Making Connections

Editor’s note: This is part one of a two part series on Systems Thinking and mental models

In writing and teaching people about Systems Thinking, we often refer to “mental models”.  For some people, this comes as a bit of a surprise, because the context usually involves building models with the iThink or STELLA software.  They don’t expect us to start talking metaphysically about thinking.  “Is this about philosophy or modeling software?” they may wonder.  The software is actually a tool to help construct, simulate and communicate mental models.

Let’s define the term model: A model is an abstraction or simplification of a system.  Models can assume many different forms – from a model volcano in a high school science fair to a sophisticated astrophysical model simulated using a supercomputer.  Models are simplified representations of a part of reality that we want to learn more about.  George Box stated: “Essentially, all models are wrong, but some are useful”.  They are wrong because they are simplifications and they can be useful because we can learn from them.

So, what is a “mental model”?  A mental model is a model that is constructed and simulated within a conscious mind.  To be “conscious” is to be aware of the world around you and yourself in relation to the world.  Let’s take a moment to think about how this process works operationally.

Imagine that you are standing outside, looking at a tree.  What happens?  The lenses in your eyes focus light photons onto the retinas.  The photosensitive cells in your retinas respond by sending neural impulses to your brain.  Your brain processes these signals and forms an image of the tree inside your mind.

So at this point, we’ve only addressed the mechanisms by which you perceive the tree.  We have not addressed understanding what a tree is or considered changes over time.   We are dealing with visual information only.  There is nothing within this information that tells you what a tree actually is.

What makes the image of a tree in your minds click as an actual tree that exists right there in front of you?  This is where mental models kick in and you start to think about the tree.  The tree is actually a concept of something that exists in physical reality.  The “tree concept” is a model.  Understanding the concept of a tree requires more information than is available through sensory experience alone.  It’s built on past experiences and knowledge.

A tree is a plant.  It is a living thing that grows and changes appearance over time, often with the seasons.  Trees have root systems.  Trees use leaves for photosynthesis.  Wood comes from trees.  I can state these facts confidently because I have memories and knowledge of trees contained within my mental models.  Mental models contain knowledge and help us create new knowledge.

Read more…

Sarah Boyar accepts Scholarship Award from Joanne Egner

The Barry Richmond Scholarship Award was established in 2007 by isee systems to honor and continue the legacy of its founder, Barry Richmond.  Barry was devoted to helping others become better systems citizens.  Systems citizens are members of a global community that strive to understand the complexities of today’s world and have the informed capacity to make a positive difference.  It was Barry’s mission to make systems thinking and system dynamics accessible to people of all ages, and in all fields.  The award is presented annually at the System Dynamics Society Conference to an individual whose work demonstrates a desire to expand the field of systems thinking or to apply it to current social issues.

Through most of his career, Barry focused on education as the key to spreading systems thinking.  As a teacher and a mentor he dedicated much of his time to developing tools and methodologies for teaching systems thinking.  With this in mind, it was a great pleasure to present this year’s award to Sarah Boyar, a recent graduate of the Masters Program in System Dynamics at Worcester Polytechnic Institute (WPI).

Sarah Boyar and Karim Chichakly enjoy the conference banquet

Sarah presented a portfolio of her work to the scholarship committee.  In particular, an essay about her teaching philosophy resonated with us.  Sarah wrote this piece while taking a seminar in college teaching in order to fulfill her Real World Dynamics course requirement at WPI.  Since she already had plenty of experience as a consultant applying system dynamics to real world situations, Sarah managed to convince the WPI powers-that-be that an essential real world manifestation of system dynamics is the way that it is taught.  This is something Barry would have encouraged and been excited about.

Her essay titled Beliefs About Teaching and Learning begins as follows:

I teach System Dynamics. While I want my students to have some knowledge of system dynamics, most of all I want them to be excited and stimulated by it. I also want them to find it beautiful: I want to teach in such a way that my students find some aspect of beauty in the work, whether it’s through the visual arcs in the model interface, or the precision of algebra in the way we write statements, or the way that system dynamics can ameliorate a social ill that concerns them. I want my students to somehow feel a sense of peace and beauty derived from some aspect of the knowledge I am teaching.

Among Sarah’s aspirations is the desire to teach system dynamics to professionals in other fields, namely lawyers (potential judges) and medical doctors.  Incorporating a systems perspective within both the judicial system and in healthcare could certainly make a positive difference for us all.  Good luck and congratulations Sarah!

A question we periodically get from our customers is: Can iThink or STELLA connect to a database? Saving and pulling information to/from databases presents a lot of advantages for storing, organizing and sharing model data. Thanks to iThink and STELLA’s ability to import and export data via commonly used spreadsheet file formats, it is possible to use comma separated value (CSV) files as a means to create a connection to database applications.

Essentially, data can be moved between a database and iThink/STELLA by using a CSV file as a bridge. CSV files are a widely supported file standard for storing table data, and both iThink/STELLA and many database programs are able to read and write to them.

The process of connecting to a database using CSV files as an intermediary

The process can be automated when you use iThink/STELLA’s ability to run models automatically from the command line (Windows only). Most database applications also have command line interfaces, allowing you to create a single macro script that moves data between your model and a database in a single process.

In this post I will use a simple example to demonstrate how to import data from a Microsoft SQL Server database into an iThink model on Windows. The model and all files associated with the import process are available by clicking here. If you don’t have access to Microsoft SQL Server, you can download a free developer’s version called SQL Server Express from the Microsoft web site.

The Model

The model used in this example is a variation of the Beer Game model. The structure shown below represents the ordering process for a simple retailer supply chain.

The model has been set up to import the initial values for On Order with Wholesaler and Unfilled Orders stocks, target inventory and actual customer orders (a graphical function with 21 weeks of data). The source of the imported data is the file named import.csv in the example files.

To set up this example, I manually created the CSV file using the initial model parameters. (Later in this post, you’ll see that this file will be automatically created by the database.) The model has been initialized in a steady state with actual customer orders at a constant level of 4 cases per week over the 21 week period.

Creating the SQL Server Database

Since the model is set up to import data from the import.csv file, we are ready to populate that same CSV file with data from the SQL Server database. But, first we need to create the database and the associated data table.

Using SQL Server Management Studio, create a new database named Simulation.

Dialog in SQL Server when adding new "Simulation" database

Once the database has been created, you can run the full CreateTable.sql script to create a table that will store the data. To open the script, select Open -> File from the File menu and navigate to the CreateTables.sql file. The script is set up to create a table named Import_Data with columns for each variable that is imported into the model. The script will also populate the table with data. It is important to note that the first row of the table contains the variable names exactly as they appear in the retailer supply chain model. Below is a sampling of the commands contained in the script:

CREATE TABLE [dbo].[Import_Data](
[RowID] [int] IDENTITY(1,1) NOT NULL,
[OnOrder] [nvarchar](50) COLLATE SQL_Latin1_General_CP1_CI_AS NULL,
[UnfilledOrders] [nvarchar](50) COLLATE SQL_Latin1_General_CP1_CI_AS NULL,
[TargetInventory] [nvarchar](50) COLLATE SQL_Latin1_General_CP1_CI_AS NULL,
[ActualOrders] [nvarchar](50) COLLATE SQL_Latin1_General_CP1_CI_AS NULL
) ON [PRIMARY]

INSERT INTO Import_Data
(OnOrder,UnfilledOrders,TargetInventory,ActualOrders)
values
(‘On Order with Wholesaler’,'Unfilled Orders’,'target inventory’,'actual customer orders’)
INSERT INTO Import_Data
(OnOrder,UnfilledOrders,TargetInventory,ActualOrders)
values
(8,4,20,4)
INSERT INTO Import_Data
(OnOrder,UnfilledOrders,TargetInventory,ActualOrders)
values
(”,”,”,4)
INSERT INTO Import_Data
(OnOrder,UnfilledOrders,TargetInventory,ActualOrders)
values
(”,”,”,10)

To run the script, select Execute from the Query menu. Note that the data shows an increase in actual customer orders in week 2 from 4 to 10 cases. In the model, actual customer orders is a graphical function which is reflecting order data over time.

Results tab after running CreateTable.sql script

Linking the Database to the Model

After the database has been prepared, the Transfer_Data.bat Windows batch file can be used to link the database to the model. Transfer_Data.bat is a script that pulls data from the database into the CSV file, opens iThink, imports the CSV data and runs the model. The batch file takes advantage of the utility Microsoft provides with SQL Server called Bulk Copy Program (BCP) and iThink’s ability to run models from the command line. You’ll need to make a few edits to the batch file shown below before you can run it.

BCP Simulation.dbo.Import_Data out import.csv -c -t, -U <Login> -P <Password> -S <Server name>

“%PROGRAMFILES%\isee systems\iThink 9.1.4\iThink.exe” -i -r -nq Supply_Chain.itm

Using a text editor such as WordPad or NotePad, replace the placeholders for <Login>, <Password> and <Server name> in the first line to match the authentication for the Simulation database that was previously created. If your SQL Server database is on your local machine, you can delete the –U, -P and –S settings altogether. This command will make use of the BCP utility to copy the contents of the Import_Data table to the import.csv file. Depending on the version of iThink or STELLA you are running (version 9.1.2 or later is required) and its location, you may also need to edit the second line of the batch file.

After the Transfer_Data.bat file has been edited and saved, double-click on the file to run it. Once the data has been retrieved from the database, iThink will import the data via the CSV file, and run the simulation. The results will appear in the graph in the model as shown below:

Updating the Data

In a real-world situation, the database that stores information we need to run a model is usually connected to another application that updates or changes the data. In the absence of a real-world application, I created a script that allows you to update the Simulation database and experiment with your own set of data.

In SQL Server Management Studio, open the script called UpdateTable.sql. Edit the values for each variable as desired.

USE [Simulation]
UPDATE Import_Data SET OnOrder=8, UnfilledOrders=4, TargetInventory=20, ActualOrders = 4
WHERE RowID=2
UPDATE Import_Data SET ActualOrders = 4
WHERE RowID=3
UPDATE Import_Data SET ActualOrders = 4
WHERE RowID=4

When you have finished editing the UpdateTable.sql script, execute the script to update the Import_Data table. Now you are ready to re-run the Transfer_Data.bat batch file and link the updated data with the Supply_Chain.itm model.

Summary

This example should give you a good idea of how the process of importing data from a database into an iThink or STELLA model can be set up and run automatically. Other database applications such as Oracle, MySQL and SQLite could also be used in a similar manner. I have not yet tried to set up examples, but these other databases also have command line interfaces for automating the transfer of data to CSV files that iThink and STELLA can connect to.

Stay tuned for part two of this post where I’ll provide an example of exporting model results to a SQL Server database.

The question we get asked most frequently by just about anyone who wants to know more about our modeling software is “What is the difference between STELLA and iThink?”  From a functional perspective, there are no differences between the STELLA and iThink software — they are two different brands of the same product.

The STELLA brand is targeted toward individuals in educational and research settings.  Supporting materials such as An Introduction to Systems Thinking with STELLA and sample models cover the natural and social sciences.

iThink, on the other hand, is targeted toward an audience of users in business settings.  An Introduction to Systems Thinking with iThink is written with the business user in mind and model examples apply the software to areas such as operations research, resource planning, and financial analysis.

Aside from the different program icons and other graphic design elements that go along with branding, there are just a few minor differences in the default settings for STELLA and iThink.  These differences are intended to pre-configure the software for the model author.  They do not limit you in any way from configuring the default setup to match your own individual preferences.

Below is a list of all the differences between the default settings for STELLA and iThink.

Opening Models

When opening a model with STELLA on Windows, by default, the software looks for files with a .STM extension.  Similarly, iThink looks for files with an .ITM extension.  If you want to open an iThink model using STELLA or vice-versa, you need to change the file type in the Open File dialog as shown below.

On Macs, the open dialog will show both iThink and STELLA models as valid files to open.

If you open a model with a file type associated with the different product than the one you are using, you’ll get a message similar to the one below warning you that the model will be opened as “Untitled”.  Simply click OK to continue.

Saving Models

When saving a model in STELLA, by default, the software saves the model with a .STM file extension.  Similarly, iThink saves model s with an .ITM extension.  If you’re using STELLA and want to save your model as an iThink file or vice-versa, use the Save As… menu option and select the appropriate type as shown below.

STELLA on Windows save dialog

STELLA on Mac save dialog

Run Specs

Since iThink is targeted toward business users who tend to measure performance monthly, the default Unit of time for iThink is set to Months.  It’s also easier to think about simulations starting in month 1 (rather than month zero) so we set the default simulation length in iThink to run from 1 to 13.  STELLA on the other hand, reports the Unit of time as “Time” and, by default, runs simulations from 0 to 12.

Run Spec Default Settings Comparison

Table Reporting

In a business context, financial results are generally reported at the end of a time period and the values are summed over the report interval.  For example, in a report showing 2010 revenues we would assume the values reflect total revenues at the end of the year.  In line with this assumption, the default Table settings in iThink include reporting Ending balances, Summed flow values, and a report interval of one time step.

In a research setting, scientists tend to prefer reporting precise values at a particular time.   For this reason, the default Table settings in STELLA are configured to report Beginning balances, Instantaneous flow values, and a report interval of Every DT.

Table Default Settings Comparison

STELLA or iThink

When choosing between STELLA or iThink, try to think about the kinds of models you intend to build and the problems you are looking to solve.  If your objective is to drive business improvement, chances are iThink will be a better fit.  If your purpose is to understand the dynamics of a natural environment or social system, STELLA will likely be your brand of choice.  Whatever you decide, both products will provide you with the exact same functionality and can easily be configured to suit your own preferences.

There are times when it is helpful to calibrate, or fit, your model to historical data. This capability is not built into the iThink/STELLA program, but it is possible to interface to external programs to accomplish this task. One generally available program to calibrate models is PEST, available freely from www.pesthomepage.org. In this blog post, I will demonstrate how to calibrate a simple STELLA model using PEST on Windows. Note that this method relies on the Windows command line interface added in version 9.1.2 and will not work on the Macintosh. The export to comma-separated value (CSV) file feature, added in version 9.1.2, is also used.

The model and all files associated with its calibration are available by clicking here.

The Model

The model being used is the simple SIR model first presented in my blog post Limits to Growth. The model is shown again below. There are two parameters: infection rate and recovery rate. Technically, the initial value for the Susceptible stock is also a parameter. However, since this is a conserved system, we can make an excellent guess as to its value and do not need to calibrate it.

The Data Set

We will calibrate this model to two data sets. The first is the number of weekly deaths caused by the Hong Kong flu in New York City over the winter of 1968-1969 (below).

The second is the number of weekly deaths per thousand people in the UK due to the Spanish flu (H1N1) in the winter of 1918-1919 (shown later).

In both cases, I am using the number of deaths as a proxy for the number of people infected, which we do not know. This is reasonable because the number of deaths is directly proportional to the number of infected individuals. If we knew the constant of proportionality, we could multiply the deaths by this constant to get the number of people infected.

Read more…

The Shifting the Burden Systems Archetype shows how attacking symptoms, rather than identifying and fixing fundamental problems, can lead to a further dependence on symptomatic solutions.  This Systems Archetype was formally identified in Appendix 2 of The Fifth Discipline by Peter Senge (1990).  The Causal Loop Diagram (CLD) is shown below.

When a problem symptom appears, two options present themselves:  1) apply a short-term fix to the symptom, or 2) identify and apply a longer-term fix to the fundamental issue.  The second option is less attractive because it involves a greater time delay and probably additional cost before the problem symptom is relieved.  However, applying a short-term fix, as a result of relieving the problem symptoms sooner, reduces the desire to identify and apply a more permanent fix.  Often the short-term fix also induces a secondary unintended side-effect that further undermines any efforts to apply a long-term fix.  Note that the short-term fix only relieves the symptoms, it does not fix the problem.  Thus, the symptoms will eventually re-appear and have to be addressed again.

Classic examples of shifting the burden include:

• Making up lost time for homework by not sleeping (and then controlling lack of sleep with stimulants)
• Borrowing money to cover uncontrolled spending
• Feeling better through the use of drugs (dependency is the unintended side-effect)
• Taking pain relievers to address chronic pain rather than visiting your doctor to try to address the underlying problem
• Improving current sales by focusing on selling more product to existing customers rather than expanding the customer base
• Improving current sales by cannibalizing future sales through deep discounts
• Firefighting to solve business problems, e.g., slapping a low-quality – and untested – fix onto a product and shipping it out the door to placate a customer
• Repeatedly fixing new problems yourself rather than properly training your staff to fix the problems – this is a special form known as “shifting the burden to the intervener” where you are the intervener who is inadvertently eroding the capabilities and confidence of your staff (the unintended side-effect)
• Outsourcing core business competencies rather than building internal capacity (also shifting the burden to the intervener, in this case, to the outsource provider)
• Implementing government programs that increase the recipient’s dependency on the government, e.g., welfare programs that do not attempt to simultaneously address low unemployment or low wages (also shifting the burden to the intervener, in this case, to the government)

Read more…

Editor’s Note: This is a guest post from isee’s training and consulting partner, Corey Peck of Lexidyne LLC.

The mid-term elections are now a month behind us and the political airwaves are still abuzz with commentary about the results.  Exit polls showed that unemployment was at the top of most voters’ list of issues, and that concerns about the federal government’s financial condition (record deficits and debt levels) were a hot topic as well.  Voters appeared to be asking “How can the federal government spend so much money and have so little positive impact on the nation’s economy?” 

The responses by politicians to such an important question are all over the map.  Democrats are claiming that economic conditions would have been much worse if not for massive federal bailouts and stimulus spending.  Republicans are touting the situation as a death knoll for the Obama platform in an effort to position themselves for 2012.  And the Tea Party movement has emerged to push for a roll-back of what they see as an intrusive and ineffective “Big Government”.

But, this political posturing reminds me that one of the true strengths of Systems Thinking is to force people to think very clearly and very operationally about the structure/behavior link embedded in such cases.  A little over a year ago, we sat down with Dr. Mark Paich, who used some very simple stock/flow language and some well-established principles of macroeconomics to lay out some relevant dynamics about the economic crisis and its aftermath:

• Why the collapse of the housing market made consumers re-evaluate their net asset position and hence started saving more of their incomes to pay off high interest credit card debt.
• How such actions on the part of consumers, in aggregate, kicked off a vicious cycle of decreased spending and contracting national output.
• Why government stimulus spending could close some, but not all, of the gap left by suddenly thrifty consumers, and that the recovery was likely to be a long, slow one.

We certainly don’t know how the future will play out, but the data suggest that consumers are indeed cutting back spending, and paying off debt.  (The Bureau of Economic Analysis has terrific historical data on household balance sheets and income.)  The unemployment numbers remain stubbornly high (around 9.5%), and although the recession is technically over, few economists are predicting rapid post-crisis economic expansion.

For a bit of clarity amidst all the rhetoric, you may want to check out Mark’s video offering.  His model and associated explanation do not provide a “magic bullet” of a solution, but they do provide some substance (and perhaps insight) to this vexing situation.  Now if only the politicians could follow suit!

To read a previous blog post about Modeling the Economic Crisis or view a 5-minute video trailer, click here.

Editor’s note:  This post is part two of a two part series on mental models.  You can read the first post by clicking here.

In part one of this series I stated “A mental model is a model that is constructed and simulated within a conscious mind.”  A key part of this definition is that mental models are not static; they can be played forward or backward in your mind like a video player playing a movie.  But even better than a video player, a mental model can be simulated to various outcomes, many times over, by changing the assumptions.

Mental Simulation

Remember the example from part one of the child reaching for the hot stove?  One possible outcome we can simulate is that the child does not get burned.  We can simulate this outcome by altering our assumptions. We could include a parent in the room who rescues the child in the nick of time.  Or, we could simulate the child slipping just before reaching the stovetop because the hardwood floor appears slippery.  This kind of mental simulation allows us to evaluate what may happen, given different conditions, and inform our decision making.  We don’t have to make any decisions while looking at the picture, but imagine what actions you might take if the scene above was actually unfolding in front of you.

It seems effortless to mentally simulate these types of mental models.  Most of the time we are not even aware that we are doing it.  But other times, it becomes very obvious that our brain is working rather hard.  For example, looking at the chess board below, can you determine if the configuration is a checkmate?

It is indeed.  But I’ll bet it took noticeably more effort for you to mentally simulate the chess game than it did with the child near the stove scenarios.  Think about the mental effort that the players make trying to simulate the positions on the board just a few moves ahead in the game.

The paper “The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information” by G.A. Miller (1956) established that people can generally hold seven objects (numbers, letters, words, etc.) simultaneously within their working memory.  Think of “working memory” as you would think of memory in a computer.  It’s like the amount of RAM we have available to perform computations within our mind.  And it’s not very much.  This means if people want to do any really complex information processing, they’ll need some help.  Over the last 50 years or so, the help has come from computers.  (In fact, IBM designed a computer specifically for playing chess, dubbed ‘Deep Blue’).

Digital computers have catapulted humankind’s ability to design, test, and build new technology to unbelievable levels in a relatively short period of time.  Space exploration, global telecommunication, and modern health care technology would not have been possible without the aid of computers.  We are able to perform the computation required to simulate complex systems using a computer instead of our minds.  Running simulations with a computer is faster and more reliable.

What makes a model useful?

Models that we can simulate using computers come in many forms.  For example, a model could be a financial model in a spreadsheet, an engineering design rendered with a CAD program, or a population dynamics model created with STELLA.  But what makes any of these models useful?  Is it the model’s results?  Its predictions?  I think the ability to explain the results is what makes a model truly useful.

Models are tools that can contribute to our understanding and decision making processes.  To make decisions, a person needs to have some understanding of the system the model represents.  A business finance model, for example, can be a useful tool if you understand how the business works.

Consider a model that does not provide any explanatory content, only results.  This type of model is often referred to as a black box.  It gives you all the answers, but you have no idea how it works.  People rarely trust these types of models and they are often not very useful for generating understanding.

The most useful models are structured so that the model itself will provide an explanatory framework that enables someone to ask useful questions of it.  Those questions may be answered by experimenting with the model (simulating) which, in turn, can help deepen a person’s understanding of the system.

This is an important feedback loop in a person’s learning process.  This feedback loop can be accelerated if the model provides explanations and can be simulated with a computer.

Transforming your mental models into visual models that are easier to understand and experiment with, will deepen your understanding, and help you communicate your models more effectively.

Read more…

Connecting at the welcome reception

Earlier this month, we had the pleasure of hosting the 2010 isee User Conference in Providence, Rhode Island. During this amazing gathering of isee customers, partners, friends, and iThink/STELLA enthusiasts, we learned about the important work that is being done applying Systems Thinking to solve real-world problems, shared ideas, and made connections with one another.

For two and a half days, I saw participants immersed in keynote presentations, breakout sessions, and hands-on workshops.  As important, however, were the less structured round table discussions, poster presentations, and social activities.  Everywhere I looked, folks were engaged in conversation and connecting with one another.  Even better, I knew that many of those connections would continue to be fostered and developed well after the conference was over.

Presentations and models

Conference presentations and models are now available on the isee systems web site.  Please download and share these materials with your colleagues and friends. You’ll get a glimpse into the wide range of fields where Systems Thinking is being used to better understand the interconnections of dynamic systems including business, healthcare, education, energy, and the environment.  You can also download and listen to audio recordings of the keynote presentations:

• Business Tsunami: Surviving Disruptive Change in a Networked World
  by Henk Akkermans
• Education for an Interdependent World: Developing Systems Citizens
  by Peter Senge
• Learning and Teaching System Dynamics Modeling: A 20 Year Journey
  by Diana Fisher
• Generating Understanding of Social, Economic and Climate Dynamics in Interaction
  by Matthias Ruth
• The Youth Violence Systems Project
  by Steve Peterson and Paul Bothwell

A Conference Highlight

Steve Peterson describes the modeling process

One of the highlights of the conference for me was listening to the story that Steve Peterson and Paul Bothwell told about using Systems Thinking and dynamic modeling to help communities in high-violence Boston neighborhoods.

In their work with the Youth Violence Systems Project, there were two objectives:

• Improve understanding of community-based violence in Boston
• Help communities strategize and achieve sustained reductions in violence

What made this project different from other attempts to research and solve the youth violence problem in Boston was that it engaged “the community” in the development of the model.  From the get go, they included youth in the modeling process.  Gang members, in particular, turned out to be an important missing link to understanding violence and the dynamic system behavior.  Both Steve and Paul described some of the harsher realities of working with young people whose family members and friends were victims of violence.  The modeling process actually helped community members to articulate the “slippery slope dynamics” that move youth through the different stocks to gang involvement.  If you have a chance, I highly recommend listening to the audio recording!

Staying Connected

Participants engaged in round table discussions

Having time to interact with other participants was an important part of the conference experience.  It was wonderful to see the excitement and energy that is created when Systems Thinkers have an opportunity to connect with one another.  The cross fertilization that occurs so naturally between field experts, modelers, and educators was inspiring.

Please stay connected and let us know if there are other ways in which we can foster our growing community of STELLA and iThink modelers!