Günther Ossimitz: "The Development Of Systems Thinking Skills Using System Dynamics Modeling Tools"

Abstract:

This paper gives an overview about the research on System Dynamics and systems thinking education. In the first section basic ideas of systems and systems thinking are being discussed. Here you find Barry Richmond's and my own definition of "Systems Thinking". In section 2 some issues of System Dynamics modeling and simulation software are addressed. In section 3 I give an overview about the empirical research on teaching System Dynamics and the development of systems thinking skills. In section 4 the main preliminary results of my study "Entwicklung vernetzten Denkens" (Development of Systems Thinking) are given. This study showed very clearly that the key factor for teaching and developing systems thinking skills is the teacher. At the end of the paper you find a list of selected Literature and some Links to my System Dynamics web site.

1. SYSTEMS AND SYSTEMS THINKING

1.1 What is a System?

1.2 System-Approaches in Different Fields of Science

• the approach of mathematics and physics (Isaac Newton) deals mainly with systems of equations, espiacally differential equations. "Classical dynamics is essentially the theory of differential equations". (Rapoport 1988, p 38)
• the approach of General Systems Theory (Systems Science) (Ludwig van Bertalanffy) considers systems like mathematical entities and uses mainly mathematical methods to describe and classify systems. "It follows from this common-sense definition that the term "system" stands, in general, for a set of some things and a relation among things. Formally, we have
  S = (T,R)
  where S, T, R denote, respectively, a system, a set of things, distinguished within S, and a relation (or, possibly, a set of relations) defined on T." (Klir 1991, p 4)
• the Cybernetics approach was founded by Norbert Wiener with his book "Cybernetics: or Control and Communication in the Animal and the Machine" (1948). Wiener dealt primarily with control and information systems. Important is the maintainance of certain system parameters by means like homeostasis or adaptation and the interrelation interrelation between system and environment.
• the System Dynamics - approach was founded by Jay W. Forrester at MIT at about 1960. He developed a powerful method for describing interrelated systems (using causal loop diagrams, stock-and- flow diagrams) and the simulation language Dynamo for the numerical simulation of dynamic systems. The main issue of stock-and-flow diagrams and of the System Dynamics simulation style is a clear distinction between stock and flow variables (or levels and rates in the original terminology of Forrester). Other than in the classical approach of systems of differential equations, in the System Dynamics approach closed solutions do not play a considerable role. The focus of interest is concentrated upon a certain subject field. Other than in the world of continuous differential equations discrete time steps are used for describing and simulating the dynamic development. Stocks are time-point related and flows are time-interval related system variables.

The first publication in System Dynamics was the classic "Industrial Dynamics" (Forrester 1961). Among all the system approaches mentioned here the System Dynamics approach is highly standardized and has a number of advantages for being taught at school.

• the ecological-biological approach deals primarily with ecosystems. Main proponents are Howard Odum (1994: systems ecology) or Frederic Vester. Vester proposes ideas for Systems thinking via the exposition "Our World - An Interrelated System" (Unsere Welt - ein vernetztes System) or via the game "Ökolopoly", which is available both as a board game and as a computer game. The system view of ecologists is often more qualitative than the System Dynamics view of system.
• systemic communication theory deals with human relationship systems, based upon communication. Paul Watzlawick formulated in his classic work "Pragmatics of Human Communication" (Watzlawick 1967) principles of systemic-oriented communication theory. This theory gives insight about human interactions and offers a systems oriented explanation for psychic disorders like schizophrenia as a result of paradox communication structures.

Most of these approaches use ideas and concepts of mathematical tools for describing and analyzing systems; some are even incomprehensible without the aid of mathematical tools.

1.3 Systems Thinking and Systemic Behavior

The German cognitive psychologist Dietrich Dörner (1989, p 308ff) says in his book "the logic of failure" (Die Logik des Mißlingens): "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.

In an online paper (http://www.hps-inc.com/st/st.html) Barry Richmond gives following definition of "Systems Thinking": "Systems Thinking is the art and science of linking structure to performance, and performance to structure-often for purposes of changing structure (relationships) so as to improve performance." In his paper "Systems thinking: critical thinking skills for the 1990s and beyond" Richmond writes that "doing good systems thinking means operating on at least seven thinking tracks simultaneously." Richmond (1993, p 121). These tracks are: dynamic thinking, closed-loop-thinking, generic thinking, structural thinking, operational thinking, continuum thinking and scientific thinking.

1.4 My Definition of "Systems Thinking"

1. thinking in models: explicitly comprehended modeling
2. interrelated thinking: a thinking in interrelated, systemic structures
3. dynamic thinking: a thinking in dynamic processes (delays, feedback loops, oscillations).
4. steering systems: the ability for practical system management and system control.

Thinking in Models
From the viewpoint of Radical Constructivism (cf. Glasersfeld 1995) thinking in models is necessary. Constructivism says that we can only think according to our pictures and views of the world, which are necessarily models of the world itself. My point is now that 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. The invention of powerful, flexible and yet standardized descriptive tools was one of the main achievements of Jay Forrester. For school purposes the representation forms of the System Dynamics approach have proven to be successful. The causal loop diagram allows qualitative modeling, the stock-and-flow diagram already gives key hints about the structure of the quantitative simulation model.

Interrelated thinking
People of the western hemisphere are usually very good in causal reasoning. If-then relations are basic building blocks of our mind and understanding of things. A foundation of this kind of thinking is a strict delineation between cause and effect. In order to explain a phenomenon we have to find its (probably single) "cause". It is supposed that this cause does exist and that the effect always can be observed whenever the cause is valid. Words and phrases like "because", "therefore", "if - then" denote such thinking concepts in everyday language. The mathematical analogon is the function-concept with one independent variable (="cause") and one dependent (="effect") variable. Accordingly the thinking in simple cause-effect relationships might be called functional or linear thinking - in contrast to interrelated thinking.
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. 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 Ami's have built 1000 new missiles." This increase of the Soviet Army Force lead 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 no longer is possible. If 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 understandig of feedback loops requires a dynamic perspective, in order to see how things emerge over time.
Interrelated thinking is a kind of thinking which takes into account indirect effects, networks of causes and effects, feedback loops and the development of such structures over time. Interrelated thinking also requires adequate representations: the causal loop diagram is the simplest and most versatile tool for denoting interrelated issues.

Dynamic thinking
Systems have a certain behavior 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, pp 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 coolinghouse out of control.
Dynamic thinking also means to foresee (possible) future developments. A mere retrospective view of past developments is insufficient for the practical steering of systems - or would you trust a car driver who uses exclusively the rear mirror in order to determine where to steer the car? Often simulation models are helpful or even necessary in order to foresee future developments - especially when reality emerges rather slowly.

Steering a System
This brings us to the fourth core aspect of systems thinking: the practical steering of systems. Systems thinking has always also a pragmatic component: it deals not just with contemplating about the system, it also is 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? In a social system it is often impossible to change the behavior of others directly, one can only change one's own behavior. In an economic system the producer usually has no direct control over the market. Marketing activities are usually actions of the supplier side in order to induce the desired reaction on the demand side.

1.5 How Can Systems Thinking Skills be Developed?

• Sensibilization for systems aspects by information campaigns for the general public (see F. Vester's exposition "Unsere Welt - ein vernetztes System" (our world - an interrelated system, Vester 1986) or the works of D. & D. Meadows concerning "The Limits to Growth" (Meadows 1972).
• Dörner (1989, p 307ff) suggests computer-simulation games (like Tanaland or Lohhausen), in order to learn systemic thinking and action.
• Some curricular concepts try to develop Systems Thinking skills via explicit teaching at schools. Examples are the Austrian Schools Mathematics Curriculum section "Investigation of interrelated systems" (Untersuchung vernetzter Systeme) or, on a more comprehensive scale, curricular projects like CC-STADUS (Cross Curricular Systems Thinking and Dynamics Using Stella http://www.teleport.com/~sguthrie/cc-stadus.html or STACIN (Systems Thinking and Curriculum Innovation Network) (see http://etsis1.ets.org/research/stacin.html or Mandinach 1989) in the USA.
• Group-dynamics oriented approaches try to develop systemic skills as holistic encounters in special seminars (e.g. the Tavistock concept for the development of systemic management abilities).

2 SYSTEMIC MODELING AND SYSTEM DYNAMICS SOFTWARE

2.1 Qualitative vs. Quantitative Modeling

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 analyzed in a completely qualitative manner. Senge uses extensively verbal descriptions and causal loop diagrams to describe (mostly economic and managerial) systems and their behavior, but you cannot find a single stock-and-flow diagram or equation in his book.

For System Dynamics modeling at school level the quantitative approach (using some graphics oriented simulation software) seems to be far ahead of qualitative modeling. 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 to present first some basic aspects of systems thinking and modeling without the computer, using just loop diagrams. Then one can proceed to the realms of quantitative modeling, 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).

2.2 Self-Made-Models vs. Ready-Made-Models

Ready-made models might help here. If they are rather complex, their inner structure will usually be adopted only partially by the students. Most of the system remains a black box (cf. Maaß/Schlöglmann 1994). The students often just learn about the system by varying parameters. The user/learner/player has no direct access to the inner model structure; one can learn about the inner structure only by changing input parameters and watching the development of the output parameters. Although complex System Dynamics models (like World3, Meadows 1972) in principle allow the study of the inner structure of the model in detail, it will be used more like a black box simulation software in practical teaching.

Predesigned, complex models should only be used with a teaching guide. This helps teachers and students from getting lost in the awesome number of parameter-selections and things that can be explored. Without a guide the work with a complex model might soon become boring or frustrating.

When making self-made-models, it is very important to begin with a basic model which is as simple as possible, then to test this model and then to add more features to the model. The first model should contain only one (or very few) stock variable(s). The appropriate flow and auxiliary variables can be defined around this variable. This yields typically sequences of models, starting with a very primitive basic model, which will be refined in several steps. In a more complex context it is advisable first to construct independent partial models for each sector and to test and calibrate these models. Only then these sub-models can be put together to form the more complex model. (cf. Ossimitz 1990). It is also advisable to choose the model parameters first in such a way that all model variables stay constant (stationary) over time. This helps to identify the kind of influence of each input parameter.

2.3 Simulation Software

Prototypes are software products, which are available only to a small group of specialists. By Standard Software I mean products like word processors or spreadsheet software. All System Dynamics software Products belong to the middle category of special application software. Spreadsheets are the only kind of standard software, which can be used for some simple System Dynamics modeling issues (for excamples see Ossimitz 1990).

2.4 Software-related Educational Research

Another serious problem of simulation software related research is the fast innovation cycle of simulation software products. If the research is bound to closely to a single software product, the results of such a study might be worthless within a few years. Thus it is advisable to design empirical research independent of specific software products.

3 EMPIRICAL INVESTIGATIONS ABOUT THE DEVELOPMENT OF SYSTEMS THINKING

3.1 How can Systems Thinking be measured?

Attempts to measure the development of systems thinking have only been undertaken in System Dynamics related studies. One of the first of these studies was undertaken in the "Systems Thinking and Curriculum Innovation Project" (STACI, Mandinach 1989). Mandinach essentially defines systems thinking as the System Dynamics modeling ability: "Systems thinking is a scientific analysis technique given prominence by Jay Forrester and his colleagues at the Massachusetts Institute of Technology. ... As defined here, the systems thinking approach consists of three individual but interdependent components: system dynamics, STELLA, and the Macintosh." (Mandinach 1989, pp 222; 225).

3.2 German Studies about teaching System Dynamics and Systems Thinking

• Klieme/Maichle(1991): "Erprobung eines Modellbildungssystems im Unterricht" (Evaluation of a Model Building System in the Classroom)
• Klieme/Maichle (1994): "Modellbildung und Simulation im Unterricht der Sekundarstufe I" (Modeling and Simulation in Grades 9 and 10)
• Ossimitz (1994): "Systemdynamiksoftware im Unterricht" (System Dynamics Software in the Classroom)
• Ossimitz (1996): "Entwicklung vernetzten Denkens" (Development of Systems Thinking)

Study	Stds/Classes	Grades	Teaching Subjects	Software	Research Method
K/M91	180 / 8	9; 10	math, biology, chemistry, soc. stud.	Modus	pre- & post-test
K/M94	240 / 10	9; 10	economy, biology, informatics	Modus	pre- & post-test, selected videos
Oss 94	7 / 2	9; 11	mathematics	Modus	pre- & mid- & post-test + interviews
Oss 96	130 / 7	9 to 12	mathematics, informatics, physics	Powersim	pre- & post-test + intervws (4/class)

In each study the students were tested before and after a System Dynamics teaching module of about 10 - 25 hours. The tests were in writing and not known to the teachers. The tasks of the post-tests were closely similar to the corresponding pre-tests. In both studies of Klieme/Maichle and in the Ossimitz 1991 study the graphical simulation software Modus (developed at the Deutschen Institut für Fernstudien (DIFF) in Tübingen by Werner Walser and Joachim Wedeking for DOS Computers) was used. (Since in Germany and Austria almost all schools were equipped only with DOS-PC's at the beginning of the 90ies, Stella or some other Windows-oriented software could not be used).

The main results of these four studies were:

• Students and teachers considered the System Dynamics teaching modules very interesting. (In some classes it was the first attempt both for teachers and students of computer-oriented teaching).
• The way to sketch a verbally described systemic situation changed considerably during the teaching. Most of the students who learned about causal loop diagrams used them in the post-test; whereas in the pre-test most students used pictorial images or verbal summaries to sketch the systemic situation. Students who did not see causal loop diagrams, but structural diagrams (like stock-and-flow diagrams in Stella), often used this type in the post-test.
• The ability to understand a systemic situation given as a text was very good even for the youngest students (aged about 14-15) in the pre-test. Thus in the Ossimitz (1996) study a more complicated text was used for the pre- and post-test.
• Measurement of systems thinking skills and their improvement is very difficult. "Systems thinking is no general ability. To understand the dynamics of Modus-models is something different than predicting effects in verbally described models." (Klieme/Maichle 1994, p 76)

• The interest of the students depended upon their readiness to work on the computer.
• The software product Modus had a considerable impact upon the teaching and the way of modelling. Some of the students' problems in the modelling process seemed to depend upon the specific way that systems are modelled in Modus. (In Modus, both inflows and outflows of stock variables are modeled as effects from the flow variable to the stock variable. Other than in the standard System Dynamics modelling paradigm, arrows of outflows are (like inflows) oriented from the flow variable to the stock. This should indicate that the flow variable causes an effect upon the stock in any case; inflows and outflows have only different signs in Modus).

• The students of teachers using a highly directive teaching style got better results concerning the achievement of model building in the post-test.
• The achievement of the students depends more upon their motivation than on their prior experience with computers.
• Through the work with Modus the ability of model building could be significantly improved. The ability to think systemically within the Modus-models could be improved only marginally.
• The readiness of the students for experimental work and cooperation was significantly improved.

4. THE STUDY "ENTWICKLUNG VERNETZTEN DENKENS"

The first task was to depict a verbally given systemic situation (the "Hilu"-scenario at the pre-test; the "Mori"-scenario at the post-test) in a kind of picture or diagram. Both scenarios described the highly interrelated hypothetical economy of a tribe in a third world environment. On a formal level, the complexity and interrelatedness of both scenarios were (almost) identical. In addition, students were asked about indirect consequences of some actions (like "What effect does using more grass-fertilizer have upon the abundance of the "tse-tse-fly?"). In the evaluation of this task, mainly the type and the systemic complexity of the resulting diagram and the quality of the additional answers were evaluated.

The second task, called "Argumente und Gegenargumente" (arguments and counter-arguments) was taken without change from the Klieme/Maichle 1994 study. Following a given example, students should write down chains of arguments (like more tourists more hotels more traffic problems less attractivity of the resort) for traffic problems in a town (pre-test) and tourist problems in a sea-side holiday resort (post-test).

In each class four students were interviewed about their answers to the Hilu- and Mori-task respectively. For the evaluation of both tasks the number of items and relations being stated by the students were counted. These basic measures were used to calculate an index of complexity and an index of interrelatedness. These indices were used as indicators of interrelated system design skills.

The measured items were also correlated with basic variables like gender, age, grade in mathematics, computer experience. About 40% of the students owned a private computer; about 10% of all students worked more than 6 hours per week on a computer.

4.1 Results of the Pre-Test

4.2 Results of the Post-Test

Type of picture/diagram used for Hilu / Mori-scenarios	pre-test	post-test
	all teachers	all teachers	T1	T2	T3	T4	T5	T6
pictorial or verbal descriptions	22%	6%	33%	.	.	6%	.	.
function charts (mostly cartesian style)	5%	3%	.	.	.	.	8%	6%
chain diagrams (lin. sequ. of arguments)	15%	3%	11%	8%	.	.	.	.
tree diagrams (mostly 2 branches)	7%	7%	11%	16%	.	6%	4%	.
causal diagrams without loops	29%	19%	28%	33%	5%	12%	21%	11%
causal diagrams with loops	17%	61%	11%	42%	95%	71%	67%	83%
Total	100%	100%	100%	100%	100%	100%	100%	100%

For the first task (Hilu/Mori-scenarios) most indicators for systems thinking in the post-test were significantly higher (on the 95%-level) than in the pre-test. E.g. the average index of interrelatedness of the Mori-diagrams was at about 2.29±0.12 (double standard error of the mean) compared with 1.47±0.14 in the pre-test. Table 3 shows that these average results differ significantly for both tests according to the teacher. The students of teacher 1 had the worst result at the pre-test (1.01) and almost no increase between pre- and post-test (1.18). The students of teacher 3 were below the average in the pre-test (1.39), but they got the best result (2.83) in the post-test.

Index of interrelatedness	T 1	T 2	T 3	T 4	T 5	T 6	Total avg
Pre-Test: Hilu-scenario (avg)	1.01	1.67	1.39	1.70	1.45	1.73	1.47
Post-Test: Mori-scenario (avg)	1.18	2.00	2.83	2.15	2.11	2.50	2.29

For the arguments-counterarguments-task several of the indices to measure the level of systems orientation (complexity, interrelatedness, number of items and number of causal arrows) were significantly higher in the post-test than in the pre-test. Again there was no correlation with age, mathematics grade or computer experience, but a great influence of the variable "teacher". I observed that the index of interrelatedness was slightly higher for the boys than for the girls (for both pre- and post-test); but this might be just a side-effect of the fact that the best teachers had a higher percentage of boys in their class. Some other interesting results of the Ossimitz (1996) study were:

• Two other classes (at different schools) were also tested as control groups (without System Dynamics teaching between pre- and post-tests). There was no significant difference in the students' behavior between pre- and post-tests. A test-retest effect (that the students learn from the pretest and thus achieve better results in the posttest) could not be observed.
• The teachers reported very positively about their teaching projects. They said, that the Windows-oriented software Powersim was (unlike Modus) very easy to learn - despite the many extra features of Powersim.
• The teachers had few problems to give homework and written tests for the System Dynamics module.
• Most students had no prior experience in project-oriented teaching, which caused some insecurities at the beginning. In the final review of the teaching project most students gave very positive comments about project-oriented teaching and the simulation software Powersim. Here are two statements by students (from their written feedback about the project):
  - "This kind of teaching was new for me, but somehow I appreciated it. I would not like all teaching to be like this, but now and then it would be fine; especially so that one can understand the connections between certain things."
  - "I liked the project. It was fun that we could work on our own. I like it better when we can summarize the items ourselves than when the teacher talks for an hour or so."

4.3 Summary and Conclusion

'Traditional empirical educational research often tries to eliminate or minimize the "teacher" as an influential factor. My study showed that this is rather questionable, if the results of educational studies are to be of any relevance for actual school teaching. Yet I must admit that it is far more difficult to design and undertake scientifically founded studies about learning, which include the teacher as a key factor of learning.

Let me conclude with a remark about "learner-centered-learning", as proposed by Forrester (1992) for teaching and learning System Dynamics. I do not think that learner-centered-learning lessens the importance of the teacher. In my opinion the teacher is the key factor for introducing and maintaining learner-centered-learning at school. We cannot expect that most students automatically have the same motivation and excitement as researchers in their laboratory; thus it is the teachers' role to induce and to guide the motivation of his or her students.

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Univ. Ass. Mag. Dr. Günther Ossimitz
Institut für Mathematik, Statistik und Didaktik der Mathematik
Abteilung "Didaktik der Mathematik"
Universität Klagenfurt
Universitätsstr. 65-67
A-9020 Klagenfurt

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