EXPERIENCES TEACHING SYSTEM DYNAMICS
AT THE UK MASTERS LEVEL.
Prof. Alfredo Moscardi ni
University of Sunderland, School of Computing and Information Systems,
Sunderland, Tyne and Wear. SR1.3SD. UK
Petia Stoyanova
University of Sunderland, Business School,
Sunderland, Tyne and Wear. SR1 3SD. UK
ABSTRACT
This paper describes what is meant by modelling at Sunderland and how
System dynamics fits into this ethos. The teaching and the examples
covered in this System dynamics module are different the usual course
and the paper deals with our experiences in these areas. The reaction of
Eastern European ( Bulgarian ) students to this type of teaching is
discussed. Students must complete a project in a work placement to
obtain a masters qualification. The reaction of companies to the use of
System dynamics ( a new experience for most ) is discussed and examples
of the types of projects that-have been completed are given. The paper
concludes with a description of a Hypercard project which extends. the use
of System dynamics to Engineering students.
1. PURPOSE OF THE PAPER
The purpose of this paper is to show how System dynamics has been used
on a Masters course by extending its range to include “harder sciences”
This idea has also given birth to a project for developing new software for
teaching engineering students.
This paper is felt to be of importance to the System dynamics community
as there is still a need in the UK to promulgate the advantages offered by
the methodology and the new teaching and learning materials that could be
developed.
The paper begins by describing the background to Masters courses in the
UK and how System dynamics has played a major role in such a course at
the University of Sunderland. It then describes the new software that is
being produced. Finally the authors evaluate what has been described and
give their thoughts for the future of this type of work.
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2. THE USE OF SYSTEM DYNAMICS ON A MASTERS DEGREE
2.1 Background.
The University of Sunderland ( the Sunderland Polytechnic ) was the first
British Polytechnic to offer a Masters Degree in the UK in 1989. The
degree was called Mathematical Modelling and Computer Simulation. This
was @ two year, part time Masters and is still running successfully. Full
time taught Masters in the UK are difficult to run as‘it is extremely
difficult for students to get financial support and thus it is impossible
for Universities to attract enough students to make such a course viable.
However, in 1990, the British government designated certain areas as
areas of special skills shortages and Sunderland ‘successfully bid for a
full time modelling course. The course was renamed Computer Based
Modelling and Simulation and students taking the course received
governmental subsidies. This course ran for its maximum. span of three
years taking thirty students a year. A new course was then devised called
“Decision Support Systems for Industry” which is currently running and
has hopefully another three year grant.
The aim of all three courses was exactly the same i.e. to produce good
modellers rather than good mathematicians and this is the special skill
area that the government and Industry have recognised. It is interesting
to note the progression of titles in the sense that first the word
“mathematics” and then the word “computing” have disappeared. This
reflects the unfortunate ( in my opinion ) movement of students from
mathematics and computing as subjects in their own right to wider, more
multi disciplinary courses which include mathematics and computing.
2.2 Teaching Modellers versus Mathematicians.
Perhaps the aim of the course given in the preceding paragraph needs more
explanation. One must start with a definition of mathematics. This is a
difficult task but most mathematicians tend to Hilbert’ view that
mathematics is a closed self consistent body of knowledge which exists
independent of the real world. If one accepts this ( as | do ) then it is
impossible to perform a one-to-one mapping of mathematics onto any
real world application. There will always be some fussiness around the
edges, some inaccuracies, some indeterminacies. This attempt to map
mathematics onto the real world is called mathematical modelling which
the authors wish to distinguish from Applied Mathematics.
SYSTEM DYNAMICS '93 369
In Applied Mathematics, one is usually starting from one of the classical
equations , deciding on the relevance or applicability of certain terms,
using some well established mathematical technique and searching for the
correct mathematical solution. Although some of these aspects are part of
modelling, mathematical modelling is much wider than this. It embodies a
different way-of thinking. In my view it is part of a wider subject.called.
problem solving. [1,2,3]
In any problem there are two stages: perception and processing. There are
also two ways of thinking: vertical and lateral thinking. It is a common
misconception that. if one is intelligent. enough, one can solve any problem
merely by throwing intelligence at it. If you perceive the problem in the
wrong way then you may never solve it. Peoples perceptions of the world
are a function of their upbringing, culture and background. People perceive
in different ways. Mathematicians, are taught to think in certain highly
structured and logical ways. One could define this as Vertical Thinking.
What is often needed at this perception stage is Lateral Thinking. [4]
Once one has a firm perception of the problem ( it could still at this stage
be a wrong one!) then the solution will probably be best achieved by
mathematical type thinking or vertical thinking. Thus both ways of
thinking are important to the modeller, but most teaching concentrates on
vertical thinking, probably as this is much easier to teachll!
2.3 Differences between Vertical and.Lateral. Thinking
Vertical thinking is based on three fallacies:
1, That the established.way of looking at the situation is the only
possible way because it is right.
2. That by working logically on the situation, you errive at the
best perception of it.
3. That it does not matter where you start, because if your logic
or mathematics is good enough, you will eventually reach the
correct answer.
Vertical thinking preserves the established order of things. It polarises
opinions or thoughts into right or wrong. It proceeds from one certainty to
the next. It categorises things into boxes. It also breeds arrogance and
smugness.
370 SYSTEM DYNAMICS '93
Lateral thinking recognises the dominant polarising ideas that are in
existence and then searches for different ways of looking at things. It
relaxes the rigid control of vertical thinking.
More information in this area can be obtained from any of the excellent
books of Edward de Bono [1] from where these thoughts were taken. The
Point the paper is making is that before the mathematics (or vertical
thinking) is employed in solving a problem, there isa space for a more
questioning, relaxed, informal logic which is rarely taught and often
dismissed as trivial. One can very crudely divide these stages into the pre
and post equation stage. There are many methods for dealing with the post
equation stage but little on the pre equation stage: What is needed is a
formal modelling methodology, bearing in mind that any such
methodology will be of its very nature a much looser softer-methodology
than normal
2.4 System Dynamics as a Formal Modelling Methodology
System Dynamics has an obvious role in any modelling course as a vehicle
for strategic planning, policy making, study of structure etc. What has
been investigated at Sunderland, is the development of System Dynamics
‘as @ formal modelling methodology. System Dynamics and Causal Loop
Modelling rely more on the lateral rather than the vertical thinking side.
This. is not denying System dynamics the ability to construct accurate .
quantitative models but stressing the teaching and learning benefits that
can be accrued. System dynamics provides the student with a set of tools
and the opportunity to construct his own perception of the problem. With
software such as STELLA these causal models can be quickly and easily
transformed into working simulations or models and qualitative behaviour
observed. It is 6 perfect way of getting involved with a problem without
the worries of whether the mathematics is correct or not. In this sense
System Dynamics and Causal Modelling satisfy the requirements of a
formal modelling methodology.
STELLA’s equations can be easily transformed into mathematical ones and
then the full power of mathematics can be applied to the problem. But
System dynamics has filled that vital gap, that questioning of reality,
that investigation of what exactly is causing what to happen, that worry
free experimentation , that pre-equation stage in fact the perception
stage of the problem solving activity.
For these reasons the Masters courses have been organised so that the
first course is one on System dynamics. The course begins with an
SYSTEM DYNAMICS '93 371
introductory module: which sets the general background i.e. the dif ference
between modelling and mathematics, Vertical and Lateral thinking and the
modelling process. This is then followed by the course on Causal
Modelling and System dynamics.
Superficially, the-course follows the normal progression of influence
diagrams, causal-models and-constructing System Dynamics models with
STELLA but the emphasis is different. The problems that are discussed
involve such entities as velocities; accelerations, forces, impulses and
momentum. By forcing the students to think causally about such entities,
new insights are revealed. The true meaning of laws such as Newton's
Laws are explored. The graphical output of STELLA is analysed in this
context. There are many difficulties. Entities such as velocity can be both
levels and rates. If acceleration is chosen as a level then what entity is
the flow into this level. An interesting aspect is that the models built
reflect an integrative approach rather than a differential one. Distance
springs naturally as @ result of velocity multiplied by time whereas it is
difficult to model velocity as distance divided by time. This illustrates
vividly the paradox of instantaneous happenings and infinitesimals. This is
one example of the many discussions that are brought forward in the
discussions generated in this course. Further details are in papers by D.
Prior: given at the last System Dynamics. meeting in Bangkok.
2.5 Evaluation of the success of the System dynamics Module
Students view
Students select study courses for many reasons. Not all courses are
memorable This may be due to the students attitude to learning, the
delivery of the course or a number of other reasons.
System dynamics was my first subject on the MSc course “Computer
Modelling and Simulation ” at the University of Sunderland and | was not
disappointed in my selection of this course. It was a striking and happy
experience. “How exciting” was what | said to myself in the first lecture.
In discussion with my colleagues | discovered that we all shared the same
opinion. Not only was the subject interesting in its own right but the way
it was delivered was exceptional.
| would now like to consider the different aspects in which this course
contributes to students’ conceptual development :
372 SYSTEM DYNAMICS '93
The course helps in smproving students mania? models af complex
sysiems. They are taught to consider the wholeness and internal
connectedness of systems.
Applying system dynamics methodology for “qualitative description,
exploration and analysis of complex systems”! #elps deaper understanding
of ihe relationship belween systems heheviour end iis structure and
daformetion Jinks. Throughout the course models of physical and social
systems (cooling of tea, production-inventory system, etc) have been
developed and simulated over time (using STELLA*) with the. purpose of
analysing systems behaviour. The effect of alternative systems structures
and control strategies on systems behaviour have been examined. This
challenges esperimenting with new ideas end avercaming the haunderies
of Hineer thinking end considers e new eprcech te description end
enelysis af systems, 18 systems tbinking .
In my opinion the course would have benefited from case studies of
solving real life problems with the help of system dynamics approach
(physical and social systems, considering the background and specific
interests of the students).
Placement View
Some of the placements using System Dynamics over the lest couple of
years are listed below:
The Promotion of Simulation for Decision Support Systems in Manufacturing
# Simulation of the Production Planning of the NEK Core manufacturing Area
Simulation Modelling of Resource Scheduling
Simulation of the Hot Metal Cycle of British Steel Teesside Works of Basic Oxygen
Steel making Plant
Modelling e Water Distribution System
The Dynamics of Dumper Trucks
A System dynamics Model of a Low Pressure Gas Holder Station
A System dynamics Simulation of Heat Transfer in a Natarium
An investigation into the Use of Hypermedia and Simulation for the praduction of
Management Support Tools
* STELLA simulation software has proved to be an ideal tool for creating computer
laboratory experiments
1 The citation is from. ‘Management Information Systems’ by Eric Wolstenholme.
SYSTEM DYNAMICS '93 373
The first four are the normal type of use that one would expect from a
System dynamics Project. But even these are not common in the UK and
firms have to be persuaded that there will be a payoff for them by using
this approach. There is also a problem in that most small UK firms do not
own a MAC. The general reaction from the firms was that they were
impressed by the ability of STELLA to portray what was happening and
most of these firms have since bought their-own copies and a MAC which
they are now using.
The second group of four are more interesting. This work fits more with
our philosophy of System Dynamics as a modelling methodology and it is
being used in areas that are quite unusual.
The first was a result of the water privatisation bill in the UK. Water
authorities needed to know exactly how much water was being used and to
plan the efficient use of various reservoirs. System Dynamics proved ideal
for this and the subsequent model.is now used by the relevant authority.[5]
The second placement was investigating the behaviour of the suspension
system of a dumper truck under very heavy loads. This would normally
have been tackled by a second order mass spring damping differential
equation. Using System Dynamics revealed new insights to both the
student and the company.
The third was even more unusual. In large electrical stations the _
conductors are surrounded by sealed containers containing an insulating
gas. The characteristics of such containers are normally modelled using
Finite Element Analysis. Again an understanding of the various components
was clearly revealed by a System Dynamics model.
The fourth one covered heat transfer. It is expensive to heat a swimming
poo! and once heated it is uneconomic to let the heat dissipate. One
solution is to cover the pool with an insulating material at night. This
study investigated how thick and how effective such a covering would be.
These are four unusual applications of System dynamics. In all cases, the
purpose of the exercise was to obtain detailed accurate quantitative
results but more to understand the processes involved and reveal what
may be counter to intuitive results. The benefit of the modelling was in
the doing of it more than the use of it. This extension of the application of
System dynamics is, in my experience, new and very exciting.
374 SYSTEM DYNAMICS '93
The last project is typical of a batch using the power of Hypercard linked
to the power of STELLA through the link of STELLA STACKS. A model of a
general production-distribution system has been developed. The model is
supplied with a proper. interactive interface which allows the user to
investigate the systems behaviour and implement. his own policies by
varying the values of the parameters.
In summery, every year, more and more students are asking for placements
that allow them to use System dynamics. The applications that are found
are more and more varied and the number of firms becoming involved is
steadily increasing.
3. EXTENSION TO NEW SOFTWARE
The success of such models led the Sunderland team, led by Don Prior, to
investigate if such methods could be useful in-the general teaching of
engineers. We decided to produce a series of modules. [6,7]
in order to access the potential effectiveness of the learning material it
was needed to decide precisely who the material is aimed at. It was
decided to aim it at the mathematically unadapted ( and physically
unadapted ) learner who is taking, or wishes to take, a degree course in an
engineering discipline. Such @ learner can be assumed-to have acquired
only a basic ability to manipulate mathematical expressions and be able
to interpret basic graphs. it will be assumed that the learner is physically
unadapted in the sense that even a nodding acquaintance with, say,
Newton’s Second Law cannot be immediately used. The underlying physical
concepts used in the modelling process will be introduced to the learner
within the appropriate micro world before the modelling process is
started. No mathematical modelling skills will be assumed. To a limited
extent these skills may be regarded as independent of the skills of the
competent mathematician who would normally enrol for a course in an
engineering discipline. In short, the unadapted learner can be described as
having acquired a limited mathematical background but be totally lacking
in the skills necessary to apply mathematical skills to the development
and interpretation of mathematical models of simple physical systems.
The intention of the project was to answer three questions:
1. Was it possible to apply the ideas of System Dynamics to
engineering situations?
SYSTEM DYNAMICS '93 375
2. Would this approach be suitable for mathematically unadapted
students?
3. Could this be achieved though heuristic learning using the full
power of the Macintosh?
The first two objectives were seen to be possible. The team knew that the
methodology was suitable but how to arrange it in a heuristic learning
situation At this stage it is important to define what we understand> by
heuristic learning.
The stugent is presented hy @ set af Séreens WwhiCh CGUid Le
jnvestigetions, experiments ar simple discoveries. lising ihe mouse
a is fart ta discaver or find a1] the relevant information, This can
then Le assembled ta farm @ madel There will he @ preferred
pethwey through the safiwere hui the sefiwere fiself is presented
in @ i0ase, Hexitle non-siructured formal where the user con
praceed in any direction whatever. Extensive help ie provided but it
is for the user ta ask far this ar eny infarmelian he mey need
in the initial stages of the project, it was foreseen that the major
difficulty would be a pedagogical one i.e. how best to present the
concepts. Although the subject area i.e. Causal Modelling and System
Dynamics was well understood and had been successfully taught for
several years to all levels of students, the novelty of this project was
both its application to “hard” dynamic systems and its delivery vie.a
computer aided or distance learning ‘mode. It was envisaged therefore that
there would be several attempts to discover “ the best method” and
certainly that a minimum of one year would be needed to determine the
Philosophy of the approach experimenting with various delivery modes.
The final approach on two processes that are essential to modelling. i.e.
representing what is physically happening ( what you see )
representing the causal links ( what you think causes behaviour.)
These two processes occur contemporaneously in every model and in the
new approach were introduced through ORACLE. ORACLE is an all seeing all
thinking guru who for the purpose of this software has two attributes : his
EYES and his MIND. The user is asked to use the EYES of ORACLE to look at
the problem and build a model representing what he sees. This will be
Physical STOCKS or LEVELS and physical FLOWS. This model is therefore
termed the PHYSICAL MODEL.
376 SYSTEM DYNAMICS '93
There are mechanisms that enable the effects of the physical model to
take place. This is normally by the existence of INFORMATION LINKS. The
user is now asked to use the MIND of ORACLE to build the more difficult
CONCEPTUAL MODEL which consists of these information links. By
combining the PHYSICAL and the CONCEPTUAL models together, the final
model is produced. Experiments and investigations are provided in both the
EYES and MIND stacks and extensive HELP is available all through. The five
areas of investigation remain the same.
Predator-prey ( Herbivore Island )
Mass. Spring Damping (‘The Baby Bouncer )
Projectiles ( The Bouncing Ball }
Electrical Circuits ( Resistor and Condenser)
Newton's Law of Cooling (The Cup of Tea }
4. CONCLUSIONS
System Dynamics is used as an important part of the.modelling.MSc at the
University of Sunderland Our experience tells us it should be an integral
part of such courses. System dynamics should no longer be considered
solely in the examination of “soft” systems as it has been successfully
extended since 1990 to cover “hard” subjects at the University of
Sunderland.
The success of the course and its popularity among students and
employers has lead to many new initiatives and the development of new
software with Hypercard and STELLA Stacks. .
REFERENCES
2.
3.
4
Moscardini A.0. rathematical Modelling.
Educational Courses in Britain. Dominion Press Vol 10.No 5 1990
Moscardini A.O.ldentification of Mathematical Modelling Skills.
Sixth Int. Congress on Math. Ed. Budapest 1988 °
Moscardini A.O. Identification and Teaching of Mathematical Modelling Skills.
Modelling Applications and Applied Problem Solving. Ellis Horwood 1989
Edward de Bono. Lateral Thinking. Penquin Books 1979
Fletcher, E, Moscardini A.0., Johnsen, P., Archer D.
Use of Simulation as Decision Support tool for Management of Water Resources.
10th IASTAC Sym.-in Mod.identification 1991
D.E. Prior, A.O.MoscardiniAn .Alternative Approach to the Acquisition
of Mathematical Insight for the Mathematically Unadapted.
7th International Conference:on Technology and Education, Brussels March, 1990.
Curran D, Moscardini A.0. Middleton W.
Hypermedia - A New Approach to Mathematics Teaching.
Proc East West-Congress in Engineering Education. Krackow 1991
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