# Perspective on Complex Systems

### Bob MacKay, Clark College and Washington State University

This essay begins with a brief description of my background in teaching, followed by my view of the important building blocks required for student understanding of complex systems. The essay ends with a brief description of some teaching methods that, based on my experience, promote student learning and understanding of complex processes. The ideas presented here are biased towards the idea that computer modeling is a very effective tool for learning about complex systems. Other highly effective teaching methods are not discussed here.

I began my teaching career in 1982, teaching introductory college physics. Soon after my first year I attended a meeting in which Arthur Beiser from UC Santa Barbara presented his ideas for using microcomputers in physics to introduce students to nonlinear dynamics. His idea was that students with little or no calculus background could use computer simulations to explore the behavior of complex systems without being overwhelmed by mathematics. My colleague and I at Clark Community College began creating learning activities on the Apple IIe microcomputer to explore such topics as air resistance, viscous drag, charged particles in magnetic fields, and damped harmonic motion.

Inspired by my graduate work in climate change science (Atmospheric Physics) I began teaching introductory meteorology to students with very little mathematical background. Over the past 20+ years I have developed, used, and modified modeling activities to help students understand aspects of topics such as the carbon cycle, air pollution, and Earth's climate system. My interests expanded into the broader field of environmental systems after being requested by my dean to teach an environmental modeling course for Environmental Science majors. My work load typically includes a variety of physics courses and introductory meteorology at the community college, and a course in environmental modeling at Washington State University. While on sabbatical over the past six months my focus has been the development of learning modules for my environmental modeling course.

There are several fundamental ideas common to all systems. These include:

- The concept of equilibrium.
- Time delays.
- Stocks and flows, total atmospheric carbon and carbon emissions are respective examples.
- Positive and negative feedback processes.
- The idea of interconnectedness; the whole is something unique from the sum of the individual parts.

Although the above list is surely not exhaustive, it does provide a base to work from when trying to develop course content appropriate to learning about complex systems.

A crucial tool used for student understanding is some sort of graphical representation or visualization. It is easy to overlook the fact that, although most students have been exposed to graphs and graphical analysis in the past, many, including our best students, need a supportive review of key ideas related to graphical analysis. The diverse mathematical background of students in any course also offers unique challenges in that we want our students to be both intellectually stimulated and successful in a course with college level content.

For students with limited mathematical ability, online JAVA or Flash type computer simulation environments offer an easy way to actively engage students with activities aimed at understanding system dynamics from a black box perspective. Equations and background information about model structure may be added as introductory material to an assignment to make the model dynamics more transparent. These environments are good for guided inquiry based learning and can also be useful as introductory exercises for more advanced students. A clear advantage of these environments is their portability. As an example, the game at http://www.atmosedu.com/Geol390/physlets/GEBM/EBMGame.htm is designed to introduce introductory meteorology students to the basic concepts of atmospheric radiative transfer.

Spreadsheet programs like Microsoft Excel, Graphical modeling tools such as Vensim or Stella II , or more comprehensive mathematical packages like MatLab or Mathematica can all be used to help students begin to learn how to build their own models. An advantage of these environments is that the model structure is completely transparent. Existing models in any of these environments can be used in much the same way that the online JAVA or Flash models are used. Assignments requiring students to follow instructions to enter the code themselves can help students learn the basics of each environment to prepare them to either modify existing models or do their own projects. One disadvantage of these environments is that all require some course time devoted specifically to learning about the environment. Spreadsheet programs are fairly easy to learn and most students already have some familiarity with this environment. Graphical modeling tools and more advanced mathematical packages have correspondingly steeper learner curves.

The above strong bias towards a modeling approach for learning about complex systems is driven from the author's background and expertise, and is not intended to imply that this is the only appropriate teaching method for learning about a complex system. Role playing games, writing assignments, critical thinking questions, and group activities are several examples of methods that can also be used to help students learn about complex systems. My experience compels me to use a variety of teaching approaches in my courses in an attempt to make the course more fun and to accommodate different learning styles. One motivation for me to participate in this workshop is to possibly gain insights into alternative methods for successfully teaching complex systems.