Working group 2:
System dynamics and systems thinking
Günther Ossimitz
Klagenfurt, Austria
|
Modelling carbon dioxide pollution — The Austrian carbon balance model |
|
|
Leadership, management and management control — A system dynamics approach |
|
|
Systems thinking and system dynamics: A new perspective for math classes? |
|
|
Teaching system dynamics modelling in secondary schools |
1 Aim of the working group
This working group, for short, SD/ST, focused its interest upon the following issues:
What are the basic didactic ideas of teaching SD
/ ST?
How can SD/ST be taught in mathematics classes?
What are the roles of diagramming tools in
SD/ST?
What are the practical experiences with teaching
SD/ST in math classes?
How is SD/ST knowledge being used in different
fields of science?
How can causal loop diagramming be learned
practically?
The last two issues have been provided by members of the "System Dynamics Austria Group" (SDA). This interdisciplinary group of Austrian scientists devoted to the propagation of SD/ST ideas and practice throughout their fields of application. None of the three guests from SDA is working in mathematics or mathematics didactics, but they all gave an excellent view into their work as systemic practitioners and thus provided valuable background knowledge for the mathematics educators community. My heartfelt thanks to Stephan Berchtold, Ernst Gebetsroither and Stefan Güldenberg for their enthusiasm in joining this working group. I am also very grateful to my old colleague and friend Franz Schlöglhofer, who reported on his experiences on teaching the curriculum chapter "Untersuchung vernetzter Systeme" (Investigation of Interrelated Systems) in Austrian math classes.
1 What happened?
SD modelling – A new perspective for math classes?
In the first time-slot, G. Ossimitz gave a very plain introduction to the main ideas of the field:
What is systems thinking?
What are the basic ideas of System Dynamics Modelling?
Can Systems Thinking / Systems Dynamics be a topic for math classes?
SD/ST: a section in the Austrian mathematics curriculum
Results of empirical studies concerning SD / ST in math classes
Three presentations of the SD/ST practitioners
A real
highlight of the working group was in the second session, when three invited
guest speakers from the System Dynamics Austria Group reported about practical
SD in their field. Stefan Güldenberg
from the Wirtschaftsuniversität Wien showed in his presentation "Leadership,
management and management control – A System dynamics approach" that SD
modelling capabilities are very useful for supporting successful business
leaders in their decisions. Ernst
Gebetsroither (Austrian Research Centre Seibersdorf) reported on a
very complex Carbon Dioxide Balance Model, which has been developed under his
leadership for the Austrian Government in order to simulate different
strategies for achieving the CO2-targets of the
Crash-course in causal loop modelling
The second very interesting and lively contribution of the three experts from the SDA was a practical "crash-course" in the technique of causal loop modelling. Here the group became really a "working" group with practical systems exercises and games, which helped the participants to get a practical feeling of systemic interrelations. Feedback loops were not just sketched, but also actually brought to life.
Teaching system dynamics modelling in secondary schools: The teacher's perspective
Franz Schlöglhofer addressed in this presentation the following issues:
What are the basic ideas of the didactics of
System Dynamics (SD)?
What aspects of math teaching are involved when
teaching SD?
What are the main ideas of the section
"Investigation of Interrelated Systems" of
What are the experiences with practical teaching
SD in math classes?
Practical examples for teaching system dynamics in mathematics classes
Günther Ossimitz presented a number of practical SD models for teaching at school. Actually the presentation turned out to be more a discussion group about the following issues:
Which
software is available / useful for doing SD modelling at school?
Is
it at all necessary to choose a quantitative modelling approach for gaining
systems thinking capabilities or would a merely qualitative modelling be
sufficient?
How
complex should the SD models, which are dealt with at schools, be? In this context
the importance of developing more complex models out of simpler ones in a
step-by-step manner was stressed.
From
which practical fields (population studies, finances, ...) can elementary SD
models be taken?
Which
literature and model-collections for teaching purposes are available? In this
context I mentioned my SD Mega Link List, http://go.just.to/sd that lists, among
others, links to all relevant SD school resources.
2 Summary
The attendance of participants was acceptable, although not overwhelming (due to the parallel offers in the conference schedule). The participants of the working group engaged themselves actively in the discussions and the practical work in a very constructive manner. The number of paper proposals was not surprisingly great. This was compensated for by the excellent presentations and the crash-course of the highly motivated members of the SDA. My heartfelt thanks to Stephan Berchtold, Ernst Gebetsroither and Stefan Güldenberg for their enthusiasm. I am also very grateful to my old colleague and friend Franz Schlöglhofer, who reported on his teaching experiences. I would like to heartily thank all who participated and contributed for their engagement. They helped to make this working group a success. All in all it was a great privilege for me to chair this working group.
Modelling carbon dioxide pollution –
The Austrian carbon balance model
Ernst Gebetsroither
Vienna, Austria
The Austrian Carbon Balance Model (ACBM) aims to provide a comprehensive description and analysis of all carbon stocks and flows within the federal area of Austria as well as interactions with the external compartments atmosphere and lithosphere. The project is based on the results of a former study about the carbon balance in Austria for the Year 1990. The developed system is a national dynamic model based on input values taken from official statistical data for Austria. The system model enables the user to make improved estimations and predictions for the future in comparison with previously used methods, which accounted the net release of carbon into the atmosphere by better avoiding the risks of double counting or omitting carbon sources. Furthermore we are able to analyse and understand the national carbon flux system. The carbon system is divided in the five main parts Agriculture, Forestry, Energy, Production and Waste, which were developed separately by relevant Austrian experts.
The findings support policy makers to establish and implement policies for reducing carbon release into the atmosphere and therefore, to guarantee a sustainable development in the future. A sensitivity analysis was performed to identify key input parameters for a more reliable prediction of the Austrian carbon system’s future.
1 Introduction
A major outcome of the 1992 Rio de Janeiro UNCED Conference was the UN Framework Convention on Climate Change (UNFCCC). Article 12 of the convention requests that signature parties provide national inventories for sources and sinks of greenhouse gases, which should be updated regularly and made public (UNFCC 1992). Article 12 also states that such release inventories should use comparable methodologies in order to be promoted and agreed upon by the Conference of the Parties (COP).
Emission inventories are estimates for the release of gaseous air pollutants into the atmosphere from standardized lists of emission sources or source categories. The emissions are calculated from data or estimates on emission-generating activities, together with the respective average source strengths of these emission source groups. Because Carbon dioxide and methane are responsible for more then 90% of the greenhouse gases the carbon flow model was built to get more insight how policymakers could reduce those emissions to the atmosphere. The emission inventories are based on an incomplete system approach shown next.
The simple One Cause - One Effect view of the world
As Fig. 1 shows, this view is based on the assumption that one effect is determined be one cause. There is no look inside of the black box, the structural underpinnings of the system are not analysed. This is a linear and a restricted view of complex systems. An improvement to this is represented by the following.
|
|
|
|
|
|
Fig. 1: One Cause - One Effect view |
|
The Causes Effect view of the world
Fig. 2 shows that according to this view it is assumed that one effect could be determined by more the only one cause, but there is still no look inside the black box. This is the common view, which is used to build the emission inventories. But this approach is not useful to explain the behaviour of a complex system such as the national carbon cycle. For example, in the emission inventories this shortcoming bears the danger that certain carbon emissions might be neglected and others double-counted. Such errors could be avoided when the overall flows of carbon in a national system are looked at. Because of this weakness we have used a new approach in this context.
|
|
|
|
|
|
Fig. 2: Causes Effect view |
|
The system dynamic view of the world
In contrast to the other two approaches, here, on the one hand, the black box is opened and the underpinning structure of the system is analysed. On the other hand, the feedback (blue arrow) between the causes and the effect is also considered. This view enables to understand the dynamical behaviour of the system. Especially for predictions into the future it is sufficient to look at the state of the system. Only when the dynamical behaviour of the system is understood, measures could be found which lead to the long term desired result.
|
|
|
|
|
|
Fig. 3: System dynamic view |
|
2 System dynamic tools
The stock flow thinking
One of the base elements of the system dynamic view is the stock flow thinking. Fig. 4 shows stocks (rectangles), in our case of carbon, which are connected by flows (arrows). The stocks characterize the state variables of the system, while the flows refer to the input-output pattern between stocks. The flows are influenced by parameters (driving parameter, DP in Fig. 4), which could be external entities or variables depending on the state of the system (feedback).
|
|
|
|
|
|
Fig. 4: Stock flow thinking |
|
Fig. 5 shows the structure of the Austrian carbon cycle developed according to the stock flow model. Sub modules for Energy (ENERGY), Waste (WASTE), Forest (FOREST), Agriculture (AGRO) and Production (PROD) have been developed as in Fig. 4 but with greater detail.
|
|
|
|
|
|
Fig. 5: The overall carbon stock and flows in Austria |
|
The causal loop diagram (CLD)
The second basic tool is the causal loop diagram. It consists of variables connected by arrows denoting the causal influences among the variables (cf. Sterman 2000). For example, Fig. 6 illustrates the loop between the stocks of husbandry, manure, soil and vegetation. The picture shows a reinforcing loop, this means that there is an exponential increase (or decrease) of the stocks within the system. In case of more soil, more vegetation can grow. With more vegetation growing (more harvest), more animals in husbandry can be fed, subsequently producing more manure. Using this manure soil can be fertilized, which again leads to more production of vegetation and so on.
|
When this system behaviour is compared with experimental data, it is obvious that the system model is incomplete, because from data no exponential growth is visible. Thus the CLD are useful for generating the full model out of a smaller sub models in a modular way, which helps to analyse the model behaviour. |
|
|
Fig.6: One causal loop in agriculture |
Advantages of this model approach
A
huge model with about 850 model- compartments (Pools, Flows, DP...) could be
handled because of the modular model building scheme.
The
coordination of project partners was possible because of the same language between
the project partners. All used the same tools to visualize their problems and
expert knowledge.
Mathematical
equations like the exponential growth can be explained by another way, which is
often easier to understand.
3 Results and discussion
In combining these tools with a sensitivity and uncertainty analysis, the dynamic behaviour of the Austrian carbon cycle was tested. Hence it was possible to find the key parameters and measures to reduce the carbon emissions to the atmosphere. This way helps, for example, not to underestimate the effects of a decreasing meat consumption per capita on the reduction of total greenhouse gas emissions. The same applies to impacts of an increasing use of wood products on the energy system or on the forest. To understand such a complex model, like a national carbon cycle, it is necessary not to go too deep into detail. In that case, on the one hand, no national data is available and, on the other hand, the uncertainties of the data will propagate so that the insight into the system behaviour would be inferior to that from a ”simpler” model (Bossel 1994, 1986).
References
Bossel, H. (1986) Computer und Ökologie; eine problematische Beziehung. C.F. Müller, Karlsruhe.
Bossel, H. (1994) Modellbildung und Simulation; Konzepte, Verfahren und Modelle zum Verhalten dynamischer Systeme. Vieweg-Verlag.
Sterman J. D. (2000) Business Dymanics; System Thinking and Modeling for a Complex World. McGraw-Hill. UNFCCC (1992) United Nations Framework Convention on Climate Change 1992. World-Wide-Web URL: http://www.unfccc.de/fccc/conv/conv.htm.
Leadership, management and management control – A system dynamics approach
Stefan C. Gueldenberg and Werner H. Hoffmann
Vienna, Austria
1. Research question and objectives
Normally leadership is understood as the capability of a single person – the charismatic leader. In this manner leadership is given someone by birth and is therefore not teachable. In contrast to this personal and determined view we understand leadership as a capacity of an organization, a human community, to create its own future. In this sense leadership is more like a discipline, which can be taught.
Utilizing a system dynamics interpretation of the term leadership, we aim to identify in our work the current challenges to companies from their environments, and to explain the consequences of these challenges for company design and control. For a company to achieve sustained development, there must be a healthy proportion of growth and balance.
The conclusion of our work is that system dynamics is a prerequisite for educating successful organizational leaders, to help them to understand complex organizations and design viable structures.
1 Research question and objectives
Why do so many brilliant management strategies lead firms directly into decline? Why do so many other strategies not produce the anticipated sustainable success? Why do some companies grow while others shrink? Why are some firms extraordinarily successful over the years while others – even those in the same industry – slide from crisis to crisis? Why do so many classical theories of business administration fail to explain these phenomena and help to overcome these problems?
Business administration – and in particular management science – is constantly seeking the best approach to understanding reality, so that the patterns and structures underlying tangible events can be more easily understood (cf. Ulrich 1970, Morgan 1986, Nelson and Winter 1982). Apparently, traditional reductionist methods – ones that analyse a system’s tangible events – are unable to adequately explain the dynamic structure of the business environment, i.e. they are unable to explain ”reality." Otherwise, systems would not so often behave differently than had been "predicted" (Sterman 1985).
Thinking in terms of determination and regularity has gradually shifted to thinking in terms of systems and chaos (e.g. Brown and Eisenhardt 1998). Little by little, our perception of today’s business organizations as "machines" is changing to regard them as evolving organisms, i.e. living systems (Miller 1978, Morgan 1986). Accordingly, a definition of the business world in terms of simple formulas, numbers and tangible events is becoming less and less pertinent. Our complex business world can be described and explained only in terms of structures and dynamic behaviour (McKelvey 1997, Sterman 2000). Linearity in our thinking has to be complemented or replaced by non-linearity.
2 Theoretical underpinnings
In Western culture, successful corporate leadership is usually measured by visible results (Freedman 1992). We look only at the ”visible” – the tip of the iceberg – and neglect its underlying structure and dynamic development patterns (see Illustration 1). In firms focused on the short term, management’s main objective is to deliver results on a daily basis. Such short-term optimisation, however, can take place only within boundaries set by the structure of the underlying system. Organizations are shaped by individual human beings. Within the same system, however, participating individuals basically produce the same results – independent of how different such individuals may actually be (Senge 1990). Consequently, we need to change our focus from visible events and individuals to the connections between them and to a system’s underlying behaviour pattern and structure.
|
|
|
|
|
|
Fig. 1: System structure and system behaviour (Senge 1990) |
|
Jay Forrester, in his 1961 classical "Industrial Dynamics," originated the ideas and methodology of system dynamics (Forrester 1961). He pointed out that traditional reductionist and static approaches of management sciences could not satisfactorily explain the causes for corporate growth and sustainable economical success:
"The solutions to small problems yield small rewards. Very often the most important problems are but little more difficult to handle than the unimportant. Many [people] predetermine mediocre results by setting initial goals too low. The attitude must be one of enterprise design. The expectation should be for major improvement (...). The attitude that the goal is to explain behaviour, which is fairly common in academic circles, is not sufficient. The goal should be to find management policies and organizational structures that lead to greater success." (Forrester 1961, 449)
Growth and sustainable success have to be understood dynamically. Accordingly, they can be analysed, understood and explained only by dynamic models. A system’s behaviour is a product of its structure. Complex systems consist of an interconnected structure of feedback loops. Therefore, the elementary behaviour of structured systems should be identified in terms of their underlying feedback loops. Such behaviour patterns include growth (caused by positive feedback); balancing (caused by negative feedback); and oscillations (caused by negative feedback combined with a time delay). Other behaviour patterns of complex systems — for examples, S-shaped growth or overshoot and collapse — are caused by a non-linear interconnection of these underlying feedback loops (Sterman 2000).
3 Balanced leadership
The structural ability to grow is necessary for the viability of evolving systems. Is growth in itself, however, sufficient for survival? Nothing grows forever. The decisive question is: where and what are the limits of growth?
The growth of social or cultural systems does have boundaries. For example, a firm’s growth can be limited by its production capacity, the market size and/or the number of competitors. The faster the company grows, the more rapidly these boundaries are reached. (Sterman 1989)
Sustaining the development of such social organizations as companies requires a balanced leadership — offsetting positive growth impulses with timely negative feedback processes. This is the only way to ensure that companies remain in a corridor of ”sound growth" as they develop and don’t exceed the carrying capacity of their environment and/or their resource endowment.
In accordance with our theory and that of Peter Senge (1998), leadership can be defined as the inner capacity of a human community to create its own future. Accordingly, a firm must have a clear vision — what it wants to create — while continually developing its capability to move successfully toward that goal. Leadership is always closely tied to designing and guiding. In a viable and learning firm, leadership assumes both functions: that of a designer who shapes the system and a pilot who guides the system to its destination. A social system that is able to shape its own future successfully has a high leadership capacity.
The process in which leadership takes place can be understood as a reinforcing and balancing cycle, allowing for a guided and controlled evolution of the firm. Subsequently, we argue that a leadership cycle requires the interaction of at least two subsystems — management and management control. While management reinforces the company’s evolution, management control regulates and balances the development, i.e. makes sure that the evolution remains within a viable developmental corridor. Together management and management control form a balanced leadership cycle for guiding and controlling development of a company.
Therefore it is absolutely essential for future leaders to understand the structure and behaviour patterns of complex and dynamic systems such as the dynamic structure of an organization. Their ability to understand, analyse and shape these structures will have a great impact on organizational performance and success. System dynamics can help future managers to understand complex organizations and design viable structures. In such a way teaching system dynamics in schools can be seen as a prerequisite for successful future leaders.
References
Brown, S.L. and Eisenhardt, K.M. (1998) Competing on the Edge: Strategy as Structured Chaos. Boston.
Forrester, J.W. (1961) Industrial Dynamics. Cambridge.
Freedman, D.H. (1992) Is Management still a Science?. Harvard Business Review 6/92, 26-43.
McKelvey, B. (1997) Quasi-natural Organization Science. Organization Science 8 (4), 352-380.
Miller, J.G. (1978) Living Systems. New York
Morgan, G. (1986) Images of Organization. Newbury Park/London/New Delhi.
Nelson, R.R. and Winter, S.G. (1982) An Evolutionary Theory of Economic Change. Cambridge.
Senge, P.M. (1990) Fifth Discipline (The Art and Practice of the Learning Organization), New York.
Senge, P.M. (1998) The Leadership of Profound Change: Toward an Ecology of Leadership. Pegasus Communications: System Thinking in Action Conference: Learning Communities: Building Enduring Capability. San Francisco, 81-89.
Sterman, J. (1985) The Growth of Knowledge: Testing a Theory of Scientific Revolutions with a Formal Model. Technological Forecasting and Social Change 28(2), 93-122.
Sterman, J. (1989) Modeling Managerial Behavior: Misperceptions of Feedback in a Dynamic Decision Making Experiment. Management Science 35(3), 321-339.
Sterman, J. (2000) Business Dynamics: Systems Thinking and Modeling for a Complex World. Boston et. al. 2000
Ulrich, H. (1970) Die Unternehmung als produktives soziales System, 2. Auflage. Bern/Stuttgart.
Systems thinking and system dynamics modelling:
A new perspective for math classes?
Günther Ossimitz
Klagenfurt, Austria
1. Systems and systems thinking
2. Systemic modelling and system dynamics software
This paper gives an introduction to the field of teaching System dynamics (SD) and systems thinking (ST) in math classes. In the first section basic ideas of systems and systems thinking are discussed. In section 2 some issues of System dynamics modelling and simulation software are addressed.
1 Systems and systems thinking
One of the main aims of teaching System Dynamics in mathematics is to promote the ability to develop something called systems thinking (Richmond 1994). In the mathematics curriculum of Austrian natural-science oriented high schools (Realgymnasium, 11th grade), the section Investigation of interrelated systems (Untersuchung vernetzter Systeme) begins with the following preamble: ”Through the analysis of systems (consisting of components which influence each other), interrelated thinking (systems thinking), which has become necessary in many areas, should be promoted. Especially the ability for grasping more complex situations, which go beyond simple cause-and-effect relationships, should be improved.” (Bürger e.a. 1991, 152ff). First I will deal with the questions "What is a system?" and "What is systems thinking?"
What is a system?
The term ”system” is being used in different fields in a variety of meanings (see Klir 1991). Yet we can state some general characteristics of systems:
Systems
consist of (definable) elements.
Between
these elements there exist (mostly functional) interrelations.
Every
system has a boundary to the surrounding ”environment”, which is more or
less permeable, material or immaterial (like the membership to a certain social
group).
Systems
often have a dynamic behaviour over time. This behaviour is often
related to the aim of the system. Biological systems (living beings) are
determined to ensure their self-preservation (essentially via homeostasis);
production systems are made for a certain output; transport systems are
designed for a certain throughput etc.
System
elements might be considered as whole sub-systems or a system might be a single
element of a larger system. Thus whole hierarchies of systems may emerge.
Rapoport (1988, 30ff) names identity, organization and goal-orientation as three fundamental features of systems. By identity he means ”stability within change”; by organization he means the design and the handling of complexity; by goal-orientation he means the destiny of a system.
Systems thinking and systemic behaviour
”Systems thinking” (systemisches Denken”, ”vernetztes Denken” etc) is a widely used phrase both in international and in German literature. Yet it is hard to find a concise definition of what ”systems thinking” is like. The German cognitive psychologist Dietrich Dörner (1989, 308ff) says in his book ”The logic of failure”: ”I hope I could clarify the fact that we cannot grasp what is often generally called «systems thinking» as a simple entity, as an individual, distinguishable ability. It is a bundle of abilities, and essentially it is the ability to use our normal, sound reasoning according to the circumstances of the individual situation.” Dörner reduces systems thinking to the formula:
systems thinking = systemic, complex situation + situation-adequate thinking.
My definition of ”systems thinking”
I would like to specify and discuss four characteristic dimensions, which are essential for my definition of ”Systems thinking”:
thinking in models: explicitly
comprehended modelling
thinking in loops: a thinking in
interrelated, systemic structures, recognizing causal loops.
dynamic thinking: a thinking in dynamic
processes (delays, feedback loops, oscillations).
steering systems: the ability for
practical system management and system control.
Thinking in models
Systems thinking requires the consciousness of the fact that we deal with models of our reality and not with the reality itself. Thinking in models also comprehends the ability of model-building. Models have to be constructed, validated and developed further. The possibilities of model-building and model analysis depend to a large degree on the tools available for describing the models. To choose an appropriate form of representation (e.g. causal loop diagram, stock-and-flow diagram, equations) is a crucial point of systems thinking.
Thinking in loops
Thinking in simple cause-effect relationships might be called functional or linear thinking - in contrast to Thinking in loops. In interrelated systems we have not only direct, but also indirect effects. This may lead to feedback loops. Feedback loops might be reinforcing (positive) or balancing (negative). The arms race between the superpowers was an example of a reinforcing feedback loop. The Americans said: Because of the armament of the Soviets we have to build 1000 new missiles”. The Soviets said: ”We have to increase our strategic arms force, because the Americans have built 1000 new missiles.” Thus the increase in the Soviet Army Forces leads to further armament on the American side and so on. Each side viewed the other side as the cause. In a global perspective a distinction between cause and effect is no longer possible. Once you have entered a vicious circle, you can no longer identify a single cause for the whole process, since any effect also affects the cause. A proper understanding of feedback loops requires a dynamic perspective, in order to see how things emerge over time.
Dynamic thinking
Systems have a certain behaviour over time. Time delays and oscillations are typical features of systems, which cannot be observed without the time dimension. Even the simple task of keeping the temperature constant in a (simulated) cooling house is for many subjects a difficult task, because changes of the temperature would require some time until they become efficient (cf. Dörner 1989, 200ff). Considering only the present state of the temperature as a guideline for adjustment might lead to serious overreaction, which might take even a rather inert system like a cooling house out of control.
Steering a system
Systems thinking always has a pragmatic component, too: it is not just content with contemplating about the system, it is also interested in system-oriented action. One of the most fundamental and most important questions of practical systems management is: which of the systems components are subject to direct change?
How can systems thinking skills be developed?
This is a very hard question. There are a number of different approaches (or claims), how ”it” could be done. Let me give an overview of some possible answers:
Sensitisation for systems aspects through
information campaigns (Vester 1986, Meadows 1972).
Computer-simulation games (Dörner 1989,
307ff)
Curricular Concepts try to develop
Systems Thinking skills via explicit teaching at schools.
Group-dynamics oriented approaches in
special seminars (e.g. the Tavistock concept).
2 Systemic modelling and system dynamics software
Qualitative vs. quantitative modelling
Although there is a structural similarity between causal loop diagrams and stock-and-flow diagrams, they belong to different modelling paradigms. Peter Senge's famous book "The Fifth Discipline" (Senge 1990) about learning organizations is an excellent example of how system models can be developed and analysed in a completely qualitative manner. Senge uses extensively verbal descriptions and causal loop diagrams to describe (mostly economic and managerial) systems and their behaviour, but you cannot find a single stock-and-flow diagram or equation in his book.
For System Dynamics modelling at school level the quantitative approach (using some graphics oriented simulation software) seems to be far ahead of qualitative modelling. Teachers and students often show a strong tendency to start immediately with the work at the computer. According to my experience, however, it is very useful first to present some basic aspects of systems thinking and modelling without the computer, using just loop diagrams. Then one can proceed to the realms of quantitative modelling, using stock-and-flow diagrams and equations. The sequence verbal description → causal loop diagram → stock-and-flow diagram → equations proved also a very natural and step-by-step progression when developing a single quantitative model (cf. also Richmond 1991, p. 2).
Simulation software
Quantitative System Dynamics modelling needs appropriate computer software. There are basically two options:
SD-Software
like Stella, Powersim, Vensim, Dynasys. All modern SD software-products are
graphically oriented: the models are developed directly as stock-flow-diagrams
on the screen; some commercial products (lVensim PLE) are even free for educational
purposes.
Standard
spreadsheet software (like Excel) can be used for very basic SD applications.
Empirical experience has shown that modern SD-software can be learned in a few days to the extent, which is needed, for doing school-oriented modelling. If the focus of learning is not on the modelling technique, but on the behaviour of SD-models, ready-made models could be investigated. The necessary know-how for "steering" a SD-software for this purpose could be learned almost on the spot.
References
Bürger, H. e.a. (ed.) (1991) Mathematik Oberstufe: Lehrplankommentar. Österreichischer Bundesverlag, Wien.
Dörner, D. (1989) Die Logik des Mißlingens. Reinbek: Rowohlt In Engl: The logic of failure. Philosophical Transactions of the Royal Society of London, Vol. B 327. (1990)
Forrester, J. W. (1961) Industrial Dynamics. MIT Press, Cambridge, Mass.
Meadows, D. e. a. (1972) The limits to growth: a report for the Club of Rome's project on the predicament of mankind. Universe Books, New York. In German: Die Grenzen des Wachstums: Bericht des Club of Rome zur Lage der Menschheit. Rowohlt, Reinbek (1973)
Ossimitz, G. (1990) Materialien zur Systemdynamik. Hölder-Pichler-Tempsky, Wien.
Ossimitz, G. (1991b) Systemdynamische Modelle aus Biologie und Ökologie. ZDM 1991/6, 221-228.
Ossimitz, G. (1994) Systemdynamiksoftware und Mathematikunterricht. Endbericht zum gleichnamigen Projekt. Universität Klagenfurt.
Ossimitz, G. (2000) Entwicklung systemischen Denkens. Profil Verlag, München.
Rapoport, A.
(1986) General system theory: essential concepts & applications. Abacus Press, Tunbridge Wells,
Kent. In German: Allgemeine Systemtheorie: wesentliche Begriffe und Anwendungen.
Verlag Darmstädter Blätter,
Richmond, B. (1993) Systems thinking: critical thinking skills for the 1990s and beyond. System Dynamics Review 9, no. 2, 113-133.
Senge, P. (1990) The fifth Discipline. Doubleday, New York.
Vester, F. (1986) Unsere Welt ‑ ein vernetztes System (3. Auflage). DTV, München.
Watzlawick, P., Beavin, J. and Jackson, D. (1967): Pragmatics of human communication : a study of interactional patterns, pathologies, and paradoxes. Norton, New York. In German: Menschliche Kommunikation. Huber, Bern (1969).
Teaching system dynamics modelling
in secondary schools
Franz Schlöglhofer
Linz, Austria
1. Teaching system dynamics (SD)
2. The curriculum chapter “Investigation of interrelated systems“
3. Experiences with practical teaching of SD in Austria
This paper reports on the chapter "Investigation of Interrelated Systems" ("Untersuchung vernetzter Systeme") of the mathematics curriculum (11th grade) for the "Realgymnasium" – a special type of high school in Austria. Both the importance, for learning systems thinking, of teaching system dynamics issues at school and practical experiences and problems therewith are discussed.
1 Teaching system dynamics (SD)
SD implies a particular way of thinking. Dealing with complex processes, different forms of growth, the development of systems etc. has become crucial for the understanding of our modern world. This method of thinking has gained significant importance in different fields of science and business. For the same reason it is important that SD is included in our educational system. Students should learn how to deal with systemic views and/or descriptions of systems in economy, ecology etc., even though at school only the most fundamental ideas can be presented using rather elementary examples. An understanding of systems has to be learned, so it is a pedagogical task. Jay Forrester, the founder of System dynamics, has written in the foreword of Nancy Roberts' famous textbook (Roberts e.a. 1983):
"Although life equips us with an intuitive feel for the dynamics of change, our intuition is reliable only in very straightforward situations. In the more complex dynamic structures, which increasingly dominate our lives, the intuition carried over from simple systems is misleading. As an example, in simple systems we learn that cause and effect are closely related in both time and space; in touching a hot stove, the hand is burned now and it is burned here. We repeatedly learn to expect a close association between action and the result. In more complex systems, however, the cause of a symptom may lie far back in time and in a remote part of the system. Only through study of structure and behaviour can we develop intuition that is reliable when confronted by complexity."
Forrester assures us that developing an understanding of systems and their evolution is by no means trivial. It is a goal of our society to develop and teach knowledge, which enables us to tackle the systemic problems of our future.
2 The curriculum chapter “Investigation of interrelated systems“
A special branch of the Austrian High School (called „Realgymnasium”) has in its math curriculum at grade 11 a chapter „Investigation of interrelated systems”. This was introduced in 1990 with the aim of promoting systems thinking. Particularly the ability to grasp more complex relationships beyond simple cause-and-effect relations, should be improved. Students should learn the following aspects of a system: Systems consist of several elements. Between these elements there exist (functional) relationships. There might be relationships between the system and its environment (input and output of the system). Instead of simple causal arguments: the more approval, the better the behaviour, etc., whole systems of causal relations are investigated. „Systems thinking” usually leads to causal loops (circular feedback structures). This can be demonstrated by Paul Watzlawick's example of the quarrelling couple. Wife: „I am complaining because you always go to the pub and leave me alone.” Husband: „I am going to the pub just because you are always quarrelling.” The more she quarrels, the more he leaves her alone. The more he leaves her alone, the more she quarrels.
|
This curriculum chapter states that examples of system-models from different areas (economics, ecology, physics etc.) should be described, using different levels of notation:
|
|
|||
|
Fig. 1 |
Causal loop diagrams
Causal loop diagrams (CLD) are graphical representations of the interrelations between the elements of a system. The CLD above shows the example of the quarrelling couple. The arrows indicate causal relationships, the „+“ sign at each arrow means that the relationship is of the kind „the more of the cause, the more of the effect.“ The upper arrow can be read as: „The more he goes to the pub, the more she will complain“. The lower arrow means: „The more she complains, the more he will go to the pub.“ Obviously the two causal links form a circle, which is in fact an escalating feedback loop, which is indicated by the small central circle with another „+“ sign in it. For a more detailed description of the CLD technique see Ossimitz (2000: 65ff). Ossimitz (2000: 158ff) has shown that students aged 14 to 17 adopt the CLD diagramming technique for describing complex systemic situations very easily.
Stock-flow diagrams
|
variables of a system and are changed over time by inflows and outflows. Stock-flow diagrams are extremely useful for discerning between stocks and flows. This helps considerably to understand the evolution of practical systems. The diagram shows a simple stock-flow diagram. The stock „People“ has an inflow „births“ and an outflow „deaths“. |
|
|||
|
Fig. 2 |
In stock-flow diagrams stocks and flows are explicitly discerned. Stocks represent state Recent empirical research (Sweeney/Sterman 2000, Ossimitz 2001) showed that even educated persons have astonishing problems in for example discerning between public debt and budgetary deficit. The public debt is a stock variable, representing the amount of borrowed money at a certain moment. The budgetary deficit represents the net increase of (resp. net inflow into) the amount of borrowed money during a certain time interval (e.g. a year). Ossimitz (2001) described how more than half of about 150 people tested believed that when the budget deficit goes down to zero, all the debt is gone! In fact that is the very moment when the debt reaches its highest level ever. Only a budgetary surplus can reduce public debt and lead thus eventually to a debt-free public sector.
Representation of systems by equations
Equations are the most formalized level of denoting a dynamic system. They allow us to simulate the evolution of the system(model) over time. In the system dynamics modelling method time is divided into intervals of equal length and a time-step is represented by going forward one time interval (e.g. one day, one month). An representation through equations of the population model above could look like this:
births(t0, t1) := people(t0) * birth-rate(t0, t1)
deaths(t0, t1) := people(t0) * death-rate(t0, t1)
people(t1) := people(t0) + births(t0, t1) – deaths (t0, t1)
The value of a state (=stock) variable at the end of a time interval (which is equal to the beginning of the next time-interval) is calculated from the value at the beginning of the time-step plus the inflows minus the outflows during the time interval. Mathematically this leads to a kind of difference equation of the type:
stock(t1) := stock(t0) + inflows(t0,t1) – outflows(t0,t1)
with t0 denoting the beginning and t1 denoting the end of the particular time-interval.
3 Experiences with practical teaching of SD in Austria
I will summarize my personal experiences with teaching SD in Austria. The main background is my personal communication with colleagues, in-service-teacher education, and an empirical investigation in my doctorial thesis (Schlöglhofer 1993). The main result is simple: although teaching SD and establishing ST has been explicitly stated in the Austrian math curriculum for the Realgymnasium since 1991, it is hardly ever taught. Let me discuss some arguments.
Traditions
Teachers are often not so familiar with a style of mathematics which goes beyond strictly formulated tasks with closed solutions. SD usually means that open situations are modelled systemically. In such a context there are no „right“ and „wrong“ solutions, but more or less simplified models. SD modelling and simulation requires that the models are taken from some field of interest. This implies that one has to deal somehow with the modelled subject, which might be from physics, biology, business or whatever. Teachers often show some scepticism towards such „foreign“ grounds. They sometimes feel insufficiently trained for teaching such content. This problem can be minimized by restricting oneself to rather obvious and non-expert contexts. Instead of modelling a complicated biochemical reaction one might restrict oneself to a simple population model. One does not need to be an expert to understand that births increase and deaths decrease a population.
CLD's and stock-flow-diagrams
In discussions, mathematics teachers argue that CLD's and stock-flow diagrams are not very useful. CLD's often are considered to be too vague and qualitative. Teachers (and sometimes students) think no „real“ mathematical assertions are possible with CLD's. This argument is plausible, if we see mathematics as a collection of truths and mathematical tasks exclusively as well-defined problems with unique solutions. However, if mathematics is seen more as a tool-set, which can be used to describe our world in a variety of ways (see Fischer 1984), then both CLD's and stock-flow diagrams fit perfectly in this view of mathematics: CLD's are mathematically special types of node-edge graphs which allow rigorous mathematical argumentation, e.g. concerning reinforcing or balancing loops. The description of SD models with stock-flow-diagrams is often considered as too clumsy and too specialized. It is often considered as preliminary description or even a substitute for a representation in exact simulation equations. De facto it is hardly possible to replace the representation of a SD model in equations by a stock-flow-diagram. From this perspective some teachers think that stock-flow-diagrams are unnecessary: one can start right from the spot with the equations. As a counter-argument one can say that the basic strength of stock-flow-diagrams is to identify the central (i.e. most important) stock (=state) variables of a system and the inflows and outflows, which change these stocks over time.
Open vs. closed models
Some teachers consider iterated models as clumsy, compared with elegant „closed“ models. They argue: why should I calculate the development of a say EUR 1000,- saving with 5 % interest rate through iteration, tediously calculating 1000*1,05 = 1050; 1050*1,05 = 1102,5 etc.? The closed formula 1000*1,05n is much easier, since it immediately yields the capital after n years. However, this example shows that the iteration paradigm and the closed-formula-paradigm have different strengths. First of all it can be said that much of the „advantage“ of the closed formula disappears when we leave the realm of „paper-and-pencil“ technology and enter the realm of e.g. spreadsheet software. With a spreadsheet the tedious iterations are done automatically, just a single formula has to be typed in and an elementary copying of this formula is required for getting not just a single value at n years, but all the values of the capital after 1, 2, 3, ... years. The resulting table answers not just one single problem „What is the capital after 9 years?“, but a whole bunch of problems in one step. Other questions such as when has the capital doubled can be answered immediately, or one can use the spreadsheet graphing methods to see exponential growth etc. immediately. With a slight adaptation of the spreadsheet model one can calculate the development of the capital interest rates not just as being constant, but varying from year to year. Closed models typically require strict model assumptions (e.g. constant rate of interest), which limit the scope of its applicability for practical situations with changing rates of interest. Nevertheless traditional mathematics teaching is restricted mostly to closed models and thus the open, iterative style of modelling is often not particularly appreciated by mathematics teachers.
References
Ossimitz, G. (1990) Materialien zur Systemdynamik. Hölder-Pichler-Tempsky, Wien.
Ossimitz, G. (2000) Entwicklung systemischen Denkens. Profil, München.
Ossimitz, G. (2001) Unterscheidung von Bestands-und Flussgrößen. G. Kaiser (ed.): Beiträge zum Mathematikunterricht 2001. Franzbecker, Hildesheim.
Roberts, N. e. a: (1983) Introduction to computer simulation. A system dynamics modeling approach. Addison Wesley; Reading, Mass.
Sweeney L.B. and Sterman, J. (2000) Bathtub Dynamics - Initial Results of a Systems Thinking Inventory. System Dynamics Review (16:4), 249 - 286.
