Thank you very much for the generous feedback on the discussion paper that we sent out on System Dynamics, for references to literature, and for software suggestions. We are satisfied that significant members of the field have commented on our paper and will limit our concluding remarks to a few of the concerns raised.
Comments on remarks by Chet Hedden [18 Oct 95]:
1. It has always been risky to suggest that cumulated knowledge be modeled by the level of a container--and usually it does not make things better to suggest a diversification in a number of containers representing various kinds of knowledge. Consequently, this example was a test balloon. In some cases, however, the accumulation of knowledge and its interpretation can conveniently be modeled that way. Let us look at a few examples on how to utilize this technique:
Various containers can be used to accumulate various kinds of knowledge (procedural vs. declarative, domain-specific, etc.) that influence different kinds of skills in different ways to establish a more efficient processing, say, of a flow of a particular kind of tasks. The efficiency may be measured in terms of number of tasks processed per time unit, errors generated per task, tasks to be reworked, products to be rejected, etc.
The mix of knowledge of different kinds required to perform a task, may be characterized by the weights assigned to the different levels in the calculation of processing efficiency.
Clearly, we face a challenge in the operationalization of the term knowledge. We think this operationalization must result from a careful investigation of the context at hand. Moreover, we recognize that both the rate of acquisition of knowledge as well as the effect of knowledge acquisition, say, on the processing of tasks, is often delayed, maybe marginally increasing in the initial stages of knowledge acquisition, and typically marginally decreasing in the later stages--resulting in saturation (i.e., the effect of knowledge acquisition is non-linear since you must be expected to acquire and integrate the most relevant information first).
In modeling of mental models and processes using system dynamics, however, this is not the typical approach. Usually what is done, is to replicate a model that represents a real system, in a simplified form so as to capture bounded rationality. Moreover, we distort/delay the transfer of information from the model of the real system to the model of the mental representation of that system so as to capture the perception, confirmation, and integration of information into the mental model. Likewise, we distort and delay information (decisions/actions) flowing in the opposite direction. In this way, we can simulate the model of the real system and its mental representation in interaction, say, in an information acquisition, policy design and selection, and decision making cycle.
2. Chet Hedden asks whether we should not search for a "completely new approach with, hopefully, greater observable learning outcomes than those well-established but not demonstrably effective principles have thus far yielded?"
We are of the opinion that quite new principles must be developed and utilized to come to an in-depth understanding of the relationship between structure and behavior in dynamic systems. This understanding is not primarily reflected in an ability to treat a non-linear feedback model characterized by uncertainties and delays mathematically in closed form. Understanding is reflected in the individual's ability to explain the structural origin of problem behavior and to effectively suggest structural modifications that robustly correct that behavior.
On the other hand, we believe that we need to utilize a number of fundamental principles in education to reach our objective, including sequencing to obtain a proper stepwise progress and the activation of a variety of senses and ways to analyze a model.
3. Hedden also asks for the building blocks of insight that we try to establish in the minds of our students and that we expect them to utilize when faced with systems and models of a more complex nature.
We call these models as well as their dynamics "generic" and introduce them relatively informally at first. They are distilled from specific instances of such models, preferably selected from a wide variety of domains so as to stress the interdisciplinary nature of system dynamics and to expand the focus of our students. Subsequently, the generic structures are being generalized, interpreted, and applied to a number of additional domains.
As such, we make use of generic models in a way that resembles an object-oriented approach (ref. object-oriented design of software). We consider them references to classes of models/systems and thus structural templates over which domain-specific models may be formulated.
Our students are expected to understand the relationship between the structure embedded in and behavior exhibited by these generic models. Each such model is often labeled characteristically like: The "shifting the burden to the intervener" Model. These are excellent learning units that may be increased in size and complexity as the students progress in skills and maturity. Having students elaborate a generic model in terms of a case or context of specific personal interests provides a highly engaging learning environment.
4. We pointed out the possibility that a predator/prey model exhibits counter-intuitive behavior. And, Chet Hedden asks "Why counter-intuitively?"
A number of even relatively simple models exhibit a behavior that most people, even after thinking long and hard, are not able to comprehend. Here are some examples related to predator/prey models.
When not in equilibrium, such systems typically oscillate: First the prey population grows increasingly as a result of a low number of predators. Then, because of the increased food supply, the predator population starts growing, reducing the rate at which the prey population grows, and, eventually, causing it to diminish. This reduction in food supply reduces the growth of the predator population and eventually causes that population to diminish so as to set the state for another increase of the prey population. A typical task for students would be to come up with a policy that dampens the oscillations. Here are three such policies associated with the prey:
As it turns out, policies (1) and (2) are extremely non-robust and they usually do not work. They bring about the desired behavior only when initiated in a very narrow window of opportunity within the prey-cycle. Otherwise, their effects are counter-productive in the sense that the oscillations are being amplified. To many, this is an unexpected (counter-intuitive) result arising from the fact that the associated dynamics of the predator population is not well comprehended. It is the reaction of the predator population that causes this amplification. Although policy (3) is very similar to policy (2), it is completely robust and succeeds to stabilize the system in ecological equilibrium. But again the result is counter-intuitive to many in the sense that this equilibrium does not change even if we vary the target prey population size. The reason is again that the predator population counteracts our efforts to change the size of the prey population. All we obtain by hunting more intensively, is to shift the burden of regulating the prey population from the predators to ourselves. This can easily be seen when we give up hunting. If our goal has been the natural equilibrium, then the predator population is in equilibrium and the system remains stable. If we have hunted intensively, then the predator population has diminished below its long-term equilibrium, leaving room for the prey population growth to take off in reaction to the termination of hunting. In conclusion, such a model, like many others, does not behave according to general expectations.
5. Another point brought up by Chet Hedden is the issue of the purpose of the model and the values either implicitly or explicitly built into the model. It is quite clear that a model can include human values and associated aspirations, targets, or goals. By choosing different sets of values, we will be able to represent a variety of perspectives or attitudes.
By representing these values, aspirations, etc., in the form of stocks, as Chet Hedden suggests, they can be brought to change over time in response to the consequences of holding these values. That is, we can study the effects of endogenous modifications of values and aspirations. In fact, in system dynamics we often model moving goals and the consequence change in focus of attention arising from different aspirations being satisfied to different degrees at different points in time.
6. We agree that hypothesis testing can take place using a ready-made game-based simulation where "you have animations of animals roaming around in the woods near the town, some sick and some eating the others. Wouldn't a spreadsheet work just as well for this type of analysis and hypothesis testing? If so, he asks, why do you need to explain it in terms of system dynamics?
The contribution of system dynamics is to provide a stock-and-flow and a feedback perspective, tools by which such a perspective can be applied to a specific system structure, and tools by which the relationship between structure and behavior become (more) apparent. This is extremely helpful when we attempt to draw fruitful conclusions from hypothesis testing beyond the binary conclusion that the hypothesis failed or passed the test. We want to know why it failed (diagnosis) and how the hypothesis could be improved (treatment) so as to pave the way for a structural theory of the model behavior. The system dynamics methodology and its tools provide substantial support in this work.
Although, this was not the point in Chet Hedden's remark, I would like to emphasize that spreadsheets are of very little use in the case of system dynamics models. There is no graphical support for the display of model structure and, consequently, no support for identifying and utilizing the relationship between structure and behavior. Moreover, spreadsheets treat poorly the feedback loops, the non-linearity, and the delays which typically characterize system dynamics models, and the model designer is forced to take the responsibility for a number of tasks that system dynamics supporting software handles far more effectively.
7. At this stage, we should emphasize our position regarding the utilization of the two kinds of diagrams for portraying system dynamics models in educational contexts--the stock-and-flow diagrams and the causal loop diagrams.
Those who recognize the significance of understanding the relationship between structure and behavior in dynamic systems need the same information which is required to simulate the behavior of a system. That is, we need the information embedded in the stock-and-flow diagram. A feedback-loop diagram is information poor since we do not distinguish between the state of the system, represented by the containers, and the change in that state, represented by the flows.
On the other hand, we recognize the need for simplified summaries of the structures that dominate the behavior of the model at any point in time. For this purpose, causal loop diagrams are excellent. In any case, whether we work with one or the other form of representation, we need to integrate a description of the behavior in a representation of the underlying structure. Sophisticated software, such as Powersim, allows us to accomplish that.
Comments on remarks by Steve Alessi [12 Oct 95]:
8. First of all, it is good to hear from people who have extensive experience in using system dynamics for educational purposes. We share the view that system dynamics is not quite easy to teach and would add that, the later you start, the more challenging it becomes. We believe that starting early with simulation experiments using water tanks and pipes is fun and educating. This can be supplemented with classroom games in which we, for example, portray a diffusion model: Initially one person has been given a rumor or a disease. Each time step, each student shakes hands with a fixed number of other students and secretly transfers the information or disease. Each person records when he or she were being informed or infected. Thereafter, the accumulation is plotted on the board to set the stage for a great discussion of the relationship between the mechanism played out in the classroom and the resulting behavior. Variations of this game, such as importing people from another class, exporting people, etc., can constitute the basis for more advanced studies.9. The book by Roberts contains a lot of interesting examples, but has two major disadvantages: First of all it concentrates for 8 chapters on feedback loop design and analysis without utilizing stocks and flows or simulation. We think this sends the wrong message. The analysis of simulation results is an integrate part of the model analysis and design. Secondly, and this is less significant, it refers to models written in MicroDynamo which is obsolete.
10. It is quite clear that teaching using system dynamics is demanding. And, it would be wrong to claim that Mandinach and Cline are very optimistic. We think it is very difficult to draw any definite conclusions from their work. The work by Davidsen, et al., is indicative of positive results in a number of Swedish high schools.
One of the problems, which we have experienced over and over again, is that the teachers have not had the appropriate grip on the stuff--and one can, consequently, expect no more from the students. Why are the teachers not well trained? Well, there are not that many good teachers (teachers or textbooks) and the teaching of SD requires fundamental insight and maturation usually only obtained through quite a bit of modeling and analysis over a long period of time.
11. Along the same lines, Alessi asks: "Is it wise to suggest such a complex methodology as a basic instructional strategy we should all use in our teaching?" We do not see the methodology as the source of complexity. Rather complexity is what characterized the real systems we try to capture and understand using this methodology. We have not found that there is a simpler way of addressing the fundamentals of complex, dynamic systems. So the question then becomes "Are we to learn about and shall we teach these fundamentals?"
We think that the fact that we are surrounded by dynamic systems and that of a number of disciplines, say, economics, demonstrate shortcomings when addressing dynamic problems clearly illustrate the need for the public to develop a dynamic intuition--at least one that allows them to critique the many static conceptions that dominate public life and politics.
12. System dynamics is not a subject on its own in any school, except as a major elective course in Norwegian high schools. It was introduced this year on our initiative. Powersim is given for free to all schools and a textbook in modeling has been printed to facilitate learning.
We believe, however, that SD should serve as a methodological element in a number of subjects, in particular in natural and social science classes. Most dynamic phenomena can be addressed using system dynamics. Few dynamic phenomena are currently being addressed adequately--precisely because teachers are not trained to introduce these phenomena and students are not trained in using adequate tools.
The System Dynamics Group, MIT, has developed quite a lot of educational material for schools under the leadership of Professor Jay W. Forrester, the founder of the field. That and other material is available from The Creative Learning Exchange, 1 Keefe Road, Acton, MA 01720; tel. (508) 287 0070, fax (508) 287 0080. Moreover, the periodical The Systems Thinker, published by Pegasus Communications Inc., Phone: (617) 576 1231, is a great source of ideas in the area of business and organizations.
13. Alessi points out that our emphasis on SD constitutes one extreme along a continuum of simulation applications; from the use of models to the building of models. Clearly in our teaching, we wander along this continuum from games, via simple structure identification, adding tasks to model structure/behavior analysis and building. With our goal in mind--to understand the structure/behavior relationship--we do need to address model structure.
14. We will pursue SD effectiveness tools and do so in close interaction with our software vendor Modelldata AS here in Bergen. We will be far more precise as to when we utilize SD in the role of a design strategy and in the role of an instructional strategy. And we will outline various kinds of use of SD along the continuum described by Alessi.
Comments on remarks by Rob Foshay [18 Oct 95]:
15. We do not want to take side in the debate on constructivism, and we therefore feel comfortably that we share Rob Foshay's views. We do recognize the inefficiencies of "pure" constructivism and our utilization of generic models for teaching and learning constitutes one of our serious attempts to enable our students to enable our students to structure their learning and get a head start.
We are inclined to agree that the traditional tools applied in SD provide us with a distillation of a much richer reality and that there is a need to demonstrate what the components of a model actually represent. Using references (electronic links) from the SD model to multimedia presentations of that reality and people describing that reality it one way to alleviate that problem. This should not substitute for the students going out to investigate that system in question and, preferably, collect source material themselves--material that they can enclose in the form of multimedia along with the model and with their simulation results. We would utilize multimedia not only to document the structure of a model, but also to illustrate behavior characteristics that show up during the simulation. For instance, we might use movie icons that refer to material of relevance to the behavior generated by the simulation--movie icons that fade in when the underlying material becomes relevant and fade out when other behavior characteristics become dominant.
16. Rob Foshay's comment on the causes of the challenge SD constitute for teachers and students has already been addressed in points 10 and 11.
And then, thanks to Bill Deterline [20 Oct 95] for your reference to Designer's Edge. We are not familiar with that software and will have a look to see how we can utilize it for our purposes. Also, thanks to Martyn Wild [19 Oct 95] for guiding us to the London Mental Models Group which seem to provide us with important insights.
In conclusion, we are extremely satisfied by the rich and insightful comments we have received and which have given us inspiration to refine our points of view. Thank you so much!
For those who want hard copies of a few of our articles on how to utilize SD and Powersim for educational purposes, please indicate with a response directly to Paal Davidsen at: davidsen@ifi.uib.no.