Anthony Ralston of SUNY Buffalo had written the paper "The Real Scandal in American School Mathematics," and it was published in Education Week on April 27, 2005. A slightly edited copy of this paper is available at http://www.doc.ic.ac.uk/~ar9/TeacherQual.html. I had read this paper earlier tonight, and I find it to be a useful paper that addresses a vital question about improving K-12 math education that is, however, rarely asked: What exactly do we do about the problems of teachers' declining understanding of mathematics over the last fifty or so years? Can this problem be easily fixed or not (assuming politics and selfish interests and other such garbage does not get in the way)? If not, why not?
Ralston mentions that one reason the severity of teachers' bankrupt understanding of mathematics continues to go unnoticed is that many mathematicians do not want to be seen as teacher-bashers, as arrogant jerks who like to belittle those who do not understand math as they do. I'm sure there are exceptions, but I imagine this general principle is most likely true since I don't hear many mathematicians speaking out against this problem. Many mathematicians do tend to steer clear of K-12 math education altogether either to avoid these controversies with K-12 math education or because they want to remain as completely focused on math research as much as possible. I don't remember where I had read this, but I do remember reading from somewhere sometime earlier this year that many high-class mathematicians consider math education as the work of minor mathematicians who couldn't cut it in math research. That is, math education is not the work of a "real mathematician."
Ralston states evidence of the severity of the decline in teachers' understanding of math: increasing numbers of math teachers without a major or even a minor in math, alarming rates of math anxiety among elementary school teachers, the study done by Liping Ma and reported in her book "Knowing and Teaching Elementary Mathematics." I had seen this book mentioned often enough that I know I must get a copy when I can. This decline is certainly well known, but apparently few people know how severe this decline really is.
Ralston makes an excellent point that NCLB is also causing severe damage to this problem because the law does not mention or implement any programs to attract qualified teacher candidates to K-12 schools and actually discourages qualified teacher candidates from even considering teaching as a career because of all the crap this law promotes by turning education and teachers' careers into a joke (here, I use "qualified teacher candidate" to refer to anyone who has at least the required understanding of the subject to teach effectively in K-12, whether that person is considering teaching or not). I can see why these people would not be attracted to teaching. NCLB has turned K-12 teaching into almost a living hell, and the reactions of most teachers confirm that. When I think about this mess resulting from NCLB, I'm glad that I changed my mind about teaching high school math. I would detest being forced to teach to mindless tests and to pass slews of students in high school math classes whose understanding of math is so low that they can't pass even a fifth grade math test (forced in the sense that I would have to do all this to keep my job, that is).
Ralston does mention that NCLB is not the only reason that teaching as a career has gotten worse over the years. Even before NCLB, benefits for teachers have declined, and workloads and stress have increased. Though he doesn't mention this, I think it is also worth mentioning that discipline and behavior have become much worse problems among students in recent years. Many teenagers I have seen myself have the kinds of attitude problems that I cannot stand. Such problems do occur among some college students, but those problems are nowhere as severe. The schools I do teach for do give me the right not to tolerate such behavior. The Kaplan Math Center does not either, and several students have been barred from tutoring because of their highly inappropriate behavior (for instance, one student had called one of the tutors a moron because she did not understand the business or finance terminology the student was using); however, such behavior rarely occurs. But the K-12 classroom is much different from that, and I don't understand how the rights of a highly distruptive student--one who clearly is making it difficult for the teacher to teach and the other students to learn--supercedes the rights of the teacher to teach and the other students to learn. If rights conflict, the greater right is supposed to win: The rights of those other students and the teacher are greater than that one student's right to remain in class, especially when that one student is clearly not respecting the rights of others. These behavior problems among students and schools' ridiculous views of student discipline are additional reasons why I'm glad I changed my mind about teaching high school.
In short, this article leads to the vital question we need to answer correctly as soon as possible: How can we attract more mathematically talented people into K-12 teaching? Unless we can find an answer that works, we will face an incredibly bad teacher shortage even if we raise the standards for teacher training to where they should be.