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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
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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
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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.
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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.
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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.
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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).
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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
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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.
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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.
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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.
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