Rarely do such broad pronouncements recognize that the problems of teacher preparation, like those of cancer, arise from multiple sources and require correspondingly different solutions.

Mathematics Teachers. Let's begin with a question of definition: Who is a mathematics teacher? For grades 9-12, perhaps even grades 7-12, one can see the outlines of an answer, since most schools have separate mathematics courses for those grades. However, often the teachers of these classes are primarily trained in something other than mathematics (e.g., French, chemistry) so they may not view themselves, professionally, as "mathematics teachers." Moreover, the current emphasis on interdisciplinary, project-oriented teaching (e.g., environmental studies) requires that even teachers who have thought of themselves as primarily (or exclusively) mathematics teachers must now take a broader view, and teachers of other subjects (e.g., history, biology) must begin to accept responsibility for using and teaching mathematics as part of their work.

Elementary school teachers rarely view themselves as "mathematics teachers," even though mathematics is a significant part of their responsibility at every grade. Nonetheless, their preparation must be primarily on the broad preparation required to teach young children, not primarily to teach specific subjects such as mathematics. Teachers of the middle grades occupy an ill-defined niche between elementary and secondary that has no established national consensus concerning appropriate preparation.

So who is a mathematics teacher? Answer: Virtually every teacher.

Prospective Mathematics Teachers. Students who become teachers take their undergraduate courses in a wide variety of institutions, only some of which have preparation of teachers as a central part of their mission. Many students study most or all of their mathematics in two-year colleges, liberal arts colleges, or research universities in courses that are not specifically designed for prospective teachers. So the mathematical preparation of prospective teachers becomes the responsibility of the whole mathematics faculty, since students who will become teachers can be found in virtually every course.

Demographic data on students reveals the dramatic growth of ethnic pluralism in our nation's public schools. Yet data on the educational pipeline shows virtually no growth in the diversity of graduates with degrees or significant coursework in mathematics. The contrast between the national portrait presented by students and by those certified to teach mathematics is outrageous. Clearly we need to use the undergraduate years to recruit mathematics teachers, not just educate those who insist on this career.

Thus our second question: Who is a prospective mathematics teacher? Answer: Virtually every undergraduate.

Curriculum Issues. Students who will obtain certification to teach high school mathematics will generally take a mathematics major along with other students, including prospective engineers, lawyers, and mathematicians. Faculty face an immense an challenge to help students in mathematics courses see appropriate connections to their greatly varied interests, ranging from engineering to high school teaching. Yet unless this challenge is met, prospective high school teachers will remain inarticulate when pressed by students with the persistent question: what good will this ever be to me? Prospective teachers need to be convinced by the same evidence as prospective scientists, engineers and economists of the nature and utility of mathematics.

Students who will obtain certification as elementary school teachers often take some or all of their mathematics courses as part of general education requirements, not in special courses for prospective elementary school teachers. This suggests an even greater challenge to the mathematics faculty--to design courses that are suitable to provide the broad mathematical literacy required by an educated public and by those who will teach young children. Is there much difference between what a citizen needs to know about mathematics and what a child should learn in a standards-inspired elementary school curriculum? Shouldn't teachers encounter the same evidence of the nature and role of mathematics, in the same classes, as prospective lawyers, journalists, and business leaders?

Thus the final question: What should prospective teachers learn about mathematics? Answer: Just what every other well-educated person learns.