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4 PLENARY DISCUSSION Panelists assembled to take questions from the floor and respond to any written questions received after the Friday sessions. PLENARY DISCUSSION Phillip A. Griff~ths (Presider), Duke University Ronald G. Douglas, State University of New York, Stony Brook Frank C. Hoppensteadt, Michigan State University Gerald J. Lieberman, Stanford University James Glimm, State University of New York, Stony Brook Daniel Gorenstein, Rutgers University 37

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PLENARY DISCUSSION PLENARY DISCUSSION Phillip A. Griffiths (Presider) Duke University DR. GRIFFITHS: Each of us has selected and will respond to some of your written questions. When all re- sponses to written questions have been completed, if time permits, we will respond to questions arising from the responses. QUESTION: Could the concerns of those of us from smaller, lesser known institutions be addressed by this body? DR. GRwElTHS: That is a very good question. We are now beginning to plan next year's colloquium. A topic centered around this issue would be very appropriate. It would help if you can be more specific about the prob- lems and issues you would like to see addressed in such a session and communicate them to Dr. Cox. QUESTION: What kind of mathematician, research or nonresearch, makes a better chairman? DR. GRiFfilTHS: First, issues of character, judgment, and interpersonal skills are important in the effective- ness of a chairman. So the question has to be understood as assuming these things. Now, a successful chairman has to understand the field of mathematics and have the respect of his colleagues. Because of the culture of our field, this may be easier for someone who has an established research career, although he may no longer be active. That does not mean that this is either a necessary or a sufficient condition. In general I would say it is helpful. Also, the job of chairman is sufficiently complicated now that it is very difficult to do it well in spare time. QUESTION: How does one get an administration to keep its promises to upgrade a poor department? DR. GRiFFlTHS: This is obviously going to vary from institution to institution. Most institutions with which I am familiar operate in a rather formal manner. My job as provost is to recruit and work with deans. First, there are negotiations. Then, a written document is presented in which I state the institution's commitment to the dean over the next three to five years-essentially, financial arrangements. The same thing should occur between deans and chairs. There should be a clear written understanding between the dean and the applicant before the chairman accepts the position. There will always be a caveat concerning maintaining current conditions because we are all subject to the vagaries of the federal government, state governments, donors, and so forth. QUESTION: Is the declining pool of employables an argument for more money? DR. GR~1THS: This will be one of the major themes of the update of the David report, which will be discussed at length this afternoon. The discussions of that committee have made several points. First, the field of mathe- matics is intellectually attractive. It is becoming even more so as mathematicians become involved in problems from the other sciences. Second, in contrast to some years ago, there are now open teaching positions, and more are projected to open in the coming years. So there are job opportunities in academe as well as industry and the 39

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CHAIRING TO MATHEMATICAL SCIENCES DEPARTMENT OF TO 1990S national laboratories. Given those conditions we ought to be attracting more talented students. Part of the dis- cussion in the David committee is that the mathematics community itself needs to try to recruit more system- atically into the field. The report will contain suggestions as to how this might be done. QUESTION: Are there ongoing studies on the demographics of the current population of undergraduates in mathematics that can tell us if we will have enough American graduate students from minority or majority groups in the coming years? DR. DOUGLAS: One of the things coming out of the MS 2000 project will probably be a great deal of statistics. The numbers are somewhat ominous. There is a large number of undergraduate majors, but not as many as there were in the 1960s. The number has gone up somewhat in the last few years. Still, most studies indicate that we need more students in mathematics. Between the David report update and MS 2000, the mathematics commu- nity will be provided a great deal of information. It is up to us to use it as best we can, both for our own planning and for convincing others. QUESTION: How does one persuade deans to provide maintenance personnel for computer hardware and software? DR. DOUGLAS: One possibility is to suggest the use of half a faculty line for this purpose. However, that kind of staffing is a little different from ordinary faculty. So, it depends on one's department and its needs. QUESTION: How can we get more students into mathematics if we don't have good introductory courses that show them what mathematicians do? DR. DOUGLAS: That is a complicated question. It is a concern not just in mathematics but in other sciences as well. A large percentage of the people who come into a university or a college do take mathematics courses. From that point of view, we are the envy of most other disciplines. QUESTION: Dr. Hoppensteadt mentioned that chemistry and physics departments have strong industrial contacts. Do you see those same individuals as potential benefactors of mathematics departments? DR. HOPPENSTEADT: Yes, I do see them as benefactors to mathematics departments. They want the people they hire to have mathematics skills. However, they may not tee a source of money for mathematics departments. That is primarily because the money they give to departments is sharply directed toward specific applications. Note that money is not the only consideration in building friends for your department. These people provide a channel to the central administration. Also, they can give insights into the kind of competitive market we are facing. We are facing an incredible gradient in salanes. For example, a student graduating with an MBA and going into a top-of-the-line brokerage will start at $75,000 and be guaranteed $150,000 after four years. If successful there, one can go to approximately $500,000. Success at that level means the sky is the limit. So the gradients we are facing are steep. We can get support for that from industry. By building a group of users in industry, one creates a network of hiring for students. This also provides good information about the salary structure in industry. QUESTION: To what extent, if any, should a dean be able to dictate to a mathematics department the research field in which an open position is to be filled? 40

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PLENARY DISCUSSION DR. HOPPENSTEADT: My view of administrators is that our first duty is to keep administration out of the way of the faculty. If there is a confrontation with a dean over a position, there could be serious problems. The position might not tee filled, or a new position could suddenly appear in some other department of the university. To avoid confrontation there should be consultation within the department. Create a consensus within the department. Most importantly, develop a plan for the department. The administration may not sign off on it, but a plan opens the door to negotiation with the administration. QUESTION: When is it proper for a chair to go over the head of a dean to a provost to get the dean's decision overruled? DR. LIEBERMAN: It is always appropriate for the chair to go over the head of a dean, provided that the chair has informed the dean of those intentions. Now, having said that, let me say what I really think. Going over the head of a dean is a terrible mistake. One must understand that, essentially, a dean serves at the pleasure of the provost. If the chair goes to the provost, the first thing the provost is going to do is talk to the dean. This is really a no-win situation for everyone. One would like to feel that a chair can cooperate with a dean. However, it may be that the dean is not sympathetic to the needs of mathematics. But there are other ways of voicing these problems that can get to the provost's ear. For example, there are budget letters that go to the dean. I presume that most provosts will be made aware of the desires of the department. QUESTION: Does the panel endorse Professor Reed's suggestions that faculty whose scholarship is failing or has failed be given dominant responsibility in the teaching program? DR. LEBERMAN: I do not agree in general that faculty whose scholarship is failing or has failed be given dominant responsibility in the teaching program. Teaching, research, and scholarship are so intertwined that one could question whether or not the failure of scholarship also indicates a failure of interest, or a failure in teaching ability. It has been my experience that people who are relatively poor in scholarship are probably not very good at teaching. However, there are outstanding teachers who are not great researchers. If they have the managerial talents required to lead a program, then, in certain instances, it may not be unreasonable to do that. This may be a way of utilizing much-needed talent, because the teaching of mathematics is an important issue. It is, also, one on which departments are frequently under fire. I cannot give an off-hand response of yes or no. One has to examine individual circumstances. QUESTION: Where can one get national data on teaching load, class size, travel support, levels of computer support, and levels of secretarial support for mathematics departments? DR. GLIMM: Data will be available from the David II report and A Challenge of Numbers.i Perhaps some of those details will not be determined. Someone should try to assemble that data. QUESTION: What can a mathematics department do to demonstrate to the administration that it is strongly interested in undergraduate teaching? DR. GLIMM: The answer to that question is "by doing it." I want to elaborate on that. Having recently come National Research Council, A Challenge of Numbers: People in the Mathematical Sciences (National Academy Press, Washington, D.C., April 1990). 41

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CHAIRING THE MATHEMATICAL SCONCES DEPARTMENT OF TO 1990S to Stony Brook, I looked over the facts there and discovered, to my pleasant surprise, that their record in teaching is excellent. That is borne out in the statistics. Their fraction of the undergraduate students may be three or four times the national average for undergraduates as a fraction of the total student body of the university. Their total contribution to the national pool of mathematics majors is a respectable percentage. St. Olaf College also has an incredible percentage of mathematics majors. The answer is in caring about the students. It is part of the culture in those departments that the teachers care about the students and that the faculty care about that fact. From informal discussion, I know thatpeople value the research of their colleagues; they also value the teaching performance of their colleagues. Caring about students involves such things as noticing when a student is in trouble and initiating a conference. At a higher level, which is the department chair's charge, or the charge of the senior people in the department, it is to communicate to all the instructors the standard of caring the department expects of its teachers. For example, part of the teaching evaluation lies in the ability to teach a large course. Even better is the ability to create a course with large enrollment, in other words, to find the students and bring them into the department. QUESTION: What are typical start-up costs for hiring mathematicians that are accepted by administrations? DR. GLIMM: That is extremely variable. Probably the most common is zero. The question probably refers to cases where start-up costs are allowed. For people who are doing computing, it could include computer equip- ment. For distinguished individuals, it could include a secondary appointment. Also, there might be research support during a time when grants are being transferred. It could include temporary support for visitors, or include a focus that could lead to a special year centered around the research interests of the person being hired. DR. GORENSTEIN: The start-up cost is usually zero. However, there are circumstances under which an administration will respond and produce funds for start-up costs. A small research stipend in mathematics goes a long way. For $10,000 one can practically run a conference or bring in visitors. The important point is that it is not always zero. One has to make the case. QUESTION: I would like to hear comments on the following statement our dean offered us about four months ago: "Mathematicians can teach more efficiently than anyone else in the sciences, and so it is natural that the student-faculty ratio is higher in mathematics than in any other science." DR. HOPPENSTEADT: I do not think it is effective to try to fight on the basis of student credit hours. One should view student credit hours as a strength of the department and not as something that is being inflicted on the department. The more a department can get in with the program of the university, the better the department is going to succeed. At Michigan State, the mathematics department deals with 10,000 students per term. That is a staggering number. One could hit people over the head with the number, but it would accomplish nothing. PARTICIPANT: May I follow up on that question? When I was chairperson I found that numbers were somewhat effective, provided they were presented in a context administrators could understand. The college marvelled at how interesting it was that every calculus section contained 75 students. The AMS published data indicating that nationally, the average section size was approximately 40. I used the educational quality argument with my dean. I did not say our quality was hurt because we had so many students. I said we needed new resources because we should at least be able to educate mathematics students the way it is done nationally. The administration agreed to that. 42

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PLENARY DISCUSSION QUESTION: We have always taught calculus in sections of about 25 or 30. Is it better to have an outstandingly motivational person, someone active in research, teach 150 or 200 students? Would this increase student understanding of mathematics, or would it sharply decrease it? DR. HOPPENSTEADT: It is amazing that those kinds of things are not known. An experiment was conducted at the University of Wisconsin in the middle 1960s. The same examination was given to large lectures and small sections. One could not distinguish between results on the examinations. So it is surprising to me that we have not done more to investigate these kinds of issues. PARTICIPANT: Formerly, we taught calculus in large sections only. We told the administration that the norm for calculus was much lower. We were allowed to cap all of our majors' calculus courses at 35. As a result the failure rate for all sections went down. DR. DOUGLAS: When we consider the question of small sections versus large sections, I am not sure that all of the relevant variables are taken into account. Also, I am not sure whether studies from the 1960s would carry over to the students of the 1990s. The difference between teaching students in small sections versus large sections is that one can do many things in a class of 30 that one cannot in a class of 100 or 150. QUESTION: This concerns the question of the calculus initiative. I am under some pressure to go to a lecture format for calculus. On the other hand, there is also pressure to introduce the computer into calculus courses. Somehow those seem to be contradictory. Can you offer any advice? DR. DOUGLAS: I am not sure there is an absolute answer to that. It depends on the resources one has. For example, at a liberal arts college where all teaching is done by faculty, it makes sense to teach calculus in small sections. In a university where there are teaching assistants, one must consider the competence of these TAs. The model one chooses depends on the personnel available. As for the question, I am not sure I see the incompatibility of having lectures and recitations versus experimentation. PARTICIPANT: The computer is more labor intensive. If a calculus section is in a laboratory with 40 or 45 microcomputers, then an instructor can only service approximately 30 or 35 students during an hour. DR. DOUGLAS: But there are other models. It is not required that every meeting of a calculus class, which meets three or four times a week, involve mathematics or involve the computer. One model is to have lectures and separate the class into smaller groups for the computer portion of the course. QUESTION: Much of our attention must be focused on pre-calculus. Will someone address this problem? DR. DOUGLAS: It is a national trend. The data show that approximately 50 percent of the mathematics classes are pre-calculus and below. If we are going to attract more students into mathematics, we not only have to teach the courses you are talking about; somehow we must make it possible for these students to take more mathematics. DR. HOPPENSTEADT: I do not see that as a problem. I am sure that a significant proportion of the people in this room did not start with calculus in their first year of undergraduate school. A number took college algebra 43

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CHAIRING THE MATHEMATICAL SCIENCES DEPARTMENT OF TO 1990S and analytic geometry or an equivalent course in their freshman year. That model has changed. There is an attitude that one must begin with calculus. I disagree. Certainly, for well-prepared students, the farther they get along in their undergraduate career the better. However, if it sets them up for failure later, they will not have been done a service. Another aspect is that arts and letters is a separate college. Some of them are requiring mathematics for all graduates. That is pre-calculus mathematics. They feel that mathematics is something their students should know. I don't see that as a problem. It is an opportunity for more resources. If that is what the administration wants to do and they support it, it gives us an opportunity to get more resources for our departments. 44