Many talented mathematicians have devoted a great deal of time and effort to improving mathematics education in the public schools. There have been a few small successes here and there, but the problem remains as critical today as it was when “A Nation at Risk,” the study that motivated much of this work, was published twenty years ago. A new book entitled Who’s Teaching Your Children, by Vivian Troen and Katherine C. Boles, argues that a large part of the reason why so much money and effort have had so little effect is the lack of qualified teachers and the culture of incompetence that makes it hard to train and to retain good teachers.
It’s all too easy to treat the problem in the abstract. Here are some concrete examples from my personal experience.
A second grade teacher asks students to divide a radially symmetric figure into four equal parts. A student divides the figure into four equal parts with a horizontal and vertical line through the center. The teacher marks that answer wrong. The student complains. The teacher shows the student the “right” answer in the book — the figure divided into four equal parts by two diagonal lines through the center. The teacher asks the student, in a scornful voice, “Do you think you are smarter than the book?” The book does not mention that there may be more than one correct answer.
A third grade teacher teaches students that the way to add fractions is to add the numerators and add the denominators. A college professor points out that this is incorrect, and gives the example “According to your rule, a half chicken plus another half chicken is two fourths of a chicken.” The grade school teacher, defiant, announces, “I’m the teacher. I can teach any way I want and you can’t stop me.”
A grade school textbook teaches that 7 – 4 + 2 = 1, because, according to the rule “My Dear Aunt Sally” we must do the addition before the subtraction.
A principal sitting in on a class where a teacher fresh out of college is teaching hears the teacher say that a square is a rectangle with four equal sides. The principal stands up and tells the class that their teacher is stupid, because everybody knows that a square is not a rectangle.
These stories exemplify the problem: If mathematicians do not have the power to keep blatant errors out of the classroom, we certainly do not have the power to institute reforms.
Who’s Teaching Your Children was written by authors who have broad personal experience as public school teachers. We had better listen to what they have to say. They provide compelling evidence that the trouble with our public schools is a culture of incompetence. According to this book, “…classroom teaching competency is lower now that it has been since the era of the one-room schoolhouse.”
The book and movie Serpico tell the true story of a New York policeman who tried to be honest. He found it impossible. Even though he adhered to the code of the schoolyard, and never tattled on another cop, the other policemen found his honesty intolerable. Who’s Teaching Your Children describes vividly an analogous situation: Incompetent teachers find competent teachers intolerable and drive them away. In one of the most moving stories in the book, the authors tell how an outstanding principal, together with a group of extraordinary teachers, tried to turn one school around. They made the mistake of letting the other teachers see what a low opinion they had of them. “[The other] teachers complained bitterly, some with shaking voices and tears in their eyes, about being snubbed, shut out, or just ignored.” The other teachers were not villains. It is human nature to resent being told you are wrong. But any teacher who tries to do a good job had better be prepared. In her employment folder there will be numerous complaints from other teachers, complaints that she is “stuck up” and “does not get along.”
Public school teachers and principals are largely autonomous in their own domain. Reform efforts fail because incompetent teachers and principals do not want, will not tolerate, reform.
The problem begins in the colleges and universities, where the weakest students are encouraged to be teachers and the stronger students are advised not to be teachers. It continues in the public schools. If a young teacher asks for guidance or advice the older teachers laugh at him behind his back. The effect is clear, and it is quantifiable. According to Who’s Teaching Your Children, “The best teachers are leaving American classrooms at an accelerating rate.” Society at large reinforces the problem because, despite the rhetoric one often hears, people seem to have little real respect for teachers. The common saying, “Those who can, do; those who can’t, teach” suggests that we expect that teachers will be incompetent.
As long as the public school culture supports bad teachers and drives out good teachers, our schools will continue to get worse and worse. To attempt reform without addressing this problem cannot possibly work.
People are reluctant to even talk about the problem, both because we do not want to hurt people’s feelings, and because we fear that criticism of incompetent teachers will reflect badly on the many good and dedicated teachers who struggle to survive in a broken system. But the incompetent teachers do not have any qualms about hurting the feelings of the good teachers or about hurting the feelings of inquisitive students.
If we want to make a difference, we have to accept that we cannot drive out or If we want to make a difference, we have to accept that we cannot drive out or change incompetent teachers. We must find ways to fight the system itself rather than getting bogged down fighting individuals within the system. We need to lobby our school boards to hire principals who support good teaching. Most important, we need to encourage good students to become teachers, while being honest about the problems they will face, and we need to support good teachers.
Here are a few things I believe would help. Citizens should start by demanding safe schools. To spend one cent on “Teacher Enrichment” when teachers (and children) fear for their safety is absurd. More than 100,000 teachers are victims of violent crimes in school every year. No wonder people leave teaching.
We should also enforce existing laws to stop incompetent teachers from entering the system. Every year more than 50,000 teachers are hired who do not meet already existing standards. School systems say that there is not enough money to hire competent teachers. It is ridiculous to spend billions testing students when their teachers cannot pass standardized tests. MADD has been successful. How about Mothers Against Terrible Teaching?
As mathematicians we should, when speaking publicly, make clear the difference between our personal opinion and mathematical fact. Say, “In my personal opinion, I do not think we should teach long division.” But also say, “7 – 4 + 2 = 1 is wrong.”
What can the MAA do? One idea is for the MAA to set up a committee to review elementary textbooks, and issue an MAA “seal of approval” for textbooks that are mathematically sound.
I am told that at some universities the least qualified professors are assigned the “Math for Teachers” course. I hope that is not true at my own school, because I teach that course. East Tennessee State University takes education seriously. The College of Education requires nine hours of mathematics for all Elementary Education majors. It is beginning to make a difference. I treasure a comment from one of the professors in the Department of Curriculum and Instruction. “I have seen a big change in students’ mathematical abilities and understanding.” Teachers use math on the job every day. Recommend to your College of Education that they require more mathematics, and let them know that you are willing to work with them to insure that their graduates have a profound understanding of fundamental mathematics.
Teachers are the most important people in the world. Without teachers we have no future.
National Committee on Excellence in Education, A Nation at Risk. USA Research, 1983.
Vivian Troen and Katherine C. 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.
Rick Norwood teaches at East Tennessee State University.