Making Connections

Joanne Egner Education

Last summer I had the opportunity to see students from Diana Fisher’s dynamic modeling class at Wilson High School in Portland, Oregon present their modeling projects to participants of the International System Dynamics Society Conference in Albuquerque. The parallel session was filled with educators and professionals from different fields, many of whom are renowned system dynamicists.

I think it is safe to say that we all were very impressed by the quality of the students’ work and how well they understood the dynamics associated with the issues they were presenting.  Perhaps more striking however, was seeing how empowering modeling real-world issues is for young people and the enthusiasm they share for their work.

Now everyone can see the effect that modeling real-world issues has on students at the CC Modeling Systems web site. Dedicated to helping educators bring dynamic modeling into the classroom, the web site features videos of students presenting their work as compelling evidence to the value of incorporating System Thinking and system dynamics into curriculum.

You’ll be amazed to see what 14-18 year olds are capable of and the excitement they exuberate when addressing challenges such as:

• How much do carbon emissions need to be reduced in order to stop global warming?
• Can automakers cope with the increasing demand for hybrid gasoline-electric vehicles?
• What is the impact of introducing an invasive species into an ecosystem?
• Will China have sufficient water resources to sustain population and agricultural growth?
• How can we improve the blood donation process in the United States?

Students are eager to understand the world better and are more than capable of building and understanding relatively sophisticated models in their attempts to understand the dynamics of real-world systems.

—Diana Fisher

Educators and administrators considering dynamic modeling curricula typically face challenges. No matter how compelling the evidence that Systems Thinking and the system dynamics methodology engages students and takes them to a higher level of reasoning, it is still difficult to justify without tying it to National Standards.

The CC Modeling Systems web site devotes an entire section to detailing very specific 21st Century Skills and National Standards addressed by curriculum that incorporates building system dynamics models.   Much of the homework has been done aligning this type of work to standards in the following subject areas:

• 21st Century Skills
• Economics
• Health
• Math
• Science
• Social Studies
• Sustainability
• Technology

Many thanks to Diana Fisher for sharing her students and her experiences teaching dynamic modeling with all of us!

To learn more about the modeling course that Diana teaches, I recommend the following links:
Recorded webinar presentation by Diana Fisher
Modeling Dyamic Systems: Lessons for a First Course

21st century skills, diana fisher, national standards

Karim Chichakly STELLA & iThink

This is part two of a three part series on Limits to Growth.  Part one can be accessed here.

In part one of this series, I explained the Limits to Growth archetype and gave examples in epidemiology and ecology. This part introduces the Bass diffusion model, an effective way to implement the capture of customers in a developing market. This is also used to implement what Kim Warren calls Type 1 rivalry in his book Strategy Management Dynamics, that is, rivalry between multiple companies in an emerging market.

The Bass Diffusion Model

The Bass diffusion model is very similar to the SIR model shown in part one. Since we do not usually track customers who have “recovered” from using our product, the model only has two stocks, corresponding loosely to the Susceptible and Infected stocks. New customers are acquired through contact with existing customers, just as an infection spreads, but in this context this is called word of mouth (wom). This is, however, not sufficient to spread the news of a good product, so the Bass diffusion model also includes a constant rate of customer acquisition through advertising. This is shown below (and can be downloaded by clicking here).

The feedback loops B1 and R are the same as the balancing and reinforcing loops between Susceptible and Infected in the SIR model. Instead of an infection rate, there is a wom multiplier which is the product of the Bass diffusion model’s contact rate and the adoption rate. If you are examining policies related to these variables, it would be important to separate them out in the model.

The additional feedback loop, B2, starts the ball rolling and helps a steady stream of customers come in the door. If you examine the SIR model closely, you will see that the initial value of Infected is one. If no one is infected, the disease cannot spread. Likewise, if no one is a customer, there is no one to tell others how great the product is so they want to become customers also. By advertising, awareness of the product is created in the market and some people will become customers without having encountered other customers who are happy with the product.

The behavior of this model is shown below. Note it is not different in character from the SIR model or the simple population model.

Read more…

archetypes, Bass diffusion, iThink/STELLA, market dynamics

Joanne Egner Training

This post is written by Rolf Olsen, a participant in our Introduction to Dynamic Modeling with iThink and STELLA workshop held last month in Colorado Springs.  We thought Rolf’s perspective would offer insights for those of you who are new to Systems Thinking or curious about applying dynamic modeling to real-world issues.

Rolf Olsen, Workshop Participant

I was very excited about a last-minute chance to attend the introductory iThink/STELLA workshop, but to be honest, on the flight to Colorado Springs, I started to become apprehensive.  Who was I trying to kid?  Sure, I’d heard the terms “stock” and “flow” and I understood their roles as the nouns and verbs of the software.  I’d even read a few chapters in Barry Richmond’s Introduction to Systems Thinking.  But the first time I started up the software and stared at that blank workspace, I had no clue where to begin!  Adding to my anguish, I was quite certain there would be others there who were much smarter than me and really knew what they were doing.

In college I spent most of my time and energy studying English and French, language, literature, cinema, art history, and so forth. I managed to avoid all higher math like the plague (although I did reasonably well in basic statistics).  My engineer father often reminded me that my degree in Humanities prepared me for almost nothing.  After college, I stumbled into a career in marketing – quite fertile territory for exploring system dynamics and modeling, as it turns out.  I spent a few formative years in an ad agency and at a regional banking system, before finding my stride marketing and managing nonprofit arts and culture organizations. Today I work in marketing and communication in a large academic medical center.

For years I’ve used spreadsheets to model various ‘what if’ scenarios.  In the arts, I used spreadsheets to create budgets and set ticket prices, always seeking ways to better predict revenue from ticket sales at different prices, for different types of performances (e.g., modern dance, string quartet, jazz ensemble), or on different days of the week.

Preparing for the iThink/STELLA workshop, I decided I’d like to try to model demand in a market area for laser vision correction surgery, popularly known as LASIK or PRK.  That seemed simple enough.  I might be able to bluff my way through this workshop after all!

Read more…

workshop

Joanne Egner News & Announcements

In 2009, the isee systems blog, “Making Connections” was created as a forum for sharing ideas and experiences with the Systems Thinking community. Blog topics cover subjects ranging from a systems perspective of current news events to modeling tips for advanced STELLA and iThink users.

As the first anniversary of the isee Blog approaches, we thought it would be interesting for folks to see the list of our most popular blog posts.

Top Ten Posts of 2009

1. Modeling H1N1 Flu Outbreak
2. Modeling Customers Switching Between Brands
3. Modeling a Watershed with Arrays
4. Matrix Arithmetic
5. Spatial Modeling with isee Spatial Map
6. “Thinking in Systems” book inspires online course
7. Physics Textbook 2.0
8. Insight-based Model Investigates the Housing Crisis
9. Building a Health Care Model Hierarchically
10. C02 in the Atmosphere Behaves Like a Bathtub

Karim Chichakly STELLA & iThink

The Limits to Growth Systems Archetype, also known as Limits to Success, combines growth with an exogenous or endogenous limit.  This Systems Archetype was formally identified in Appendix 2 of The Fifth Discipline by Peter Senge (1990), but made its first prominent appearance in World Dynamics by Jay Forrester (1971) and then The Limits to Growth by Meadows, Meadows, Randers, and Behrens (1972).  The Causal Loop Diagram (CLD) is shown below.

Real growth processes have inherent limits to growth.  Identifying these limits can help avoid problems in the future, whether the problem is overpopulation, increasing demand for a product that cannot be met, or growing a business in a mature market.  When growth is desired, but limited, it is always better to find ways to increase the limit before pushing for more growth.  Excessive growth in the face of a limit often leads to collapse.  Driving the system to the point of collapse can erode the ability to continue after the collapse, for example, by reducing the production capability of a piece of farmland or destroying the reputation of a company.

Classic examples of limits to growth include:

• The collapse of the deer population on the Kaibab plateau and on St. Matthew Island due to overpopulation and the attendant overgrazing of their habitat
• The overshoot and collapse of the human population on Easter Island
• Overgrazing in the Sahel region of Africa by cattle herders
• Overfishing of the oceans by fishermen
• The collapse of People Express due to sharp customer growth combined with slow personnel growth
• The sharp exodus of America Online subscribers after an intense marketing campaign increased the number of subscribers far beyond their capacity
• The contraction of the world economy in 2008 due to limiting oil supplies
• The productivity of staff deteriorating as a company grows, due to increased interactions and reporting overhead
• Business growth limited by the size of the potential market
• Yeast cells in the fermentation process, who suffer from both the loss of exogenously supplied sugar and the increase of endogenously produced pollution

Read more…

archetypes, Causal Loop, CLD, h1n1, population dynamics

Joanne Egner Education

Jeremy and I recently attended the MODSIM 2009 Conference in Virginia Beach where we facilitated a pre-conference workshop with the help of Mark Clemente, a local high school science teacher.

We’ve been working with Mark over the past year to incorporate dynamic modeling and computer-based simulation into the STEM curriculum at Ocean Lakes High School in Virginia Beach.  Ocean Lakes is serving as a demonstration school for a broader initiative in Virginia to use Modeling and Simulation (MODSIM) as an engine for 21st Century workforce development.

One of our goals for the pre-conference workshop was to provide participants with STELLA models and lessons that they could use immediately in their classrooms.  To attain this we put together a packet of sample lessons that would cover the spectrum of STEM education courses—Science, Technology, Engineering and Mathematics.

Science: Exploring an H1N1 flu outbreak model

Educators at all levels have found that physical activities or games can often be a good way to introduce students to STELLA models. Activities can be a lot of fun and provide a physical model for kids to make the connection with the more abstract computer-based simulation.

In our workshop, we decided to introduce a STELLA model of the H1N1 flu outbreak by first engaging the class in a simple exercise that demonstrates the spread of infectious disease using cups of water.  Each student was given a cup of water and a pipette.  One cup of water however, was contaminated with sodium hydroxide.   We then began the process of walking around and dropping a pipette filled with liquid from our own cup into the cups of fellow students.  At the end of several rounds, Mark (our teacher) put a drop of phenolphthalein solution into everyone’s cup.  If the liquid turned pink, we were infected.

With a new understanding of how quickly infection can spread, the class was ready to be introduced to a STELLA model of the H1N1 flu outbreak.  The core structure of the model is based on the same model that epidemiologists use to track a population through the various stages of infection including Susceptible, Exposed, Infected and Recovered (SEIR).

The simulation provided several controls for students to experiment with different policy options for controlling the spread of the virus.   Along with the model, we provided a sample lesson with a set of questions to help guide students through their exploration.  To download the H1N1 model and sample lesson, click here.

Technology: Inquiry-based learning with STELLA simulations

It was fascinating to watch how each student in our workshop experimented differently with the model and began asking their own set of questions.  STELLA simulations and computer technology provide the perfect platform for students to learn using an inquiry-based approach.  Rather than being told how something works, students can discover for themselves by exploring “what-if” scenarios and finding out what happens. For teachers, this can mean shifting from a traditional teacher role to that of a facilitator or coach, guiding students in their inquiry without knowing in advance the path they’ll choose.

Engineering/Physics: The Pendulum Story

Another STELLA model that we introduced to workshop participants was one that Mark and I modified for the Physics Flexbook project earlier this year.  The original version was developed by Diana Fisher in her book Lessons in Mathematics: A Dynamic Approach. The model provides a practice field for learning how the variables of simple harmonic motion are related.  Controls in the simulation allow you to explore what effect, if any, string length, initial displacement, and pendulum ball mass have on the amplitude, period, and frequency of the pendulum’s motion.  To download the pendulum model and sample lesson, click here.

Mathematics: Algebra Word Problems

You may remember from your own experience in math class that word problems typically give students a lot of trouble!  It is especially difficult to understand what is important in the problem and how to translate words into mathematical equations.  STELLA can help by allowing students to create a visual representation of the problem and making it easier to understand the symbolic representation.

For the workshop, we used the following word problem as an example of a typical Algebra I assignment:

Imagine your class is going to try to raise $400 by making school T-shirts. There is a $150 set-up charge for the T-shirt design that you have designed. Once the design is set, it costs $4 for each T-shirt. You feel it is possible to charge $10 for each T-shirt. How many T-shirts do you have to sell before you break even, i.e., make enough money to cover your costs?

Together we created a STELLA model that provided a visual representation of the word problem and gave everyone some hands-on experience building models from scratch.  It also inspired some participants to think about ways they could expand or change the model to answer additional questions that weren’t part of their immediate assignment. 

To download the T-shirt model and lesson, click here.

We’d love to expand our library of STELLA lessons and models so that we can share them with teachers.  If you’ve got any ideas of things you’d like to try in your classroom, please feel free to contact us – we’re here to help!

Algebra, h1n1, inquiry-based, lessons, Mathematics, MODSIM, pandemic, Physics, Science, STEM

Jeremy Merritt STELLA & iThink

It seems like everyone has been talking about H1N1 (swine flu) the last couple of months.  If you have children in school, then you are probably very aware of how fast the virus is spreading.  Schools are the perfect environment for a virus to spread.  To help understand why, we created a STELLA model of a high school that introduces the H1N1 virus.  You can experiment with vaccination and “stay at home” policies to limit the spread of the flu.

The STELLA model is based on the SEIR compartmental model that epidemiologists use to model the progress of an epidemic.  SEIR models divide the population into compartments: Susceptible, Exposed, Infected and Recovered.  These ‘compartments’ translate nicely into stocks within the STELLA model where we can observe the dynamics of the spreading virus.

While developing the model we decided to explore some strategies that schools are pursuing to limit the virus’ spread.  We wanted to know if the “stay at home” (when you are sick) policy would be effective in the case where vaccines are not available quickly enough, (which as of November 2009 is the case).

Take a look:

Click the ‘Simulate’ link on the home screen above and try some different scenarios.  Be sure to click the ‘How does this simulation work?’ link for a guided tour of the model behind the simulation.

As you experiment with the simulation, consider the following:

• How does varying “% vaccinated” effect the number of sick students?
• How many days do infected students need to stay home to have a significant impact on the spread of the virus within the school?
• What impact does the “% effectiveness of vaccine” have on the flu outbreak?
• What combination of decisions results in the lowest number of sick students?  Are these decisions realistic in a real-world setting?

Note: Each time you dial in parameters and press run, a new plot will be added to the graph so you can compare the effectiveness of the different decisions.  Clicking on the blue reset button will clear the graph and reset all Knobs to their default value.

If you think this simple model is useful, feel free to share it or embed it on your own website; just click the sharing icon in the lower right corner.  If you want to dig deeper into the STELLA model you can download the model by clicking here.  You can open the model with STELLA 9.1, or the free isee Player.

embedded, epidemic, flu, h1n1, infection, netsim, seir

Karim Chichakly Modeling Tips

This is the last installment of a four-part series.  The first three parts can be accessed by clicking on the links below.
Methods for Using Arrays Effectively
Modeling a Watershed with Arrays
Modeling Customers Switching Between Brands

Generalizing the Model

When I showed Steve Peterson (at Lexidyne) my brand switching model, he told me there is a more general version that separates the customer loss fraction from the fraction won by another competitor.  This has been presented in Pharmaceutical Product Strategy by Mark Paich, Corey Peck, and Jason Valant.

In my original formulation, the switching probability matrix was the product of these two variables.  However, in many practical cases, the data available comes from two different places and reflects these two separate components.  The revised model structure is shown below.

Instead of one composite switching probability, this model uses a switching out probability that is distinct from the switching in probability.  The switching out probability is a one-dimensional array that, for each product, contains the fraction of customers lost to rivals every time unit (in our case, month).  A sample for the five brands A, B, C, D, and E appears below.

switching out probability

We can see from this table that Brand B is losing 17% of its customers to rivals each and every month!  Whoever is managing that product had better do something quickly.

The other side of the story has to do with which brand the customers are switching to.  The switching in probability matrix contains, for each brand, the fraction of lost customers that migrate to a rival brand.  Thus, each row of this matrix must add up to one (100% of lost customers).  A sample appears below.

switching in probability

Note the diagonal will always be zero.

We can determine a lot of things from this table.  For example, brand B offers no competition to brand D, brand D is the biggest rival of all the other brands, and brand C is brand D’s biggest rival.

Read more…

2D array, arrays, iThink/STELLA, market dynamics