The Real Scandal in American School Mathematics


Anthony Ralston
Professor Emeritus of Computer Science and Mathematics, SUNY at Buffalo

As printed (slightly edited) in Education Week 27 April 2005




The recent results from the PISA (Program for International Student Assessment) study have highlighted once again the continuing failures of American school mathematics education. This failure has been the subject of continuing controversy, the so-called Math Wars, between research mathematicians and mathematics educators. This controversy has centered mainly on matters of curriculum and how or whether technology should be used in math education. But by far the most important issue with respect to math education, the quality of the cadre of American school 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 for the Math SAT at a private high school, when he asked the students how to express 5 + 9/100 + 3/10000 as a decimal, every student started punching numbers into a calculator. A cautionary tale, indeed. But it tells us, I think, less about the use or misuse of calculators in schools than it does about the math teachers who allowed students to develop such appalling habits. In fact, all the arguments in recent years about curriculum and calculators are almost irrelevant compared to the single greatest challenge affecting American school mathematics: How to do something about the steady decline in the past half century of the intellectual abilities of those who teach mathematics in American schools.

There have been urgings from both mathematicians and mathematics educators about improving the pre-service education of mathematics teachers and about providing more and better in-service programs to upgrade the skills and knowledge of elementary and secondary school mathematics teachers. But (almost?) not a word about the quality of the input to college and university mathematics teacher education programs?

Why not? One reason, I think, is that mathematicians, although they seem to be quite happy to engage in college and university mathematics educator-bashing, do not want to be seen as teacher-bashers since this would smack of elitism and, as well, there are already more than enough politicians, parents and others who criticize school teachers.

Nor do I wish to be accused of teacher-bashing. Of course, 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. Nevertheless, if there has been and continues to be a decline in the quality of entrants into school mathematics teaching, this needs to be said because until this trend is first arrested and then reversed, nothing else that is done about American mathematics 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 two former teachers, Who's Teaching Your Children? Why the Teacher Crisis is Worse Than You Think and What Can Be Done about It by Vivien Troen and Katherine Boles (Yale University Press, 2003) claims that "the number of good classroom teachers is in perilous decline and will continue to worsen". And whatever is true about classroom teachers generally will be true in spades for mathematics teachers since the intellectual demands of teaching mathematics are greater than those for almost any other school subject.

But how do we know that this decline in the quality of mathematics teachers has actually taken place? There is some direct evidence: the number of uncredentialled secondary school mathematics teachers throughout the US, 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 her book, Knowing and Teaching Elementary Mathematics (Lawrence Erlbaum, 1999), various studies showing widespread math phobia among elementary school teachers. Then there is the anecdotal evidence such as that at the beginning of this piece.

But quite aside from all the evidence there is, at least for me, an irrefutable logical argument that the intellectual level of American school mathematics teachers must have been declining for the past half century or longer. The large majority of American school teachers, particularly elementary school teachers, are, as they always have been, women. Until World War II, the only professions generally open to women were teaching and nursing. But since WWII all the hitherto male-dominated professions have gradually become accessible to women, some completely so, others less so. All these other professions are better paid than teaching; many are much better paid. Moreover, over the same period American schools, particularly in urban areas but not only there, have steadily become more unpleasant, less safe and more stressful workplaces. Of course, some people embrace teaching as a profession from the sheer love of it. But surely not all that many now or ever. So even though there are many more women in the workforce than 50 years ago, I submit that it must be the case that fewer and fewer of the best and the brightest go into school teaching, particularly school mathematics teaching since there are so many opportunities outside of teaching for the mathematically proficient. Indeed, the surprising fact is not that the US has far fewer mathematically competent teachers than it needs but rather that it has as many competent mathematics teachers as it does have.

There is, I think, a second reason other than a wish to refrain from teacher-bashing why mathematicians generally stay away from this issue. This is that they despair of being able to have an impact on this problem because they have no special expertise, as they think they do on such matters as curriculum and teacher training, which could be brought to bear on it. I share that despair. Attracting the needed numbers of mathematically competent teachers to American schools will not happen in my lifetime nor in the lifetimes of most people who read this. The words in the No Child Left Behind (NCLB) act about having a qualified teacher in every classroom are pure cant because there are no programs in that act that might attract those qualified teachers to American schools. In fact, the opposite is true because the testing regimen in NCLB is sure to dissuade people from taking up teaching as a profession. And the increasing use of direct instruction must be an anathema to anyone who really wants to help kids learn mathematics.

It is thus a scandal that so little attention has been paid to attracting better qualified teachers to American schools. What can be done? I can only suggest that, instead of all the time and energy spent on arguing about curriculum and related matters, mathematicians and mathematics educators should devote their energies to make the case that those we attract to elementary and secondary school mathematics teaching need to be as intellectually able as those attracted to law, medicine and, yes, to the academic world. This means making the case for 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 mathematics educators but, of course, not only by them, the future of American education will depend. NCLB is at least correct that quality teachers are needed in all classrooms. Without them future generations will be as mathematically impoverished as the current generation already is.