Lessons in Mathematics Section 9: Appendix 

Author(s):
Diana M. Fisher 
Subject:
Math 

This book provides a set of tools that enables educators to teach mathematics using the framework of System Dynamics. Section 9 is a useful reference for all lessons in the book. Included are generic modeling structures, a summary of motion, distancevelocityacceleration graphs and examples of differential equations with their growth patterns. Available from iseesystems. 

More about the book at: http://www.iseesystems.com/store/college_university/MathBook.aspx

Lessons in Mathematics: A Dynamic Approach 

Author(s):
Diana M. Fisher 
Subject:
Math 

The abstractness of a traditional approach to mathematics causes many students to falter. This book focuses on making the abstractness more concrete with interesting and fun lessons. It uses STELLA software's iconbased, nonabstract language to structure problems in ways that students can easily visualize. Students use the software's simulation capabilities to explore solutions to the problems. Some sections can be used as building blocks to understand the behavior of complex systems, while others illustrate one or more characteristics of complex systems. Available from iseesystems. 

More about the book at: http://www.iseesystems.com/store/college_university/MathBook.aspx

Living Lands — Forest and Town Simulation 

Author(s):
Anne LaVigne, & Jen Andersen 
Subject:
CrossCurricular 

This lesson with multiuser simulation explores the management of a national forest and its surrounding towns. Student teams log in and make decisions for a local town or for the surrounding forest that has a large level of accumulated fuel. The decisions of individual teams impact all other teams. Damage from potentially catastrophic fires looms, and students must try to manage the situation to protect the area, both now and into the future. 


Model Mysteries: An Exploration of Vampires, Zombies, and Other Fantastic Scenarios to Make the World a Better Place 

Author(s):
Anne LaVigne, & Lees Stuntz 
Subject:
CrossCurricular 

This book contains six main chapters, each with a new mystery to solve. Each chapter has a number of similar stories to try, depending on your interest. The modeling activities are intended for students from ages 10 to 110. In other words, if you’re interested in thinking about how to solve mysteries and like the idea of creating computer models and applying them to realworld problems, this book is for you. You can use it independently as a student, work with a group of students, or if you’re a teacher, share it with interested students to complete a guided or independent study project.
In addition to the main chapters, Chapter 7 provides an extension to build additional capacity in modeling, and Chapter 8 includes next steps, additional resources, and information about modeling software. You can also reference the appendices for details about completing the chapter mysteries.



Modeling Dynamic Systems Section 10 

Author(s):
Diana Fisher 
Subject:
System Dynamics 

There are several characteristics of complex systems that can be discussed with students during these lessons. The fictitious city seems to face a dilemma; the tanning industry provides needed jobs in the present, but water pollution can cause serious detrimental effects over the long term. This is closely coupled with the idea that cause and effect in complex systems are often separated by time and space.
In the case of pollution, contamination can take decades to produce measurable effects. In the meantime, the range of impact can spread far from the initial source via transport in water, wind, etc. Finally, the lesson mentions that tanning has been outsourced from this country to developing countries; a classic case of "shifting the burden." Rather than allowing the true costs of tanning to be reflected in the prices of the finished goods, the industry itself escapes pressure to reform by sending the negative consequences to other, less regulated countries. 

PDF
Link to the simulation: http://www.iseesystems.com

Modeling Dynamic Systems Section 6 

Author(s):
Diana Fisher 
Subject:
System Dynamics 

In the classroom example provided in this section, the author lists many "potential systems problems" that are related to the issue of overpopulation. As an extension exercise, students can be asked to identify ways in which people have attempted to solve these related problems. Did the solutions address the underlying population issue in any way? Were they successful interventions? In complex systems, proposed solutions that do not recognize and address the underlying dynamics that need to be changed are lowleverage policies; they usually fail to achieve any significant change in the overall behavior of the system. Students can be asked to undertake a similar analysis in their own investigation of a news story. 

PDF
Link to the simulation: http://www.iseesystems.com

Modeling Dynamic Systems Section 7 

Author(s):
Diana Fisher 
Subject:
System Dynamics 

The dynamics of epidemics can be used to impart an intuitive understanding of what it means to say a policy has "high leverage." Students can be tasked with conducting policy analysis to determine the leverage points in preventing an infectious illness from becoming an epidemic. Along the way they will learn why wellintensioned but lowleverage policies in real life often fail to have the desired effects in complex systems.
For some illness/disease, symptoms appear long after initial infection. Sometimes people travel great distance while infected because they are unaware of the infection. Medical "detectives" faced with an epidemic must understand how the infection spreads and how quickly. Delays in the system make this more difficult. 

Link to the file: http://www.iseesystems.com

Modeling Dynamic Systems Section 8 

Author(s):
Diana Fisher 
Subject:
System Dynamics 

Policy analysis gives students an opportunity to learn firsthand that complex systems are rich in feedback. They will experience the frustration of implementing wellmeaning interventions, only to have them defeated by the feedback mechanisms of the system itself. They will learn why some policies have more leverage than others, and why those policies are often the most difficult to implement correctly in real life. 

PDF
Link to the simulation: http://www.iseesystems.com

Modeling Dynamic Systems Section 9 

Author(s):
Diana Fisher 
Subject:
System Dynamics 

Supply chain dynamics are useful for illustrating the complex system characteristic that cause and effect are often separated by both time and space. Supply chains are often global, with decisions taken today causing impacts into the future and across national boundaries. The lessons of this section can also be used in conjunction with the Oscillations curriculum, particularly the lesson on commodity cycles, to illustate that the cause of a problem is within the system. 

PDF
Link to the simulation: http://www.iseesystems.com

Modeling Your Future 

Author(s):
Bob Allnutt, J. Harvester, & J. Miller 
Subject:
CrossCurricular 

From CCSTADUS. A STELLA Model for use in the classroom; explores educationincome dynamics.
Complex Systems Connection: Short/Long Term Conflicts. Managing money, in personal finances or in running a business, often involves setting both shortterm and longterm goals. Sometimes goals are in conflict between these timeframes, such as spending now versus saving/investing for future financial wellbeing. This also applies to choosing to spend time on education early in life for the opportunity to earn a higher income later. This simulation helps students explore the longrange implications of choices they make now. 

Zipped (Models & PDF)
