# Reflections on Teaching System Dynamics Modeling to Secondary School Students for over 20 Years

## Abstract

**:**

## 1. Introduction

## 2. Learning Theory

Deep understanding implies that the information is well-represented and well-connected. The greater the number and strength of the connections, the deeper the understanding. New information can be well-connected to existing knowledge and/or the pieces of the new information can be well-connected from within.([15], p. 3)

If concept development is to be effective in the formation of scientific concepts [those new ideas learned in school] instruction must be designed to foster conscious awareness of concept form and structure and thereby allow for individual access and control over acquired scientific concepts.([16], p. 312)

## 3. Introduction to the System Dynamics Modeling Icons

## 4. Teaching System Dynamics Modeling

#### 4.1. Model-Building in Algebra Classes

#### Pre-Lessons

#### 4.2. The Nine-Month System Dynamics Modeling Course

- To prepare students to identify and analyze problems in the world from which they could gain understanding by building and analyzing SD models.
- To develop the student’s skill in model building, analyzing model design, identifying and explaining feedback control and how it is evidenced in model output, and explaining clearly what they have learned in the modeling process.

- Problem Articulation: Selecting an appropriate problem, determining the necessary time boundary for the problem that captures the problematic behavior, determining the key variables, and sketching appropriate reference graphs (behavior over time graphs of key variables).
- Formulating a Dynamic Hypothesis: Identifying key feedback loops that can produce the problematic system behavior identified in problem articulation.
- Formulating a Simulation Model: Creating the stock/flow model that can produce the problematic behavior identified in problem articulation.
- Testing the Model: Testing occurs throughout model development, as model development is an iterative process. Tests include sensitivity analysis on parameters and reasonable model behavior recovery from introducing extreme values in certain model components.
- Policy Design and Evaluation: Identifying practical policies that can be implemented within the system that could mitigate the undesirable behavior of the system. Model structure may need to be altered to make the new policy work.

Forecasting of future conditions is not a measure of model suitability because forecasting is nearly impossible, and the goal is to understand how changes in policies affect behavior.

#### 4.2.1. The First Modeling Lesson

#### 4.2.2. The Sequence of System Dynamics Modeling Lessons

- Build small generic structures: There are a few generic modeling structures that capture important dynamics that are often parts of larger models. Having students develop some skill building and analyzing these small models and applying them to multiple scenarios was a useful early modeling experience. Some typical behaviors that were captured by generic structures included the following: exponential growth, exponential decay, convergent (goal-seeking) behavior, logistic (or more generally s-shaped) behavior, and overshoot and collapse behavior. Note: oscillating behavior was treated separately, later in the course.
- Combine generic structures: A logical next step was to create stories in which the dynamic behavior is produced by a combination of the generic structures already studied. As an example, a pharmacokinetic model would involve a patient connected to an intravenous drip. The inflow was constant, but the outflow (metabolizing the drug) was exponential. Many scenarios contained basic population structures (i.e., births/deaths, immigration/emigration, aging chains) and fitted within this category.

- Learn to build a dimensionless multiplier (DM): Most SD components are defined using either constant values or simple mathematical formulas. However, SD modeling also allows components to be defined graphically. Best practice usually requires the graphical definition to follow a prescribed design that produces a component known as a dimension multiplier. Learning to implement dimensionless multipliers in an SD model moves the modeler to a higher level of expertise. It is essential that the students understand why one would want to use, where to apply in a model, how to design, and how to implement a dimensionless multiplier in an SD model. Dimensionless multipliers are used to implement the non-linear behavior of the system within an SD model. They are essential to producing transfer of loop dominance. In early lessons, students built scripted models that incorporated dimensionless multipliers. Students were asked to explain how the dimensionless multiplier affected the behavior of the model (by interpreting the purpose of the (DM) graphical shape, the reason for the (1,1) stability point, and the choice of scale boundaries). Thus, students were gaining experience in the use of a DM before actually implementing one independently.
- Learn why systems oscillate: Oscillations can be produced wherever an SD model contains two stocks that are connected within a balancing feedback loop. One of the virtues of SD modeling is that students come to understand the structures that produce oscillations in a system, rather than just using trigonometric functions within a model to produce this behavior.
- Capture delays: Another extremely valuable feature of SD modeling is the ability to capture material delays (i.e., the time it takes for a letter to travel from sender to recipient) and information delays (i.e., the average time it takes for a person to change his/her mind about an issue) in SD models. These delays were incorporated in earlier lessons, without explicitly identifying them as delays. When delays were formally introduced, students were expected to reflect on the earlier models and identify the delays that were included in those models. Students were then to implement delay structures and explain the correct delay concepts when delays appeared in future story scenarios.
- Practice creating a stock/flow diagram from a news article: This is the one lesson in which direct instruction was used. Students were asked to read a news article. Then, as a class, students decided which variables might be important in the article. They identified which of those variables might be stocks. For the stocks, a reference behavior graph was developed, the time horizon was chosen, and the time units were chosen for the model. A stock/flow diagram was then developed, progressing until the first major feedback (containing more than three components) was closed. Finally, the feedback loop was identified and its polarity was determined. Students were then told to repeat the process on an article from the news that was of interest to them. Students have mentioned that this lesson was one of the most important lessons in preparing them to start to build their own (original) model for their project. Note: In this lesson, students did not simulate these models on the computer. The models were simply stock/flow maps without equations.
- Build and test an original system dynamics model from scratch: Building an original model from scratch was done in teams of two students. Students spent approximately two weeks selecting and researching two system problem ideas. Two topics were researched because students sometimes found one topic too difficult for them to understand or found they could not locate sufficient data for one of the topics. Students were also required to find an expert on their topic who would agree to talk to them periodically throughout their model-building phase, because it would become clear to them that they could not model a topic they did not understand well. (It was a pleasant surprise to find that an overwhelming number of adults who were solicited by the student modelers were quite willing to help them understand their project topic by answering student questions.3) By the end of the two weeks, students had to settle on one topic. The model was built and tested in stages, following the strong recommendation from SD modelers, “always have a working model.” This process took about four weeks. Students were given extra credit if they could get their model to start in equilibrium. Thus, the time frame for this part of the project included two weeks for initial research, two weeks to develop a draft model that simulates,4 and one to two weeks to polish the model. Forrester states that the process of building models is more important than the models arising from it [36].
- Write a technical paper explaining model behavior, model testing process, and a policy recommendation: Students wrote a technical paper explaining the model and the testing protocol that was followed to “validate” the model. Sterman [32] claims that it is not possible to actually validate or verify a model, since all models are wrong. However, there are procedures that should be followed to give the modeler (and the client) some confidence that the model may provide useful information about the problem being analyzed. Firstly, units had to be consistent. Secondly, sensitivity analysis had to be used to determine which parameters were most sensitive. Thirdly, students needed to conduct extreme value tests. In the final stage of this project a reasonable, realistic policy had to be designed, tested, and explained in an attempt to help mitigate the undesirable behavior produced by the system (which was captured by the model). A paper outline format was provided as no student had ever written a technical paper before (at secondary school level). The paper took between 1.5 and two weeks to produce, with a draft paper submitted after one week and feedback on the draft provided by the teacher so students could polish their final paper and resubmit. Paper drafts were not started until students had received feedback on their model drafts from the teacher.

- Present modeling insights to an audience: Students were given the option of doing a videotaped presentation of their model to the class or producing a poster to explain their model to an audience. Guidelines for the video presentation and the poster presentation were given to the students.

## 5. Assessments

During one of the Sym*Bowl events, we included a “Hotshots Challenge” problem that gave a non-trivial modeling challenge to the HS [high school] students to be solved within one hour. The problem we chose was highly relevant to HS students, and involved a person who goes to a party, and begins consuming alcohol at a relatively modest rate. The challenge is to predict when they will start feeling “under the influence” and, responsibly, stop drinking. The problem goes on to ask if, at the end of the party, fours hours after it began, was the person’s blood alcohol low enough for them to be safe to drive. Several of the HS students correctly solved the problem. I was very impressed. Since then I have given this problem to PhD students on their comprehensive exams, and not all of them solve the problem as well as the HS students.(Dr. Wayne Wakeland)

The breadth, and depth of these inquiries were impressive! In particular, the SD modeling and simulation fostered led students to ask perceptive, in-depth, and insightful questions far beyond their years. One project still stands out. Two girls with an interest in forensics developed a simple model of exponential heat loss [of a dead body]. They then conducted systematic experiments to monitor temperature loss from one-gallon milk bottles exposed to various ambient temperatures and various levels of wet and dry ‘clothing’. This information allowed them to extrapolate back in time to determine a ’time of death’ under various environmental conditions. Innovative and experiential learning at its best!

## 6. Conclusions

## Conflicts of Interest

## References

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1 | Bi-directional flows (bi-flows) are not displayed in Figure 1. Bi-flows have an arrowhead at each end of the flow pipe (one is a dotted arrowhead in order to differentiate the arrowheads). Positive flow values flow numeric information toward one arrowhead (perhaps filling the stock) whereas negative flow values flow numeric information toward the other arrowhead (perhaps emptying the stock). |

2 | Vernier Software & Technology, (Go!Motion), vernier.com. |

3 | Students were cautioned that they should not contact their expert frequently, that they should have their questions written out in advance, that they should use professional etiquette in email correspondence or phone conversations, and that they had to respect the time constraints on their expert with regard to responding to their questions. |

4 | The draft model was submitted to the teacher who gave students recommendations for improvements. |

5 | This student was unable to get his model to start in dynamic equilibrium. This is a flaw in the model definition, but not a fatal one. It is still possible to see that a rise in oil prices in quarter 30 produces reasonable model behavior. |

**Figure 3.**Student walking in front of a motion detector, and the SD model used to capture the idea of distance changing (linearly) over time. Assume the student initially stands 0.5 m away from the detector and then moves away from the detector at a velocity of 1 m per second for 4 s.

**Figure 4.**The graph and table produced by the SD software, and the equation for the situation described in Figure 3. In the equation, D represents the student’s current distance from the motion detector and t represents the time lapsed (in seconds) since the simulation commenced.

**Figure 5.**The stock/flow diagram that secondary school algebra students built and analyzed in a 45 min class period in the second half of the academic year.

**Figure 6.**Model of hybrid car production and sale created by an 18-year-old student. The model includes segments representing hybrid car factory capacity (blue), car inventory (green), and delay and perceived delay (brown) in ability to purchase a hybrid car [11].

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**MDPI and ACS Style**

Fisher, D.M.
Reflections on Teaching System Dynamics Modeling to Secondary School Students for over 20 Years. *Systems* **2018**, *6*, 12.
https://doi.org/10.3390/systems6020012

**AMA Style**

Fisher DM.
Reflections on Teaching System Dynamics Modeling to Secondary School Students for over 20 Years. *Systems*. 2018; 6(2):12.
https://doi.org/10.3390/systems6020012

**Chicago/Turabian Style**

Fisher, Diana M.
2018. "Reflections on Teaching System Dynamics Modeling to Secondary School Students for over 20 Years" *Systems* 6, no. 2: 12.
https://doi.org/10.3390/systems6020012