October 1996 € Volume 23 € Number 5
October 1996 € Volume 23 € Number 5
One of the more unusual aspects of this summer's IFORS meeting in Vancouver, B.C. &emdash; and one of special interest to teachers &emdash; was a series of sessions called "Innovative Approaches to Teaching Management Science." I organized this track (at the urging of Andres Weintraub) in order to bring together in one place, and for an international audience of MS/OR professionals, some of the teaching innovators I have known and learned from over the last couple of years. A number of us have been offering short papers on teaching at professional meetings but have not had the opportunity to discuss our ideas in depth. More particularly, we have not had the time in the typical meeting format to demonstrate some of the experiential or active learning approaches we have employed in our teaching. Our idea this time was to devote a full 90-minute session to a single topic and a single speaker and, to the maximum extent possible, to involve the participants in our methods by having them actually experience them.
The line-up consisted of Sam Savage on spreadsheets, Judith Liebman on cooperative learning, Peter Bell and Christoph Haehling von Lanzenaeur on case teaching, myself on teaching modeling, and Val Belton and Helyn Thornbury on the multimedia project MENTOR.
Following are my impressions of the high points of each of these
sessions. If you are interested in learning more about any of the
topics or speakers, I have provided e-mail and Web addresses where
possible. If you are interested in issues surrounding the teaching of
MS/OR and are not already a member, by all means join INFORMED, the
INFORMS Forum on Education
(www.ualberta.ca/~informed/).
Innovative Use of Spreadsheets in Teaching
Sam Savage, Stanford University
e-mail:
savage@leland.stanford.edu
Web:
http://www-leland.stanford.edu/~savage
Sam Savage began his session with a discussion of the pros and cons of the spreadsheet as a modeling tool for management science. Among the problems with spreadsheets Sam cited were difficulties in documenting models and difficulties in scaling small models into large ones. However, one positive feature of spreadsheets dominates all the negatives: 30 million or so users. This feature alone makes the spreadsheet the modeling tool of choice for most actual and potential users of management science. And since we're stuck with spreadsheets, we might as well turn them to our advantage.
Next, Sam did a short demonstration of the Data Table feature of the spreadsheet to show its power not only for simple sensitivity analysis, but also to reveal the behavior of fairly complex mathematical functions. His example was a graph of a three-dimensional conic section in which he used the Data Table to calculate the values of the function. By isolating the parameters of the function, Sam was able to show, for example, how changing the power of the exponent changes the shape of the function.
This example represents an experimental style of mathematical investigation using the spreadsheet that I believe has a great deal of untapped potential. Many of our students do not have strong traditional mathematics backgrounds, but they can easily learn to explore mathematical questions using a spreadsheet. One of our tasks is to train our colleagues in other disciplines in these techniques so that they can, in turn, train their students.
The heart of Sam's session was devoted to some challenging ideas about the teaching of statistics. He gave the participants a short quiz on the shape of the distribution of a single uniform random variable and on the sum of two uniform random variables. He then shared the results of his experience in administering this quiz to roughly 500 people per year in industry, most of whom have had a statistics course in the distant past. Roughly half of this group draws a uniform distribution and the other half a (roughly) normal distribution, regardless of whether the question concerns a single, random variable of the sum of two random variables. Furthermore, these percentages hold for students currently enrolled in advanced statistics courses as it does for those whose statistical training is a distant memory.
It thus appears that there are some deep intuitions about distributions, not all of which are correct, that many people share and that are not particularly influenced by technical training. With this sobering demonstration as a base, Sam went on to demonstrate, using software he developed for Monte Carlo simulation, how easy it is to explore basic statistical issues using a spreadsheet. I was particularly impressed by his graph of the convergence of a parameter estimate to its true value as a simulation run progressed. I cannot think of a more effective way to introduce a student to statistical issues in simulation than this visual demonstration of the effect of run length.
Sam is rightly known as something of a spreadsheet wizard and, as
with all masters, sometimes the wizardry may distract from the
underlying message. What Sam does best is show how to extract basic
insights by using simple models in a highly exploratory, experimental
manner. One comes away from a session with Sam with a stronger sense
of the power of the spreadsheet not so much to "solve problems," as
to provide a platform for one's own intellectual exploration. We
would do well to convey that sense to our students along with the
mechanics of spreadsheets and the tools of management science.
Focusing on Learning Rather than Teaching
Judith Liebman, University of Illinois Urbana-Champaign
e-mail: jliebman@uiuc.edu
Judith Liebman has been studying and using cooperative learning techniques in her engineering classes for a number of years. She has also written an excellent survey article on the topic in the International Transactions in Operational Research ("New Approaches in Operations Research Education," Vol. 1, No. 2, April 1994, pp. 189-196).
Judith's strategy at IFORS was to demonstrate the techniques of cooperative learning by having the participants in her session actually practice them. She began by discussing the importance of clearly articulating the objectives of each session in the course. She then set out her learning objectives for the participants in her session:
After organizing ourselves into groups of three or four, we immediately went into the first activity, which was to discuss "Why build mathematical models?" This is the kind of question she would likely ask early in a course after the students have read a textbook chapter on the topic. After five minutes of small group discussion, we discussed the question in the entire group and went on to the second question: "How complex should models be?" In this case, Judith provided a short paragraph of explanation to focus our discussion, which explained the difference between exogenous and endogenous factors, and gave a simple example involving a model of a fast food operation. This somewhat more meaty problem generated lots of discussion, both in the small groups and in the larger group.
These first two activities were examples of small group discussions that can be used to help students cement the basic concepts of a topic. We then moved on to a more technical discussion question: formulating the dual of a linear program. Here we were given a verbal description of a small LP and asked to formulate the primal, then construct the dual, and finally to identify the units of the dual variables, objective and constraints. For those of us who teach MBAs, and whose LP skills are rusty, this was an interesting challenge. It also provided an interesting lesson in the power of small groups to work out solutions cooperatively and to teach each other in the process.
By this time the small groups had gotten the hang of doing these group problems. Some camaraderie had formed within the groups and my group, at least, had begun to have some pride in its work. The next task Judith gave us was to match a list of definitions of basic concepts associated with Markov chains with a list of topics. This task, again, was just challenging enough for us that it gave a good indication of the high level of energy and commitment to the group one might expect from student groups.
The final task in Judith's plan was to reflect on the types of cognitive processing that we had used in each of the tasks to that point. This was a quite different exercise; not one involving MS/OR per se, but one that made us teachers reflect on the kinds of cognitive skills we expect our students to use. Here is the list of types of cognitive processing Judith provided:
At this point in the session, Judith concluded her prepared activities and an open discussion took place. Primed by our experiences with the discussion questions she had taken us through, we had a lively discussion of the wide range of different activities one can design for a classroom, including lectures, case discussions, turn-to-your neighbor discussions, small group discussions, individual time using computers, and so on.
Many of those attending this session can look forward to one day
soon facing a class of students, each of whom are equipped with a
laptop computer. The possibilities offered by this new technology for
interactive and group learning were discussed as well. Someone
offered the following summary: Just as we now use multimedia to draw
on the strengths of a wide range of media, perhaps we should think of
our teaching as "multi-modal"; that is, drawing on the appropriate
teaching techniques from the entire menu of options at the right
time. The challenge for many of us is to add to our long-standing
capabilities in lecturing or case teaching the newer techniques of
cooperative and active learning.
Teaching MS/OR with Cases
Peter Bell, Richard Ivey School of Business,
University of Western Ontario
e-mail: pbell@ivey.uwo.ca
Web:
http://www.business.uwo.ca/~msis/bell.html
Christoph Haehling von Lanzenaeur
Free University of Berlin
e-mail:
Haehling@CCMailer.WiWiss.FU-Berlin.de
Peter Bell and Christoph Haehling von Lanzenaeur are both successful and longtime users of cases in teaching management science/operations research to MBA students and managers in executive development programs. Until recently, both were at the Richard Ivey School of Business at the University of Western Ontario, which is known for its dedication to teaching and developing relevant teaching material. Many who are not familiar with the case method wonder how one can teach technical skills using this approach. Peter and Christoph are both masters, and they set out to show how it is done in this session.
Christoph began with a discussion of how MS/OR and case teaching fit into a larger framework of general problem solving. After some discussion of what constitutes a case and the different uses of cases, he pointed out that cases can serve as a motivator for managers to use MS/OR for white collar productivity improvements. Furthermore, cases can be used in teaching MS/OR in a number of different ways, depending on the specific teaching objectives for a particular audience.
The heart of the session was an actual case discussion, based on the case of Ohio Polymer, Inc., which had been handed out at the plenary session the day before. Although the key issue in the case is the necessary background work for negotiating a long-term contract to cope with an imbalance of supply and demand, there are many other ways to deal with the case. Emphasis can either be placed on technical simulation aspects or on the more important issue of developing an appropriate pay-off table for the upcoming negotiations. During the session, a companion case &emdash; Probut Hydrocarbons, Inc. &emdash; was distributed, providing the perspective of the other side in the negotiations. This pair of cases provides an opportunity to carry out a negotiation session in class and introduces relevant concepts from game theory. (Both cases are available from the University of Western Ontario.)
The discussion of the case itself became lively after a slow start, due presumably to a group of teachers not being used to participating from the floor. Christoph led the case discussion and, in something of a tour de force, commented on his teaching techniques while he was leading the case. There are inevitably limits to how realistic one can make a classroom at a professional meeting, but Peter and Christoph took us a long way toward actually being in their classroom as they worked through the intricacies of a case with students.
Among my many impressions of this session, two that stand out are the amount of preparation the case teacher has to undertake in order to be prepared to follow the discussion down unpredictable paths; the second is how much the case method relies on conscientious preparation by the students. Not surprisingly, many of the best teaching techniques take the highest levels of investment by both teachers and students.
One final point Christoph made that stands out for me is his observation that, in his eyes, a case discussion is not complete until implementation issues are addressed and generalizations are made as to what has been learned and where else one could apply these lessons. Ideally, these generalizations are made by the students, since knowledge one has synthesized for oneself is recalled far longer than knowledge given by others.
My students sometimes clamor for "lessons learned" at the end of
class, whether a case discussion or not. I have usually resisted this
demand, thinking that I was "spoon-feeding" my class. I realize now
that I need to build time into my classes for the students to
synthesize their own summaries before class ends.
Teaching the Art of Modeling
Steve Powell, Amos Tuck School of Business
Administration, Dartmouth College
e-mail:
spowell@dartmouth.edu
Modeling is at the heart of management science, but in most of our courses we teach the tools of management science rather than modeling skills. In this session I described and attempted to give the participants a hands-on understanding of a course I have offered for a number of years to MBAs on the art of modeling itself (see "Teaching the Art of Modeling to MBA Students," Interfaces, Vol. 25, No. 3, May-June 1995, pp. 88-94). This is an elective, second-year course offered to students who already have had a short course in the basic tools of management science. In this course, I try to help the students learn the craft skills of modeling, such as how to determine the level of detail to model, or how to decide whether a prototype needs improvement. Because the focus is on craft skills, I call the class a "modeling studio." (I think Mike Magazine was the first to coin this phrase.)
I began the session with a discussion of what a model is and why we model. Then I described the type of modeling that I attempt to teach in this course by making a distinction between "end-user" modeling and specialist modeling. The latter is typically carried out by our Masters and Ph.D. graduates, and it involves large-scale problems, large budgets and long development periods. The models developed by specialists, which might apply to yield management, oil refining or telecommunications planning, are often complex, sophisticated and are typically implemented in permanent decision-support systems. The type of modeling MBAs are likely to do, by contrast, involves small-scale problems, short time frames, small budgets and limited expertise. Nonetheless, I believe there is enormous potential for effective modeling of this kind. But before MBAs will feel confident doing modeling on their own, they need to learn some of the critical craft skills that experienced modelers take for granted.
The course I teach uses two different types of activities to help students learn modeling skills. First, we work on modeling exercises together for a 90-minute class period once a week. A typical problem is to determine whether it is cost-effective for Kuwait to use icebergs from the Southern Ice Cap as a source of fresh water. These classes give me a chance to act as facilitator as the group models together, to coach them in good modeling approaches, and to model those approaches for them myself. The second type of activity involves week-long modeling cases that the students prepare in teams of two.
After a week of work, each group submits a short paper to the client in the case, describing the problem as they see it, along with their analysis and recommendation(s). No paper will be graded unless it includes a recommendation. Each week three groups also make oral presentations of their work, both for practice in the all-important task of translating one's analysis into managerial language, and also to reinforce the principle that there is no one correct model, just better or worse analyses.
We had advertised our sessions in this track as being interactive, and in order to live up to this promise and give participants a good feel for the type of problem I assign students, I handed out one of the week-long cases ("Retirement Planning") and gave the participants time to read it and sketch some approaches. After a few minutes I encouraged them to pair up and develop a joint approach to the problem. After about 20 minutes I brought the groups, who at this point were talking animatedly about different modeling issues, back together for a discussion of the first half hour in the life of a model. The discussion touched on issues such as whether the model should be deterministic or stochastic (and what difference that might make), how much detail to include, how to model the possibility of death before retirement, and so on.
The Retirement Planning case is one I wrote for the students to work on early in the course when their skills are still rudimentary. The case gives financial and personal information on a 46-year old man who is trying to decide at what rate to save for retirement. This is a problem many of the participants had worked on for themselves, but I have found few of my students who have given it much thought.
The problem is appropriate because it is rather simple in its mathematical structure, but quite complex in the number of modeling issues it raises. The hardest challenge for my students is to keep from getting buried in details. Some of them, for example, built elaborate models of the yearly budgets of the client, when there was no data to support this and these details really have no effect on the larger problem of how much to save.
One of the critical modeling choices is to decide how to model the client's consumption of funds after retirement. Many students discovered the idea of relating post-retirement income to pre-retirement income by assuming consumption at a fixed percentage of final salary. This is a felicitous use of parameterization, one of my favorite heuristics.
Heuristics play a central role in my teaching; in fact, they
provide the organizing principles for the course (see "Six Key
Modeling Heuristics," Interfaces, Vol. 25, No. 4 July-August
pp. 114-125). Prototyping is an important one of these heuristics, as
is parameterization. Some other less well-known heuristics involve
separating idea-generation from evaluation, working backward from the
final result, and modeling the data. I have found that being
conscious of the heuristics I use gives me a language for
communicating my skills to my students that I would not otherwise
have. Donald Schon has written an interesting book (Educating the
Reflective Practitioner, Jossey-Bass, 1987) on how teachers and
students of art and architecture struggle to find a common language
with which to discuss the early, somewhat clumsy attempts of the
students to paint or sketch structures. Those of us who would teach
modeling face the same difficulties. Focusing on heuristics has
helped me to some extent to find that elusive language.
Using Multimedia in Teaching MS/OR: The MENTOR Project
Val Belton, University of Strathclyde
e-mail:
val@mansci.strath.ac.uk
Helyn Thornbury, University of Strathclyde
e-mail:
Mentor@strath.ac.uk
Web:
http://www.mentor.strath.ac.uk/mentor.html
The MENTOR Project, now in its fourth year, is a teaching and learning technology project sponsored by the U.K. government and based in the Department of Management Science at the University of Strathclyde. Its aim is to develop a portfolio of multimedia modules on commonly taught operations research topics. At IFORS, Val Belton (one of the originators of MENTOR, along with Mark Elder), and Helyn Thornbury, project manager and a graduate student at the University of Strathclyde, presented the background and history of MENTOR, and gave demonstrations of some of the existing modules.
The MENTOR Project has received $1 million in funding since 1992 from the University Funding Councils of the U.K. Its aim is to use computer technology, especially multimedia, to improve the effectiveness and efficiency of teaching OR. Efficiency in this context means that the technology should allow students to learn quicker with fewer staff resources (teachers and assistants); effectiveness means the technology should support active learning, different learning styles, and learning at the student's own time and pace.
Val Belton and Mark Elder came to this project with a background in visual interactive modeling. Early on they established several critical development objectives. In order to make the modules as widely accepted as possible, each was developed by a team of subject matter experts in consultation with the academic OR community as a whole through a series of workshops. Second, in order to make the modules flexible, teachers can easily modify the software to customize it to their particular needs. Finally, they developed an authoring language ("LearnOR") so that modules can be created easily without learning a complex computer language.
Each MENTOR module contains hypertext, still and interactive graphics, animations, video, and visual interactive technique software integrated into a common format. A single module is designed to cover roughly 10 hours of traditional lecture. Students can work through the modules at their own pace, they can move ahead or back to topics of their choice, and they can pursue details to the depth they choose.
The modules that were developed first have been used in teaching for three years, meeting with a positive response from the students. Helyn is carrying out doctoral research investigating the way in which students learn from multimedia materials as an integrated element of teaching.
Nine modules are ready now for student use:
Six more modules are currently under development on the following topics:
IFORS96 was one of the first public showings of MENTOR outside of
the U.K. Judging from the interest and enthusiasm shown at the
meeting, where there were far too many participants for the limited
number of demonstration PCs (calling for an interactive update of the
session plan), and a consistently busy MENTOR exhibit booth, there is
broad interest in the possibilities of multimedia for teaching and
learning MS/OR. The best way to get more information on MENTOR is to
go to the Web site. There you will find information on the modules
currently available, how to obtain a sampler over the Web, how to
obtain the modules themselves and the authoring system, and much
more.
Summary
This group of conference presentations showed two things. First, that
there is significant innovation going on in the teaching of MS/OR,
and (I believe) much more to come. Second, there is a large group of
teachers interested, even thirsty, for new ideas and new approaches
to the problem of teaching difficult but powerful and rewarding
technical skills to skeptical students. It certainly was a rewarding
experience for the presenters, and one we hope to repeat in different
venues.
Stephen G. Powell is an associate professor at the Tuck School of Business, Dartmouth College.
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