The Real Scandal in American School Mathematics
Results from the most recent study of the Program for International Student Assessment, or PISA, have highlighted once again the continuing failures of American school mathematics education. ("Poor Math Scores on World Stage Trouble U.S.," Jan. 5, 2005.) These failures have been the subject of a long-running controversy, the so-called Math Wars, between research mathematicians and mathematics educators. The debate has centered mainly on matters of curriculum and how or whether technology should be used in math education. By far the most important issue, however, the quality of the nation’s cadre of K-12 mathematics teachers, is seldom mentioned.
Recently, a member in good standing of the Anti-Calculator Brigade told me the following story. While giving a review course at a private high school for the math section of the SAT, he asked the students how to express 5 + 9/100 + 3/10000 as a decimal. Every student assembled started punching numbers into a calculator.
It is a cautionary tale, to be sure. But it says less about the use or misuse of calculators than it does about the math teachers who allow students to develop such appalling habits. In fact, all the arguments in recent years about curricula and calculators are virtually irrelevant when compared with the single greatest challenge facing American school mathematics: how to do something about the steady decline over the past half-century of the intellectual abilities of those who teach math in our schools.
Both mathematicians and math educators have urged improving the preservice education of math teachers and providing them with more and better in-service programs to upgrade their skills and knowledge. But practically nothing has been said about the quality of those entering teacher education programs in mathematics.
Why not? One reason may be that mathematicians, who seem quite happy to disparage collegiate-level mathematics educators, don’t want to be seen as “teacher bashers.” This would smack of elitism. It also might seem to be overkill, since more than enough politicians, parents, and others are ready to criticize school teachers.
Nor do I wish to be accused of teacher-bashing. There are many excellent secondary school mathematics teachers, and many elementary school teachers more than capable of teaching just about any mathematics curriculum they are given. Yet if there has been and continues to be a decline in the quality of entrants into school mathematics teaching, this needs to be said. Until such a trend is recognized, arrested, and reversed, nothing else we do about math education will make much difference.
That the quality of people going into teaching has been declining for decades is hardly an original thought. A recent book by former teachers Vivien Troen and Katherine Boles, Who’s Teaching Your Children? Why the Teacher Crisis Is Worse Than You Think and What Can Be Done About It (Yale University Press, 2003), claims that “the number of good classroom teachers … is in perilous decline and will continue to worsen.” And what is true of classroom teachers generally will be true in spades for mathematics teachers, since the intellectual demands of teaching math are greater than those for almost any other school subject.
But how do we know that this decline in the quality of math teachers actually has taken place? There is some direct evidence: the high number of uncredentialed secondary school mathematics teachers—indeed, the number who have neither a major nor a minor in mathematics; the poor grasp of basic arithmetic by the “above average” elementary school teachers studied by Liping Ma in Knowing and Teaching Elementary Mathematics (Lawrence Erlbaum, 1999); various studies showing widespread math phobia among elementary school teachers. And then, of course, there is the anecdotal evidence, such as my colleague’s calculator story.
Quite aside from the evidence, however, there is an irrefutable logical argument to be made that the intellectual level of American school mathematics teachers must have been declining for the past half-century or longer. We know that historically the great majority of schoolteachers in this country, particularly those in the elementary grades, have been women. Until World War II, the only professions generally open to women were teaching and nursing. Since that war, however, all the hitherto male-dominated professions have gradually become accessible to women—some completely, others less so. These other professions are better paid than teaching—many are much better paid—and exert a powerful career pull for exceptionally talented women who once might have been teachers.
Moreover, during this same period, American schools—particularly those in urban areas, but not only there—have steadily become more unpleasant, less safe, and more stressful workplaces. Some people, of course, embrace teaching as a career because of the sheer love of it. But surely not all that many, now or ever. So even though many more women are in the workforce than were 50 years ago, it must be the case that fewer and fewer of the best and the brightest go into schoolteaching, particularly mathematics teaching. So many opportunities exist outside of teaching for the mathematically proficient. Indeed, the surprising fact is not that the United States has far fewer mathematically competent teachers than it needs, but that it has as many competent ones as it does.
Other than a wish to refrain from teacher-bashing, there may be another reason mathematicians generally stay away from this issue: They despair of being able to have an impact on the problem. They have no special expertise here, as they think they do on such matters as curriculum and teacher training.
I share this despair. Attracting the needed numbers of mathematically competent teachers to American schools will not happen in my lifetime, nor in the lifetimes of most of those who read this essay. The language in the federal No Child Left Behind Act about having a highly qualified teacher in every classroom is pure cant, because there are no programs in that law that might attract those qualified teachers to American schools. The opposite is true, in fact, because the testing regimen in the law is sure to dissuade people from taking up teaching as a profession. And the increasing use of direct instruction must be anathema to anyone who really wants to help kids learn mathematics.
It is a scandal that so little attention has been paid to attracting better-qualified math teachers to American schools. What can be done?
Instead of all the time and energy spent on arguing about curriculum and related matters, mathematicians and mathematics educators should devote their energies to making the case that those we attract to elementary and secondary mathematics teaching need to be as intellectually able as those attracted to law, medicine, and, yes, the academic world. This means supporting higher salaries and better working conditions for all teachers, in the forums where mathematicians and mathematics educators have some influence: the national academies, the National Science Foundation, and whatever other bodies can be influenced in Washington and the state capitals.
This will be a long, hard slog. But on the eventual success of such efforts by mathematicians and math educators (but, of course, not only by them), the future of American education will depend. The No Child Left Behind Act is at least correct in its assertion that high-quality teachers are needed in all classrooms. Without them, future generations will be as mathematically impoverished as the current generation already is.
Vol. 24, Issue 33, Page 35Published in Print: April 27, 2005, as The Real Scandal in American School Mathematics