1994 INTERNATIONAL SYSTEM DYNAMICS CONFERENCE
Learning about Modelling for Learning
Leroy White, Tony Ackroyd, and Michelle Blakeborough
Centre for Applied Statistics and Systems Modelling _
University of Greenwich
Wellington St, London SE18 6PF, UK
Abstract
It is widely recognised that modelling organisational systems can be used to provide insights into the
problems of an organisation, and to induce learning about the context. The objectives are to increase
the effectiveness of thinking about the situation, to enable a wide participation in the construction of
the models, and to allow an analysis that minimises the need for Opaque technical reasoning. It is
important, therefore, in the training of future modellers on und and p courses,
to appreciate the need to identify a system's structure and behaviour, without necessarily placing a
strong emphasis on the underlying mathematics.
This paper describes how system dynamics was used to re-design a course on systems modelling,
with an emphasis on system dynamics. In the approach adopted, cognitive mapping in conjunction
with drawing influence diagrams helped to conceptualise and to think about the situation, and a
workshop environment was adopted to design and analyse the models of the course.
In addition, the paper will discuss the nature of the modelling process, and the problems of the
distinction between qualitative and forms of rep ion. Finally, lusions will be
given on the potential of system dynamics modelling in the education of Systems Analysts, modellers
or Operational Researchers.
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Learning about Modelling for Learning
Introduction
The need for change has been recognised by many disciplines and in many ways. This paper will
address the effect on modelling given the backcloth of change. The paper, in particular, will discuss the
nature of the modelling process, and the problems of the distinction between qualitative and qi
forms of reference. It then looks at how. System Dynamics was used to re-design a course ‘on System.
Dynamics, In the approach adopted, cognitive mapping in conj ‘ion with drawing influence diagrams
helped to conceptualise and to think about the situation, and a workshop environment was adopted to
design and analyse the models of the course. Finally, conclusions will be given on the potential of
System Dynamics modelling in the education of System Analysts, modellers or Operational
Researchers.
Modelling: the need for change
Cc insist on proclaiming that immense changes have taken place in organisational and
economic life over the last decade or so. Many and academics have edged this view
by reminding us that society today is not what it use to be. As a result it is becoming increasingly
apparent that the traditi pproaches to solving 1 or probl and the use
of the conventional management sciences, as taught at the universities and dly d in text
books, have become obsolete. What response is there to this image of change? Is it a simple case of
modifying or replacing the traditional tools? Jt would appear that this vision has a limited wisdom. Many
writers on management and organisations, such as Peters (1982) and Senge (1990) have indicated that
the terrain of organisational life has changed beyond recognition, and to cope with the new horizons we
need not only new methods and organisations, but also a new vision.
It seems there are few adequate tools available to delve the concepts of change. The surface effects are
the only things available to us to explore. From these effects a plethora of interpretations may abound,
which may leave us feeling as though we are drowning; not an easy feeling to dispel. Even the higher
education sector has not escaped this situation, which seems to be running in tandem with changes in
organisational life. It appears that the uni ty education system is justing itself. Within it, new
patterns of courses are emerging, and the structure of the curriculum is being re-drafted. The course
content of degrees are justified either by what the outside world wants or a perception of a change in the
order of knowledge. It would appear that no university course is immune from the contagious spread of
aneed for change.
At the University of Greenwich, the of Math ics, Statistics and C ing has
undergone a lot of soul searching over the past few years to establish what identity it has in the provision
of mathematics education. In essence the department has realised that its identity lies in that region that
makes it di : an emphasis on modelling. This is the heart of its identity, with courses and options
feeding into it or using it. Modelling at Greenwich is not only the core of the curriculum, but is also the
core of its research and consultancy. For example, it is the home of the Journal of Applied Mathematical
Modelling. The main focus of the modelling research has been towards industrial processes (see Cross
1993).
The main text book used for teaching modelling at Greenwich is a book written by two of its lecturers
(Edwards and Hamson 1989). The reason for modelling that the authors put forward is that:
., learning to apply mathematics is a very different activity from leaning mathematics. The skills needed to be successful in
applying mathematics are quite different from those needed to understand concepts, to prove theorems or to solve equations”
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Of a model they said that it ~ can be defined as a simplified representation of certain aspects of a real
system. A mathematical model is a model created using mathematical concepts such as functions and
equations, When we create mathematical models, we move from the real world into the abstract world
of mathematical Concepts, which is where the model i is built. We then manipulate the model using
or ided ion. Finally we re-enter the real world,
taking with us the solution to the mathematical problem, which is then translated into a useful solution
to the real problem’.
U ially, most ics schools would agree that the objective of teaching modelling is
not just to provide the student with a set of techniques to use, but to allow them to apply common sense.
Although it is appropriate to use mathematical principles that are based on sound reasoning, when it
comes to modelling some given problem the student is free to construct the model using whatever
mathematical relationships seem appropriate.
All this fits a traditi Applied Math ics course with traditional students. The trend, however, is to
attract different students by offering courses that reflect not only Industrial, Management or Business
but also Envi and Social Scientific ones as well. The question this raises is,
would the traditional view of modelling be justified on these courses? Given that modelling is to remain
at the heart of these courses, a new rationale for the modelling process needs to be explored. In this
paper we will discuss one of these courses, called Business Systems Modelling.
The Business Systems Modelling degree was designed to have systems thinking and Operational
Research (OR) as the central modelling methodology. The members of the course design team were well
aware of the soul-searching OR and other management sciences have been going through, and thought it
might be pertinent to bring some of the outcomes of the reflection to the design of the course.
The course would have to be designed to maintain the idea of a practically based philosophy as opposed
to a theoretical one. A different rationale was needed so that it would be possible to move away from
courses based on modelling methods that were relevant only to prescribed problems, as in hard systems.
This would not mean rejecting hard modelling, but showing it is part of a more general soft modelling
framework, ie. those that deal with “messes' or complex systems. We accepted this premise recognising
that the general level of theorising on the relationship between hard modelling and soft modelling was
relatively young, and realising that it was not even clear to a mathematics school that such a relationship
should be explored. However, even amongst the hard modelling staff they recognised that the nature of
modelling had changed (as can be seen from the fact that much of the research work of the department
now is in the area of simulation in all its forms) and that novel methodologies should be adopted.
Alternative views on modelling
What were the changes in perceptions about modelling? The view taken by de Geus (1992), seemed to
us to capture the feeling about a new attitude to modelling. It was that:
" we are no longer talking about the model as the understanding of this world as it has been acquired by a modeller or a planner.
We are no longer talking about a modelled understanding of this world as it has been acquired by an academic or some outside
institution like a plan bureau to be use to make predictions. We are talking about the understanding of [a clients'] world as it has
been acquired by them....[M]odelling the world we give them a toy... with which they can play, with which they can experiment
without having to fear the consequences”.
Or alternatively the view from Morecroft (1992)
" Models should capture the knowledge and mental data of the [client]; models should blend qualitative mapping with friendly
algebra and simulations; models can be small; their purpose is to support team reasoning and learning; they encourage systems
thinking. Simulations provide stories about the future not predictions”.
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The above quotes are taken from practitioners and thinkers in the System Dynamics field. They have
been remarking on the timely re-emergence of System Dynamics as an important modelling
thodology for Others like holme (1982, 1990) have provided a
detailed description on how to use System Dynamics as a soft modelling methodology. In particular, he
outlines the modelling process in terms of a ipti phase and an exploration phase, saying that “the
qualitative analysis facilitated by this is often sufficient in itself to generate problem understanding’.
Such a view of modelling would ask a modeller to describe and explore complex systems by drawing a
systems diagram as a model to ise and icate images’ of problems which would lead to an
understanding of a given situation in a way that language can not. These models could then be used to
facilitate quantitative modelling, to further explore the system under investigation, using, for example,
simulation.
The quotes seem to make clear the importance of modelling the qualitative aspects of the situation as
well as the quantitative, and explore the relationship between the two regions. Following on from this
the system representation is sufficiently rigorous to be tumed into accessible mathematical equations
(for example difference equations) capable of being handled by a computer.
Outside the system sphere, qualitative representation or modelling has been well established. The most
prominent example is the Cognitive Mapping technique developed by Eden (1983) for modelling
complex i What is about the in the q ive modelling
methodologies are that they have emerged in a wide field. For each of the techniques it is claimed that
they would be able to incorporate subjective elements in models. There is no space here to discuss the
implication of the above, but a paper by Taket and White (1994) has provided a discussion of this ina
wider context.
Modelling as Learning
Interestingly, another aspect of modelling that certain System Dynamics authors are espousing is the
idea of modelling as learning. They ask, how can models influence thinking and action in teams?
(Morecroft 1992) The answer suggested i is, by stressing the use of conceptual models, that they can be
used to aid the learning pi of individuals and groups. bers of a group will “use models when
it is clear to [them] that their ideas and knowledge are represented in the model... learning takes place
when people discover for themselves the contradictions between observed behaviour and their
perceptions of how the world should operate’ Ade Geus 1992), or even when the contradictions between
different individ p are
Returning to the development of the course, some members of staff were familiar with System
Dynamics, and were interested in soft modelling methods. System Dynamics was thought to be an
ip for modelling on the degree, because it helped to stress that models should help
decision makers understand the world and the way that they construct that world; it provided a toy to
support decision making in teams, and it induced learning, among the decision makers, about the
complex systems they are part of.
In the event, System Dynamics was seen as the lynch-pin modelling methodology on the Business
Systems Modelling degree. It was used to emphasise the need to assimilate novel ideas on modelling
and to stress an alternative orientation for Id-be dellers. L ly, our view of the grand
order of things was not shared by the students. Even after the first year of the course they still had a very
narrow reductionist view to modelling, and found it difficult to look at issues holistically, and they could
not see the point of the unit. Whilst acknowledging their right to this view, we felt that it was a view
based on limitation rather than choice. The course was failing to get its points across. Whilst feedback
about units is often produced at the end of the course using questionnaires, the course team decided to
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use issue-structuring approaches to explore how staff and students saw the unit. There were four reasons
behind this choice.
First, the review team wanted to tap into the staff and students experience of the unit -it was a chance to
learn from them and thus about modelling in general on the course.
Second, there was the need to get active involvement in the structuring of the issues, and in thinking
through how to tackle them.
Third, it was an opportunity for staff and students to learn from one another and to break down barriers
of profession and authority.
To tackle this issue it was thought appropriate that System Dynamics should be used to learn about the
unit on modelling for learning. Last, it was an opportunity to practice what we preach.
Evaluation of the process
How should we explore and learn about the impact of the modelling unit? We might try interviewing
some students and staff to generate data of the situation ‘as they see it’. However, would this data be
amenable to analysis, induce learning, and facilitate change? One of the authors has used cognitive
mapping as a tool to explore p with ity groups (Rosenhead and White 1994). Can this
tool be used in conjunction with System Dynamics?
It is now accepted that cognitive mapping is a reasonable modelling tool. It can be used to produce a
picture of the situation as the individual ‘sees it, by sketching the relationship between ideas, values and
attitudes. The picture produced is a construction using arrows that imply causality between concepts. In
its abstract form, the map can be seen as a directed graph. An influence diagram can also be seen in its
abstract form as a directed graph. Can a cognitive map be related to an influence diagram?
Eden shows, in his book (Eden 1983) how a cognitive map can be the basis of an influence diagram for
a System Dynamics model, recognising that they are from different provinces. The link between the two
provinces is established through the process of ‘problem-helping’. The process for ‘problem-helping’
does not preclude the use of quantitative modelling. If required, a System Dynamics model could
potentially be incorporated in the process of *problem-helping' because, in Eden's own words, “it can
take into account the dynamic consequences of perceived feedback loops... and because they are
relatively easy to construct using influence diagrams which are similar in form to cognitive maps (my
emphasis)’. Eden (1983) points out that a cognitive map ‘is so called in order to lay emphasis on the
idiosyncratic [and subjective] aspects of the model constructed - it is not supposed to be a scientific
model of an objective reality in the same way some influence diagrams are (for example, those used by
System Dynamics modellers)... - it can never be shown to be right or wrong in an ‘objective’ sense.’
(Here Eden is referring to Ist generation system dynamics). Eden sees System Dynamics as modelling
some ‘objective’ reality and cognitive mapping as representing the ‘reality’ as defined by an individual in
their own “language and theories’.
Morecroft (1988) has recently written about how System Dynamics has been used for group model
building with and has di: d that this devel: might be used to influence thinking
and actions in management teams. He states that “increasingly modellers have turned their attention to
the mental models of managers and the learning processes of the individuals and groups’. He sees the
System Dynamics model, like other methods for generating mind maps, ie. as a tool to “support
cognitive processes and group problem structuring’. It seems reasonable to conclude that although
cognitive mapping has a different origin to influence diagrams, it has a place in generating group
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coherence, which can be sub i ped into inflv diagrams or using the System
Dynamics concepts.
Once the cognitive map is drawn up, through iation it can be developed into an i diagram.
Eden suggested that in the process of the transformation the problem-helper concentrates on the nature
and significance of feedback loops, usually meaning that concepts are translated into monotonic
concepts (which may mean some of the rich meaning is lost in the translation). During this
‘ion some of the relationships common to itive mapping and infl di can be
discussed with the team. This provides the motivation for the members of the group to sketch out the
influence diagrams, to implement the rules for putting in the System Dynamics ‘plumbing’ and to use the
model for further analysis. The model produced can be then seen as a ‘toy’ which, following Morecroft
(1988) can be used as a “microworld environment’, where playing and learning, (with facilitation) can
take place. This tentative sketch of a process was used as a basis for exploring the modelling unit.
Procedure
As a first step the research team brought together some members of staff and students as the review
group. Of course they had experience in the learning and delivery of the unit. Their remit was to explore
the issue of running the unit, and set out what were the impacts, the opportunities and weaknesses.
The research team used the approach shown in Figure 1. After the review team has been selected each
member of that team would be interviewed using cognitive mapping. The maps would then be analysed
and fedback to the individuals. Following this, the revised maps would then be merged and the
composite map analysed. The composite map could then be used by the review team in a workshop
environment where they could explore the issues and feedback loops. The aim of the workshop would
be to produce an influence diagram (available for further analysis) and a structured debate of the issues.
Individual interviews
The individual interviews were intended to give each member of the review team the opportunity to
raise pee issue they saw affecting the running and understanding of the unit. This was conducted in an
open, and where the individuals were free to say what ever they wished.
Each member of the review team was allowed to elaborate freely on their views of the course, and were
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asked to raise any issue they saw as being significant. The interviews were unstructured. The research
group then had the task to translate the interview results into a map, which was consequently fedback for
clarification and modification. From the feedback an explanation of the mapping structure was given, to
help guide the interviewee in their thinking about the issues raised and the connections between them.
Workshop
The interviews were followed up by a workshop with the review group as a whole. A concept map was
Pp d ( the reduced ite map), and the research team facilitator gave an overview of the
issues, arguments, concerns and options which had been raised during the interview stage. It was
explained to the review group that the map had been reduced to a concept map (see Eden ()) in which
clusters of ideas were identified and the relationships between the clusters were drawn up (see Figure 2)
in order to structure and stimulate discussion. The review group then prioritised which concepts (issues)
they wanted to tackle.
For each concept, those that vaned monotonically were identified, as the discussion developed, in the
form of feedback loops. The relationship of the loops with each of the other loops were built up into an
influence diagram. During thiy process differing viewpoints, opinions and assumptions were aired and
discussed. This helped to clarify a lot of implicit misunderstandings, especially between staff and
students. Many criticisms of the unit were made and yet it all took place in a very positive and
constructive atmosphere. The result was 4 shared understanding of the methods and aims of the unit
which led to an easy acceptance ot the resultung influence diagram. This diagram was then used as a
focus to discuss the dynamics between sanous concepts and to identify the polarity of feedback loops.
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oe eS
et ah a
igure 3. sntuence Diagram
Figure 3 is the influence diagram agreed by the review group at the end of the workshop. There were
numerous influences and concepts modified during the workshop due to initial differences of viewpoints
and experiences. The five main ones were:
Relevancy to the degree
Incentive to work and assessment
Level of maths to include
Value of presentations
Importance of examples.
To explore one: the value of p ions. At the beginning of the p the staff saw
as being relevant to the degree and a good way of ii ing student und ding of their
topic. On the other hand, students saw little relevance to the course, and the presentations leading to
stress which actually reduced their understanding. After discussion the review group drew up the
influences shown.
The final step in the analysis of the issues affecting the unit was to build a System Dynamics model of
the influence diagram. This inevitably led to modification and simplification of the influence diagram
into a combination of quantifiable stocks, rates and constants. Whilst this helped us look at the influence
diagram with a different view, and clarified the ideas of what could (should?) be quantified, the resultant
model did seem a gross simpli The itative results de ded upon jud; Il concepts (eg
goodness of examples, effects of stress) and led to no conclusive results apart from those that could be
deduced from the influence diagram.
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Conclusion
Our education system helps to perpetuate an accepted view of models and modelling. It is the traditional
view of modelling, where it is held that knowledge is about something ‘out there’ which is either
uncovered or discovered. Models are held to be built in order to reflect or mirror reality and it will be
morte or less accurate a representation of reality depending on the ingenuity of the modeller. Such
models can then be tested to declare them to be a “good reflection of reality’. Senge (1990) elaborates on
this as a problem for managers, for example he states:
" We are taught to break apart problems, to fragment the world. This apparently makes complex tasks and subjects more
manageable, but we pay a hidden ‘and enormous price. We can no longer see the consequences of our actions, we lose our
intrinsic sense of connection to a larger “whole”.
He claims that managers should be encouraged to change the way they perceive issues about the
changing world. In attempting to model the world it is not a case of finding some simplified objective
abstraction of reality, but a need to represent the diverse and rich view of individuals “as they see the
world’.
In this way, we believe that students need to be educated about differing viewpoints (many of which are
valid), about levels of appropriateness, not about extremes of right or wrong. Furthermore, they should
try to view the system being investigated as a whole and not a set of parts. We think System Dynamics
helps to achieve this by encouraging groups to look at complex systems as a whole and allowing them to
represent their views (and other peoples) explicitly.
Our use of System Dynamics and Cognitive Mapping reinforced the view that they are both useful tools
for representing different viewpoints and helpful in leading groups in constructive debate. Their visual
similarity and conceptual differences made the transfer from cognitive maps to influence diagrams
straightforward and also thought-provoking at the same time. This ensured we re-examined our ideas on
a i basis. The ion from infl diagram to System Dynamics plumbing was not as
successful. Once more the transfer made us re-examine our ideas, but we could not place much faith in
the enforced quantification necessary to produce a working model.
This failure at the last hurdle does not discourage us nor invalidate the process. The visualisation and
communication needed to build the maps and diagrams had enormous benefits. It does, however, make
us aware that System Dynamics is a many faceted jewel, with some facets bringing a clarity to the issues
and others distorting them. It should be handied with care.
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References
Cross, M., Pittman, J. and R. Wood. 1993. Math ical Modelling for Materials Pi ing. OUP
Eden, C., D. Sims and S. Jones. 1983. Messing about in Problems. Pergamon.
Edwards, D. and M. Hamson. 1989. A Guide to Mathematical Modelling. MacMillan, Basingstoke.
de Geus, A.P. 1992. Modelling to Predict or to Learn. pean Journal of Operational R h 59:1-
3
Morecroft, J.D.W. 1988. System Dynamics and Microworlds for Policy Makers. European Journal of
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Peters, P.M. and R.H. Waterman. 1982. In Search of Excellence. Harper and Row.
Rosenhead, J. and L. White. 1994. Nuclear Fusion. Mimeo.
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Conference, Stirling.
Wolstenholme, EF. 1982. System Dynamics in Perspective. Journal of the Operational Research
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Wolstenholme, E.F. 1990. System Enquiry. Wiley.
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