TIMSS release, which gave results for the 8th grade. American students placed well below the world average. A spate of "perhapses" was put forward: Perhaps our inner-city and rural schools were being pitted against other countries' elite schools, their top students against our democratically diverse ones. Perhaps other countries' students did more homework, or watched less TV, or ...
But then when the 4th grade results came out and our students placed respectably above average, a lively flurry of self-congratulatory statements and op-ed pieces were aired. The reforms were said to be taking hold nicely in elementary schools, while high school reforms had not yet come into place. Despite these brave words, the performance slippage between 4th and 8th grades caused a good deal of uneasiness. Still, this was a warning, however insufficient, of the coming 12th grade meltdown.
TIMSS goes far beyond the simple fact of relative weakness of performance of American students. The results provide useful evidence about some of the sources of our problems. TIMSS refutes the earlier "perhapses" and goes on to diagnose our K-12 math and science instruction as suffering from the "mile wide and an inch deep" syndrome. Ominously, it seems that many of the reform efforts have actually added to this syndrome.
Put another way: Our school systems take our bright, normal children and turn them into dummies. Mass malpractice is perpetrated by insufficiently trained teachers, further constrained by unfocused and often incoherent curricula and textbooks.
Unable to refute TIMSS, some educators have chosen to espouse a strange new paradigm. This suggests that so long as America produces innovative, successful entrepreneurs (like Bill Gates), it does not matter that the rest of our children leave school innumerate and illiterate.
While this is not a view many can be expected to accept, the fact that it was even put forward is troubling. Mathematics and science are basic ingredients of the competence of our young people in the age of advanced technology.
Evidence of breakdown in the K-12 system, pervasive for years, has up to now been swept under the educational carpet in a variety of guises. Complaints of student inability to read, write, and do arithmetic are dismissed as "inevitably" due to a large immigrant and/or "disadvantaged," "inner city" population. Parent questions and complaints are denigrated as "uninformed" and "anecdotal." The 85 percent of community college students who must begin there with remedial courses in what are properly primary, middle, or high school subjects is not considered relevant. The decreased competency of students coming into colleges and universities, and the consequent increasing burden of instruction for those institutions, is similarly shrugged off. School shortcomings also fall heavily on growing numbers of businesses and industries, forced to pay for retraining employees in everything from the three R's to calculus.
Fortunately, Congress still holds to the vision if not the timetable of the Goals 2000 Act and sees TIMSS as a resource that can and should be examined and used to reset the act's proper implementation. The vehicle for this review, to come with recommendations, is embodied in the House and Senate bills introduced simultaneously by Rep. Constance Morella (R-Md.), HR 3411; and Sen. Bill Frist (R-Tenn.), S 1739, as the proposed Commission for American Mathematics Leadership Act. To ensure the highest degree of impartiality and competency, the commission is to act in coordination with the National Academy of Sciences.
The fundamental elements for the proposed commission to address should include the following:
- Establishing the principles and techniques of Teaching to Mastery. The basis of other countries' success is teaching a core of fundamental topics to mastery. Fewer topics are taught, but each is taught deeply. Otherwise, lack of discrimination results in the "mile wide, inch deep" syndrome.
- Aligning mathematics curricula relative to international levels. At present, American mathematics curricula drag behind international levels by as much as two years. Further, topics are presented in a totally superficial way (again, the "mile wide, inch deep" syndrome). Our curriculum for middle school years (grades 4-7) is especially in need of attention, often consisting of aimless repetition without perceptible development.
- Teacher knowledge of basic mathematical materials and enhancement of professional-development criteria. A large percentage of math teachers have studied only a small amount of mathematics at a college level. Further, the professional-development criteria they themselves have studied under tend to ignore knowledge of the subject matter taught. Accordingly, teachers often have only vague and confused understanding of the material they are teaching.
- Teacher preparation in terms of appropriate pedagogy in mathematics teaching. Math teachers in American schools, as the TIMSS analysis reveals, are given little training or practice in effective techniques of presentation of the material in a way helpful to student efforts to master the mathematics.
- The quality and structure ofmathematics textbooks. The criteria by which U.S. textbook publishers form their books are dominated by commercial rather than correct pedagogical considerations. For reasons of expediency (or simple incompetence), most textbooks cover material in a totally superficial way ("a mile wide and an inch deep").
- The development of high-quality state and national standards of mathematics education. Benchmarking is needed in order to have a broadly consistent national set of standards, with considerations of alignment with international standards. This will also be of great value as a reference for local school administrators and school boards, and is desirable in order to deal with our intensely mobile school population.
- The development of adequate administrative structures in school systems to ensure an adequate quality of mathematics teaching. Considerations of cost, or expediency, too often lead to the situation that teachers with totally inadequate preparation and skills are put in charge of mathematics classes.
The proposed commission, and its charge, are bold and hopeful steps for the country to take in setting American mathematics education toward a renewed orientation to excellence.
Madge Goldman has been a leading advocate in the private philanthropic community for the funding of basic mathematical research in the United States and abroad. She is the president of the Gabriella and Paul Rosenbaum Foundation in Chicago and lives in Bryn Mawr, Pa.