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*Tom Rishel*

Once again, predictions are being made that there will be a phenomenal growth in the number of entry-level mathematicians into academia in the next ten years. Of course, we have heard such predictions before, notably in the mid-eighties, right before a dramatic downturn in the fortunes of American mathematics departments. This time, however, the projections seem to be more accurate.

What is the evidence? Well, for one, the percentages of retirees and deaths among college mathematics faculty have increased rather steadily from 1.4% in 1986 to 3% in 2000. College and university buyout plans continue unabated. Some institutions are trading their tenure lines for part-time positions, but these only increase the absolute numbers of positions. Further, the numbers of graduate students rose, from 8,100 in each of 1998 and 1999, to 8,900 in 2000. This number is expected to increase again for this year. Finally, the NSF's VIGRE program has created openings at universities for post-doctoral fellows.

Meanwhile, there is strong evidence that schools are looking for more mathematicians. The numbers of unfilled tenure-track doctoral positions in all colleges, bachelor's granting and above, went from about 140 in 1995 to just over 400 in 2000. Advertisements in AMS/MAA publications are up 22% over last year at this time. As of last November, there were 544 advertisements on EIMS online. That's up over 25% from last year. The fact that the number of tables taken by colleges at the Employment Service at this year's Joint Mathematics Meeting is the same as last year seems to imply that schools have multiple openings, not that the market has leveled off.

Some cite as contrary evidence the decline in majors: from about 25,000 in mathematics in 1970 to 12,800 twenty-seven years later. However, when we look at the total enrollment in undergraduate mathematics, the numbers are exceptionally stable over the last six years ? from 2,085,000 in 1996 to 2,087,000 in 2000.

On a related note, the call for more quantitative literacy courses, more remedial and developmental mathematics, more teaching "across the curriculum" will not decrease the need for mathematicians; it will simply force a broader range of skills upon the new PhD.

Before we discuss what kinds of professional development might be needed and how it can be obtained, we should spend a little time on the evidence for a need for college teaching skill among PhD mathematicians.

I mentioned quantitative literacy. In fact, there is a need for teaching ability of a new and different kind for increased numbers of nontraditional courses, whether they be "freshman seminars," math for poets, or writing across the curriculum programs (Joseph Harris, the recently chosen director of writing programs at Duke University, says, "mathematics is the toughest nut to crack," but he's going to try).

Another indicator of the importance of teaching is an increased emphasis on service courses. While mathematics has always been a "service discipline," an increase in econometrics and business majors, to name just two, in our mathematics courses will challenge us to reach out to other disciplines for our methods, our examples, and our classroom materials. Anecdotally, I know that I myself saw an immediate increase in physics and engineering students in my topology class a few years ago right after it was said that homotopy theory might have some applications in those fields.

Various other forces help point to a need for better teaching. Increased tuition costs lead to demands for accountability on the part of parents on one hand, and legislators on the other. With its VIGRE program; the NSF is leading us, or maybe is itself being moved to lead us, in the direction of more funding for teaching.

The employers of mathematicians, even at the PhD level, are more often companies and governmental agencies than they used to be. These employers are asking for more of a "liberal arts training" in mathematics; i.e., more writing and speaking skills, more cooperative work ? in short, more of the skills that are developed by enhanced emphasis on nontraditional teaching skills in graduate programs.

Those schools that employ newly minted PhDs are still likely to be comprehensive colleges and baccalaureate institutions; such schools put great emphasis on "teaching ability."

Further, foundations and associations are getting into the mix. The Carnegie Foundation, for instance, has spent the last ten years working to recreate academia through the Ernest Boyer model of "the scholarship of teaching." Meanwhile, the Pew Charitable Trusts and the NSF have been funding "Professors for the Future" programs.

In fact, I have seen no evidence that there is a decreased emphasis on teaching in academe. So let me stop belaboring the obvious. There is a serious need for professional development among the new cohort of mathematicians.

Ideally, audiences for professional development programs should include all faculty. In practice, graduate students, junior faculty, postdoctoral fellows and adjunct and part-time faculty comprise the majority of the audience for these initiatives.

It is easiest to attract graduate students to developmental programs. TA training is supposed to be a no-brainer, yet so many schools ignore it or do it badly. Graduate students, after all, are first-timers in the profession; if we can start them off right, we can all reap forty years of pure benefit. Meanwhile, the students are begging for help with their teaching. They don't want to start with pedagogical theory at first, that will come after they have some experience. What they want to know at the start of their careers is where to pick up their textbooks, how to find their teaching assignments on the message board, and where the classrooms are. In other words, first they want the "nuts 'n bolts" of teaching.

Programs for graduate students usually include a component of "microteaching," which is a short mini-lecture or problem session conducted at the board by the new graduate students. Other activities usually include a mock paper grading session, discussion of various strategies for problem solving in class, or a seminar on cooperative learning techniques. These and other techniques can be extremely helpful if they are conducted in an atmosphere of cooperation, that is, if the students are made to feel, "I can do this, and if something goes wrong, I have someone I can ask about it." In such a case, the first major hurdle of teaching will have been cleared. It is amazing how learning to relax in the first few weeks can make all the difference in a career.

Until the last year or two, there were essentially no books that concentrated on the pedagogy of college mathematics, Steven Krantz' *How to Teach Mathematics* being a notable exception. That has now changed.

Let's do the "infomercial" first. The best book I know of for basic TA training is (of course) my own: *Teaching First: A Guide for New Mathematicians*. (Of course, it's easy to claim to be "best" when you're also the only one.) But before you decide that the point of this article is to sell you the book, let me tell you a poorly-kept secret: an early, somewhat rough, version, when it was named *A Handbook for Mathematics Teaching Assistants*, is online at /programs/tahandbook.html. And there it is absolutely free!

A few people at other schools have put together their own locally distributed manuals. A nice one is *Teaching Mathematics: A Handbook for Graduate Teaching Assistants*, by Eileen Shugart at the Virginia Tech Department of Mathematics. Her book has a similar flavor to mine. Some of the topics are what is day one like, how do you go over homework, what if you get completely stuck, what should you do in office hours. If those topics interest you, write Eileen and get a copy.

A more advanced approach to teaching is contained in Solomon Friedberg's book, *Teaching Mathematics in Colleges and Universities: Case Studies for Today's Classroom*. Sol's idea is to bring the case study methodology, a staple in law and business schools, into the teaching arena. His examples are quite sophisticated and nuanced, and even faculty who have taught for a while can profit from discussing them.

Another opportunity for graduate student development is the aforementioned Professors for the Future (PFF) program. There actually have been a few such programs with various funding sources; I believe that the original one was called PFP (Preparing Future Professors), begun at Syracuse University about a dozen years ago. The fundamental idea of all these programs is to give graduate students a feel for what it will be like to be faculty members at small colleges, where "small" seems to be defined differently by each program. The union of all such definitions seems to exclude only research-one institutions, however.

There seem to be two basic models of PFF programs: what I will call "the high-priced one," and "the other one." The high-priced model usually includes some component of teaching, maybe at one of the local community colleges. The upside of such a model is that it gives the graduate student first-hand experience in teaching an audience of students significantly different from those usually seen at a graduate institution. There is a tradeoff, of course ? not all faculty advisors are happy to see their graduate students spending a large amount of graduate school time involved in what becomes a very intense teaching experience.

In "the other model," graduate students gain some experience by giving "job interview" style of talks to "math club" audiences of undergraduates and their faculty advisors at regional colleges, or at Sectional meetings of the MAA. Other activities include mock job interviews, discussions with faculty at other schools about their life at the college, or workshops on teaching methodologies in pre-calculus and calculus.

There is no doubt that these Professors for the Future programs have had some significant impact at institutions that have initiated them. Students gain a much greater comprehension of the pleasures and pitfalls of the life of a faculty member at, for instance, a four-year teaching-intensive college, before they make the decision to commit themselves to such a career because they are "fed up with their thesis."

Apropos that last comment, I recall the first year I had such a program. One afternoon, driving home the graduate student coordinator of our program, I idly asked her, "What did you learn from this experience, Rachel?" She immediately answered, "When I began, I though I wanted to teach at a school like that. Now I see that I want to do research." At that point, I knew that the program had serious value; Rachel had made a professional judgment based on real information.

Another program, this time for junior faculty, is the MAA's Project NExT. This is a nine-year-old initiative funded by the ExxonMobil Foundation. The goals of the program are similar to those of PFF, but this time the stakes are higher. Participants are no longer students, and the tenure-clock is running. NExTers are brought to the summer meeting of the MAA where they take two days of seminars and discussions of teaching-related issues: how can I use technology in my classroom, what's the best linear algebra book, does anyone have any resources for a non-traditional calculus course. Other topics that are usually discussed are how do I get tenure, what's inside a teaching portfolio, how can I keep a research program going at my small college. The faculty then stay for the MAA summer meeting, after which they go to their home institutions and get onto a list-serve for advice and encouragement for the next year ? which usually continues for the rest of their careers, actually. This program accepts about seventy recent PhDs each year, and I strongly recommend that you suggest it to your new hires. Of course, the MAA website has all the information you need.

Junior faculty, part-timers and visitors are in some ways similar to graduate students, in other ways not. As with graduate students, they also need to know which staff member collects the course grades and where the syllabus file is located. I can't tell you how much tension between new faculty and staff I have alleviated over the years by explaining the copy machine policy. Do not hesitate to give all these people a one-day training; the feeling that "they won't like being treated like the grad students" is, to my mind, foolishness. I have never seen a new hire who didn't appreciate a "short orientation." An example of a way in which they are not like graduate students: they will really appreciate a discussion of how to fill out the benefit forms.

It is important to recall, too, that the needs of part-time faculty are quite different from those of essentially all the other categories I have mentioned. Some will be with the department for only one semester or one year; others will be hired ad infinitum. In each case, the training needs vary. One example: If you give the "benefits" talk to a mixed group of full-time visitors and one-course part-timers, you may stir up resentments from those who don't have the benefit package. This does not call for your not giving this talk, only for sensitivity as to the way you do it.

Who's left? Ahh, yes. The tenured faculty. Well, there are difficult cases?

The goals for tenured faculty need to be built around acquiring critical skills for departments, as well as for keeping oneself invigorated. There need to be more incentives than post-tenure reviews for tenured faculty to improve their teaching.

Many older faculty see professional development programs as an indicator that they are perceived as dead wood; if such programs are sold as such, they do a disservice to departments. Each department has holes that must be covered, whether they come from the retirement of the resident specialist in statistics, a marked increase in the number of math education majors, or a shift in college policy towards more quantitative literacy courses. All faculty, including tenured faculty, should be encouraged to take advantage of enhancement activities.

An example of one such program is the MAA's Professional Enhancement Program (PREP), which offers a variety of workshops designed to increase faculty awareness and ability in a broad range of topics of interest to faculty. This program, funded by NSF through DUE, is going into its second year. See the article in this issue and check out MAA Online, at /pfdev/prep/prep.html. Next year's PREP workshops will cover a broad range of topics, from regression analysis to being a departmental chair, from assessment of student learning to knot theory, from finite mathematics to authoring online mathematical materials.

One especially notable workshop will be on preparing mathematicians to educate future teachers. This workshop, to be held over the next two summers, is meant to address the serious lack of mathematics educators at American colleges ? a lack that is reflected in the job listings every month.

One organization with a more diverse representation that is worth noting is called POD, the Professional and Organizational Development group, made up of professional development officers at colleges and universities around the United States. The organization has a list serve that can be found on the web at http://lamar.colostate.edu/~ckfgill/.

A lot of what POD discusses is not directly related to mathematics itself. However, that brings me to an editorial that needs to be made, about this and similar groups. Over and over again, people post to the POD listserv that they really need and cannot find pedagogical materials relevant to mathematics. The mathematics community, meanwhile, seems to have the approach that "We are so unique that there are no cognates to our discipline in other areas of academia." Yet, I have seen professional development activities at colleges that are of direct importance to mathematicians and mathematics educators. One example is workshop on cheating and plagiarism, a topic that is directly relevant to all aspects of the professorate. Another is a workshop on tenure issues that brought together not-yet-tenured faculty with colleagues who had just received the good news, along with the provost of the college. The end result, I am sure, was a better understanding of the entire process on everyone's part. I would wager that the portfolios sent in for evaluation the next year were substantially easier for chairs and administrators to read. Another panel and workshop discussed grade inflation and its effects on all aspects of college. Finally, there was a series on cognitive studies and the use of such studies in the classroom.

There are many important discussions of professional development issues that are going on in all areas of academia; we mathematicians ignore these discussions at our own peril. We need to involve ourselves in these debates before we find ourselves being dictated to, to everyone's detriment.

Professional development in mathematics departments is necessary. Now is an especially good time to do it, and now is also a good time to decide on the criteria by which it is to be accomplished. We need to enter this arena, for our own good, and for the future of mathematics.

*Tom Rishel is Associate Executive Director of the MAA. This article is based on a talk given at the National Academy of Sciences Board of Mathematical Sciences annual department chair's meeting in Washington, D.C.*