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2 CURRICULAR ISSUES Under this topic, discussion centers on how to create an atmosphere that encour- ages and motivates faculty members to initiate curriculum studies and stimulate change; the roles of discrete mathematics and statistics; and how to keep up, be relevant, and profitfrom curricular change. THE BREADTH AND DEPTH OF CURRICUEUM Frank L. Gilfeather (Organizer), University of New Mexico THE ROLE OF THE CHAIR IN SHAPING THE CURRICUEUM Michael C. Reed, Duke University TNTERDISCIPEINARY STATISTICAL SCIENCES Ingram Olkin, Stanford University 13

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CURRICULAR ISSUES THE BREADTH AND DEPTH OF CURRICULUM Frank L. Gilfeather University of New Mexico Mathematical sciences departments, in all but a few of the top institutions, are driven by their various instructional roles. There are six distinct and often competing instructional missions for most mathematical sciences departments. Each of these yields unique curricular challenges for us. The purpose of this note is to set out a few of these issues for our discussion. 1. Graduate students. The 250 Ph.D.-granting departments are the primary instruments in the current effort to maintain U.S. leadership in our discipline end replace the aging research workforce. In addition, the master's level programs are the feeders from which significant talent, especially in underrepresented groups, will come. Are our programs giving an appropriate educationfor the varied jobs our students will be talking? Are our programs fragmented between pure and applied? Do we provide sufficient postdoctoral experi- ences?Isa postdoctoral necessary?Desirable? What are possible barriers to underrepresented groups in graduate studies in mathematics? How do we reduce these barriers? 2. Undergraduate mathematics majors. Our ability to stimulate students to pursue degrees in the mathematical sciences and then go on to graduate school will ultimately determine our viability as a discipline. This mission is shared by the 1,500 baccalaureate mathematics deparunents and is supported by the two-year institutions and the related secondary mathematics programs. Are we identifying mathematical talent early and encouraging it? Is our course selection varied and exciting to our majors? Do we have special honors courses and seminarsfor our majors? Do we provide monetary and other supportfor mathematics majors? Special recognition? Can we identify barriers to becorn~ng a mathematics major for underrepresented groups? Do we especially encourage students from these groups? 3. Teacher preparation. How successfully we deal with curricular issues and the quality of our effort here may be our most important task. This mission falls mainly to schools outside the top research institutions and emphasizes the interdepen-dence of all mathematics departments. Future generations of students are affected by the efforts of those training our future teachers. Are prospective teachers challenged and provided stimulating and varied courses? Are they given exposure to computing and modern topics? Are they aware of trends and popular literature about mathematics? Do they share in the "mathematicalfamily" in your department? Do you even know who these students are? 4. Upper-division service. This instructional role is unique to mathematics. No other discipline has as large, or as important, a role in preparing students in other disciplines. With the accelerating emphasis on mathematics 15

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CHAFING TO MATHEMATICAL SCIENCES DEPARTMENT OF TO 1990S in all fields, this role will be an increasing force in our curriculum and will have an impact on our departmental priorities. Do you regularly consult with the client disciplines to guide curricular decisions in these courses? As appropriate, do you provide computational supportfor these copses? Are they relevant as taught? Do faculty know why they are teaching these courses and to whom? 5. Introductory service. Mathematics is truly the gateway to most fields of study and is becoming more so each year. This fact will surely have an impact on our instructional programs in all post-seconda~y institutions. These courses, through calculus and including introductory statistics courses, are required in order to begin study in all science and engineering fields and increasingly so in the social sciences. The fact is that the largest high-school-level instructional units are found in our universities and colleges, not in our high schools. The transition from secondary to post-secondary mathematics instruction will continue to be a major issue facing our mathematics departments in all but the highly selective institutions. These issues become most urgent as we seek to bring more underrepresented groups into science and engineering fields. How relevant are your pre-calculus courses? Do you know if you prepare students adequately for the transitionfrom pre-calculus to calculus andfrom calculus to engineering and advanced mathematics courses? Is your "business calculus" simply a hurdle? Are you being used by others as a filter? If so, what do you do? What use of calculators do you make? 6. General studies. Mathematics is becoming a required subject of liberal arts. This trend will create pressure to redefine these general courses and add staff to accommodate the additional students. These courses are hard to teach because the students often have poor mathematics skills and have anxiety about quantitative concepts and logical reasoning. While this is the least critical of the instructional areas, it takes on real meaning if, for example, your institution recently introduced a "quantitative reasoning" component. Are these courses of value? Should a liberal education include some calculus instead? Is this a placefor introductory discrete mathematics or a statisticslprobability course? The instructional missions set forth above are clearly interdependent. Yet each is distinct, because each has a unique set of challenges and critical issues. Each mission requires a lot of our attention, energy, and resources (human and financial). Clearly, not all faculty see all these missions as of interest or of importance. This makes the challenge for us as department leaders even more difficult. How well we deal with them will shape our future as mathematics departments and ultimately as a nation. 16

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CURRIED ISSUES THE ROLE OF THE CHAT: IN SHAPING THE CURRICULUM Michael C. Reed Duke University This presentation highlights four points related to the chair's role in shaping the curriculum. 1. Mathematics departments are treated quite poorly by university ad~unistranons. Mathematicians have higher teaching loads than our colleagues in the sciences. Departments have so few faculty resources that much of the teaching burden is home by graduate students and part-time people. And then, the administrators complain that teaching isn't very good. Many university faculty members and administrators regard mathemat- ics as a service department for the rest of the institution. The good news is that we can all agree on this. The bad news is that this situation is mostly our own fault. Most mathematicians are not good entrepreneurs. They have contempt for "public relations" and they have a very short-term view of university politics. As a result, typical departments do not have strong allies in other departments or in the administration. In addition, most department chairs are very unimaginative in the use of the faculty resources that they do have. 2. Differential teaching loads are a necessity. In most departments, nearly everyone has the same teaching load, in the major universities it is two courses per term, two and one. For simplicity I will discuss only this case. Most faculty feel that they have two responsibilities, teaching and research, and that when they have finished in the classroom they have discharged their departmental duties. The rest of their time is their own, although they occasionally agree to sit on departmental committees or perform "other" service. The trouble is that curricular reform (that is what we are here to talk about) and many of the tasks that are listed in item 1, which are very important for the long-term health of the profession, all fall into this "other" category. Faculty members are willing to participate, as long as they don't have anything important to do. The only way to break the logjam created by these attitudes and to free up time for curricular reform and other service is to have differential teaching loads. Salary differentials for a given year are typically small and only partially under control of the chairman, and promotion and tenure decisions will simply not be made on the basis of such "other" activities. That leaves differential teaching loads as the only effective carrot and stick that a chairman can use to encourage and reward faculty effort. Let me clearly state what I think those teaching loads should be. I believe that faculty members with excellent research programs (say at the level normally supported by the NSF or other federal agencies) should normally teach one and one. I believe that faculty who do not currently have significant research programs should teach three and three. Faculty with "high" teaching loads should be allowed to reduce the load by important service to the department and the profession. I for one would interpret "service" very broadly to include, for example, involvement in local and state elementary and secondary education, programs to encourage women and minorities in mathematics, etc. I am familiar with the usual objections to differential teaching loads (Who will decide? You are creating two classes of faculty! This will interfere with the collegiality of the faculty!), and I think they are very weak. Faculties or chairmen who routinely judge hundreds of job candidates can create mechanisms for making these decisions with reasonable fairness. Faculty at the research institutions who do not have active research programs are already treated as less valuable. And, as for collegiality, I can only say that we are a professional organization, not a country club. Let's face it; teaching two courses a term is not, in and of itself, a full-time job. 17

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CHAIRING TO MATHEMATICAL SCONCES DEPARTMENT OF TO 1990S It would be humiliating to list mathematicians from the 1920s, 1930s, and 1940s who taught three (or more!) courses per term and whose research contributions exceed those of most of us at this meeting, so I will refrain. 3. Let's experiment. I am continually amazed at the resistance of the mathematics community to experimentation with the curriculum and with teaching methods. We really are stuck in the mud. Perhaps it's because mathematics is forever that we think the methods of teaching should be forever too. This does not mean that I am convinced that the new ideas, computers in the classroom, computer labs, writing in mathematics courses, joint student projects, and so on, will turn out to be reforms that we will want to keep, to enshrine as the new standard. But, I believe that all departments should experiment and try new things. 4. Nothing beats knowing some current exciting applications of mathematics. Let's face it, we won't win their hearts with the harmonic oscillator. That's a seventeenth century application and they've all seen it before anyway. There has been a tremendous explosion of mathematics outside of the physical sciences in biology, economics, business, and computer science, as well as dramatic successes in the physical sciences. Many of these applications are exciting and serious but use only undergraduate mathematics. Why aren't they in our courses? Mainly because most mathematics departments have few faculty who are knowledgeable. It simply takes a tremendous amount of work for a typical mathematician to find some juicy examples from these new areas, so it's just simpler to use the old stuff from the seventeenth century. Here is a perfect example of how a chairman could use faculty resources creatively. He can take a faculty member who has a closet interest in (say) economics, and give him or her the job of creating 25 excellent examples of the applications of mathematics in economics, five for calculus, five for the linear algebra course, five for the ODE course, five for linear programming, and five for the graduate real variables course. Faculty compensation would be one course off per term. Not only would the courses be better and more exciting, but the faculty member would be enriched and the department would gain valuable connections to the economics department. 18

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Cal ISSUES ~TERDISCIPLINARY STATISTICAL SCIENCES Ingram OZkin Stanford University My tank is the summary of a report of a panel to the Institute of Mathematical Statistics concerning cross- disciplinary research. The following is the introduction of this report: and sets the stage for the discussion. The development of modern statistics has its origins in applications. Driven by the need to solve practical problems in agriculture, industrial production, medicine, and many other fields, statisticians have achieved signal advances in theory and methods. In turn, statistical clinking has gready stimulated the development of virtually all areas of science. The application of the principles and methods of experimental design, the role of statistical modeling, and the pervasive use of simulationmethods are but three instances of statistical developments that have had a deep impact on science. The widespread influence of interactions between statistics and other disciplines and the very nature of statistics as the science of the "meaning and use of data" establish the statistical sciences as the discipline with the most central and complex cross-disciplinary activity. It is consequently no surprise that there is almost universal acceptance among the statistical profession of the need to nurture cross-disciplinary research. Yet, the last few years have witnessed growing concern about the health of that part of the research enterprise devoted to cooperative efforts between statisticians and other scientists. Questions raised include: What are the current needs for new thrusts of cross-disciplinary research? To what extent are statisticians and scientists paying sufficient treed to the opportunities and challenges of recent advances in computing technology and large-scale data collection? To what extent is there adequate funding for cross-disciplinary research? To what degree do institutional structures support and encourage cross-disciplinary collaboration? How can perceived needs for stimulating cross-disciplinary research be addressed without impairing support for the disciplines? While theoretical developments and the application of statistical methods have proceeded rapidly over the course of this century, it is only recently that the advent of inexpensive and powerful computational resources has opened the way for major advances in the statistical study of complex models. At die same time, greatly expanded data collection and processing capabilities have created opportunities and challenges for analysis with large, multidimensional data sets. Yet, tile statistical and scientific communities appear to have paid insufficient attention to the opportunities presented by these advances in computational and data resources. Moreover, although it is increasingly evident that failure to adopt useful statistical methods and techniques is costly to science and industry, there has been a lack of a concerted effort to address the interactions between statistics and other disciplines. In recognition of these circumstances and die need to answer Be questions raised above, the National Science tRepnnted, with permission, from Cross-DisciplinaryResearch in the Statistical Sciences (Institute of Mathematical Sciences, Hayward, Calif., September 1988). 19

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CHASING TO MATHEMATICAL SCIENCES DEPARTMENT OF ME 1990S Foundation (NSF) in 1985 funded aproposalby theInstitute of Mathematical Statistics ~IS) to assess the current status of cross-disciplinaryresearchinvolving statistics end to make recommendations forits future. Four divisions within NSF Mathematical Sciences, Social end economic Science, Chemistry, and Cross-Disciplinary Research (Engineering Directorate~provided funding. The IMS formed a panel to carry out the project whose members were Alfred Blumstein, Amos Eddy, William Eddy, Peter Jurs, William Kruskal, Thomas Kurtz, Gary McDonald, Ingram Olkin (cochair), Ronald Peierls, Jerome Sacks (cochair), Paul Shaman, and William Spurgeon. We note that the terms cross-disciplinary, multidisciplinary, and interdisciplinary have at times been used interchangeably. We take advantage of these alternatives in order to draw some distinctions. Following Epton, Payne, and Pearson (Managing Interdisciplinary Research, John Wiley & Sons, New York, 1983), we adopt the following definition: a research task requiring a combination of disciplines is cross-disciplinary. In contrast, the terms multidisciplinary and interdisciplinary refer to the organizational forms used to carry out cross-disciplinary research. The multidisciplinary form is that in which research tasks are carried out by separate single-discipline units and their results brought together by a coordinator. In the interdisciplinary form, the research is carried out collaboratively and interactively within a single unit representing all the necessary disciplines. Our report is about cross -disciplinary research that has a statistical component the work may have multiple objectives, but it includes the advancement of statistical science. One of the concerns of our study is the development and support of organizational structures that will foster successful cross-disciplinary work. The panel developed a series of recommendations to enhance support for cross-disciplinary research. Par B of the report presents our recommendations, which are addressed to the National Science Foundation and other funding agencies; to research managers and members of the statistical community resident in academia, industry, national research laboratories, and statistical agencies; and to the professional associations. Part A of the report presents the findings that underlie the panel's recommendations. The panel believes that advances in statistical theory and methods are stimulated by the need to solve problems in substantive areas and that these advances in turn stimulate the development of substantive knowledge. In support of this premise, Section A.1 summarizes, and Appendix I describes more fully, several prototype examples of past success in collabora- tive research among statisticians and scientists in other fields. The panel believes that there are important current problems in many disciplines that would greatly benefit from close collaboration among statisticians and other scientists to push forward the frontiers of theory, methods, and knowledge. Indeed, without adequate support for cross-disciplinary research, there is a risk that major opportunities for significant new developments in many fields will be lost. To indicate what is needed, Section A.2 summarizes, and Appendix II describes more fully, several examples of specific research areas that could greatly benefit from cross-disciplinary work. A persistent theme is the impact of large-scale computer technology and data sets, both of which afford great potential to researchers but present equally formidable problems of effective use. Indeed, the phenomenal amount of data being generated in all of the sciences is creating a need for new ideas to deal with the compression, presentation, and analysis of large data sets. The panel believes that statisticians must give priority to developing adequate theory and methodology for handling the complex models and large multidimensional data sets that characterize today's scientific research. The panel finds constraints in funding and institutional support for cross-disciplinary statistical research on the part of NSF and other funding agencies. This conclusion rests in part on a review presented in Section A.3.1 (with additional details in Appendix m' of reports from other committees and panels over the past 10 years that considered the health of cross-disciplinary research. Uniformly, these reports document problems In obtaining support for work proposing to develop statistical theory and methods directed to the application needs of other disciplines. The panel also notes that recent funding problems experienced by federal agencies generally are haying a deleterious impact on statistical research and particularly on collaborative work. Section A.3 .2 presents some data on this point. Although the panel calls for many of the same ameliorative efforts that earlier committees urged, we 20

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CURRICULAR ISSUES point to some approaches that can have a marked impact on the support and encouragement provided by funding agencies for cross-disciplinary research. The panel further finds that institutional support for collaborative research between statisticians and other scientists in academia and industry is problematic and could tee substantially improved. There are successful efforts by some government agencies such as the Bureau of the Census, the Bureau of Labor Statistics, and the National Center for Education Statistics to bring together multidisciplinary teams for needed research programs. The example set by these agencies and their approaches are worth transferring to other agencies and other arenas. Maintenance of these efforts and added support for them by other interests in and out of government are recommended. Section A.4 summarizes the responses to a questionnaire sent by the panel to statistics departments and programs in colleges and universities across the nation. The information gathered from this survey provides useful insights into problems connected with cross-disciplinary activity. (Appendix IV gives a full description of the survey.) The panel has sought in its recommendations to take account of the perceptions of the community at large in identifying targets of opportunity and suggesting approaches to buttress and extend the support for cross- disciplinary research in all environments in which statisticians work. Finally, in order to provide a necessary long-range view and to establish a structure for maintaining the health of the field and its cross-disciplinary character, the panel recommends the establishment of an Institute for Statistical Sciences. The panel calls upon professional societies, committees of the National Research Council, the National Science Foundation, and other units in academia, industry, and government that have responsibility for die well-being of the discipline to review We panel's findings and recommendations and to act upon them. 21

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CURRIER ISSUES QUESTION-AND-ANSWER SESSION PARTICIPANT: I was intrigued by Dr. Reed's ideas concerning the involvement of faculty in curriculum development in institutions other than our own. Our teaching loads are similar to yours, a little heavier for those who do no research. I understood you to say one could go to one and three and allow those with three courses to buy their loads down to two. DO YOU have any suggestions as to where one might find the resources to do that? DR. REED If you do not get the additional resources to teach the required courses, then cancel them. I am not implying that you should take this action without thorough consultation with your department and your dean. However, for historical reasons mathematics departments are understaffed in terms of teaching. Over the last 30 years, we allowed university administrations to decide that essentially all freshman teaching would be done by nonprofessionals, by graduate students or by part-time staff. As a result, most departments do not have the number of faculty they need to support the kind of undergraduate program in which there is sufficient faculty- student contact, seminars, and faculty-supervised projects by undergraduates. Those things are extremely expensive in faculty time. Most universities do not have the faculty time. We are understaffed. Additionally, now we are being asked to take on many important social responsibilities. Something has to give. We cannot do all these things. We must make that clear to the university administration. PARTICIPANT: Part of the answer to the question seems to be that by aggressively dealing with issues that the department and the university consider important, one is in a good position to get resources allocated to his department. As Dr. Douglas said earlier, we are dealing with issues to which the university gives priority in its strategic plan. PARTICIPANT: I would like to point out that the freshman experience is where, perhaps, we do not do our best job. Reassigning people who have not been strong in research to this extra teaching load may not be in the best interest of undergraduate students. DR. REED: Running a department is a human operation. The faculty in your departments are your colleagues. Many of them will have talents and time that would be useful for one or another of this broad range of issues. We must get out of the mode that we only do research and meet classes in the classroom. Chairs must manage departments in a way to which we are not accustomed. We must consider the faculty as multitalented and multidimensional people who have a variety of things to offer. We have not found ways of using all of those talents. One needs to look across the board and, over a long period of time, encourage faculty into these other things. PARTICIPANT: I am chairman of a department of operations research at an engineering school. My position as chair is only one-third of my time. We have a three-course teaching load. The only way to reduce it is to divide off with research or proposal writing. I will have to approach my dean and request release for my faculty to help with various programs and tasks. I am trying to do all those things as chair. A faculty member can legitimately say, "I am required to teach three courses or buy off some of my time, which means I must run after money and do the work." Given that my school runs in the red, it will be difficult just getting down to a reasonable teaching load. 23

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CHAD~G TO MATHEMATICAL SCONCES DEPARTMENT OF TO 1990S PARTICIPANT: I am from a master's degree-granting school. One of the things about schools of this type is that faculty are required to be superhuman. They must teach 18 hours per year, do research, go out into the public schools, serve on committees, increase minority representation, and so on. Many of the things Dr. Reed discussed in the response concerning shifting personnel are extremely important. This is one place where the mathematical sciences community fails. For instance, we have people in my department who really are excellent teachers. They work very hard on a variety of service projects with the public schools, for example. However, it is very difficult for them to get pay raises equivalent to those generated by publishing research articles. The whole mathematical sciences community must face the issue of rewarding persons for work other than publishing. DR. GILFEATBR: If one can identify excellence, then I would say that this person is in the front line of trying to do something about adjusting the reward structure. It should be based on excellence. PARTICIPANT: Consider a person who is active in research but does not generate continuous support, or a young faculty member who has not yet generated support but is expected to generate support These are the persons who should be nurtured. Is there room for a middle ground? Could there be three differential teaching loads? DR. REED: I think junior faculty should automatically get low teaching loads. The burden comes with tenure. If one is a tenured faculty member in an institution of higher education, there are serious responsibilities that go with the job. It is the responsibility of the chair to get faculty members to live up to those responsibilities. PARTICIPANT: Do you have any comment on the relationship between effective curricula and class size or effective teaching and class size? DR. GILFEATHER: Curriculum, class size, and so forth, are driven by resources. We have been discussing resources. As we fry to address other things, as Dr. Reed has suggested, I do not see lowering class size as aresult. There are variables. If one variable is manipulated, then He others are affected. 24