Perhaps Nobody Will Count
In the National Research Council's recent report, "Everybody Counts,'' a distinguished group of mathematicians, scientists, engineers, and computer scientists outline the problems facing mathematics education and recommend changes in both the curricula and the teaching methods used in American schools. (See Education Week, Feb. 1, 1989.)
Written by Lynn Arthur Steen, professor of mathematics at St. Olaf College, the study eloquently describes the sorry state of math education and persuasively explains the importance of mathematics for the future of this country. For these reasons alone, it should be in the hands of educators, parents, and legislators across the nation.
But many mathematicians have serious reservations about other aspects of "Everybody Counts": It neglects influences outside the field on our students' poor performance, and it de-emphasizes the importance of rote learning and pencil-and-paper skills in mastering the applications of mathematics.
The report does not adequately place students' inability to do mathematics in the context of broader educational failure. The causes of "innumeracy" cannot be isolated from those of illiteracy or of the general ignorance characterizing so many of today's young people; these problems have common origins unrelated to specific subject areas.
The litany can be found in any educational publication: If parents will not involve themselves in their children's education--for example, by turning off the televisions and reading books themselves--how can we expect many students to apply themselves? If we are unwilling to encourage our best young people to go into teaching, how can we expect to find enough inspired teachers in our schools?
The fact is that as long as students perceive that there is no need to work hard--some college will accept them, and parents don't really care--they will not learn much, regardless of the subject, curriculum, or teaching method.
The committee that prepared the report apparently felt that these issues either were not in its purview or were too obvious to repeat. Instead, it directed its attention to curricular and pedagogical reforms. This is the standard approach of educators--after all, instructional plans and methods are the only educational mechanisms they control.
But most experienced educators are also familiar with the futility of this exercise. At the University of California at Los Angeles, we have changed the calculus text and syllabus every two or three years for the last 30 years in an attempt to address the deteriorating situation. But this effort has been a complete waste of time.
And if we examine those countries with more successful educational institutions, we find a wide spectrum of different curricula. The one characteristic shared by these countries--but absent here--is a strong commitment to education.
Although we probably cannot improve mathematics education by changing the curriculum, we can certainly make things worse. One way to do so is to pretend that because students can use calculators, they no longer need to master the basic arithmetical and algebraic manipulations. Sadly, such an approach is endorsed by the report.
It is true that calculators are an essential tool to anyone who uses arithmetic and that everyone should be comfortable with them at an early age. But ignorance about these instruments is not one of the major problems in math education.
At ucla, we have students who do not know the multiplication table. Would the committee agree with these students that such rote learning isn't important since they can always use their calculators? In Los Angeles, advertisements for bank tellers indicate that candidates "should know fractions." The need for such a stipulation suggests that many of our young people do not know which buttons to push on their calculators when they must manipulate fractions.
In one of its most shocking pronouncements, the report claims:
"Weakness in algebraic skills need no longer prevent students from understanding ideas in more advanced mathematics. Just as computerized spelling checkers permit writers to express ideas without the psychological block of terrible spelling, so will the new calculators enable students who are weak in algebra or trigonometry to persevere in calculus or statistics."
Having taught calculus for nearly 30 years, I can state categorically that if students can't factor x9 instantly (and many of our students cannot), it is extremely unlikely that they will pass the course. To succeed in calculus, students must be fluent in algebra--and that means the algebraic language must be in their heads, not just in their calculators.
The committee has refused to confront the fact that an appreciable amount of what we teach, in mathematics as in other disciplines, is learned by rote. Is the necessity of such learning really a surprise? Do we tell young musicians that they need not learn their scales because they can use synthesizers? And what about those electronic foreign-language dictionaries that are now appearing--should students not bother to learn vocabulary before taking a French literature course?
Mathematics is above all a language, and its basic elements are first absorbed through drill. Although we can give conceptual explanations of every operation--as the "new math" set out to do--this tedious exercise uses sophisticated methods to prove boring facts. The payoff in mathematics is not in the remarkable self-consistency of its grammar, but in what one can say with it.
As the report correctly emphasizes, it is the application--the "word problems"--that ultimately justifies mathematics to students. Motivation in any language comes with fluency--the power to express new ideas. But if students do not have an immediate command of the arithmetical and algebraic vocabulary, calculations and formulas become gibberish.
The "legacy of misunderstanding, apprehension, and fear" cited in the report is not a consequence of the curricula or teaching methods. Rather, because of a lack of motivation, our students do not learn enough of the basic manipulations to build any self-confidence. It would seem that only in athletics do parents and students accept the validity of the slogan "no pain, no gain."
The photographs illustrating the report accurately suggest its content. We see lots of calculators, computers, and other gadgets--but not a single picture of a student with just a pencil, paper, and a mess of calculations.
This omission reflects another serious weakness of the report: the confusion it creates between the tools mathematicians might use and mathematics itself. The public perception of the importance of computers in virtually every facet of modern life is sound; it is now just as important to be able to program as to use a library. But such skills should not be taught in mathematics courses, although both computers and libraries should be used to enrich math classes (how many students today are encouraged to look up mathematics books in their libraries?).
Our students' problems lie not in their pencils or books, but in their weak grasp of essential skills. The nation's problem is that only the educators seem to care.
Vol. 08, Issue 29, Page 36Published in Print: April 12, 1989, as Perhaps Nobody Will Count