INTRODUCING SYSTEM DYNAMICS INTO THE TRADITIONAL SECONDARY
CURRICULUM: THE CC-STADUS PROJECT'S SEARCH FOR LEVERAGE POINTS
Ron Zaraza, Wilson HS, 1151 SW Vermont, Portland OR 97219, USA
Diana Fisher, Franklin HS, 5405 SE Woodward, Portland OR USA
Teachers are among the most “conservative” professionals. While they may be extremely creative
in their classrooms, and tremendous risk-takers in the way they work with students, they remain
staunchly conservative and protective of their subject matter. Tradition has defined what the
appropriate content is in a Global Studies class, a Literature class, or an Algebra class. Any changes
in instruction that threaten a teacher’s ability to present the great bulk of material they feel they
must cover will be met with resistance. Every change in education is met by the question “How can I
add... when I’m already having a hard time covering the syllabus?”
Attempts to bring systems thinking and system dynamics into the K-12 classroom have faced the
same problem. Teachers are pressed for time and skeptical about changes that may appear to add
new topics to an already full curriculum. When such new ideas are outside their own professional
content expertise, they are nervous about their own mastery of the material as well. Traditionally,
educational innovations have emphasized positive change in outcomes: Students will learn
better/faster/more. Yet most educational innovations, even though less “foreign” than the
introduction of systems concepts, are only slowly and often incompletely implemented.
Better/faster/more simply isn’t enough to insure acceptance. Successful integration of systems
concepts into the curriculum will suffer a similar fate unless the unique capabilities of systems work
can be made obvious. While systems thinking and dynamics can help students learn content
better/faster/more, the truly impressive advantage of systems work is the way it allows students to
ask better and more important questions. That results in learning through “conversations”, through
thoughtful involvement of students. The opportunity to experience such learning is a powerful force
in convincing teachers to begin to use systems. However, the initial entry into the use of systems
remains a stumbling block.
During the four years the CC-STADUS (Cross-Curricular Systems Thinking and Dynamics Using
STELLA) Project has trained teachers in the development of models and curriculum for K-12
classroom use, the more than 160 participants have gained a wealth of experience in how system
dynamics can be introduced to students in both single discipline and cross-curricular environments.
It has become clear that single-subject use is the easiest way to introduce systems ideas to both
teachers and students. Further, it is clear that there are certain natural "entry points" into the
traditional courses.
Each subject includes topics that are natural systems topics. Those topics constitute leverage
points, topics that clearly show the potential of dynamic modeling. Introduction of dynamic models at
those points opens up both the discipline and system dynamics for student inquiry. The advantages of
dynamic models in addressing the topics are dramatic and obvious. Thus, those topics should be
emphasized in training of teachers as they begin to use system dynamics. The power of these basic
models presents a compelling argument for the introduction of systems into courses. Too often
complex and detailed models are presented to novices as an example of the power of dynamic
modeling to build knowledge. Those complex models are often intimidating and tend to obscure the
real power of dynamic modeling: even simple models can have a major impact on student learning.
These simple but powerful models provide the real leverage that can attract teachers to modeling.
Within the sciences, each field has distinct topics that can be used to introduce system dynamics.
Two approaches are being used by CC-STADUS teachers in physics. The first focuses on the basic
mathematical definitions of the concepts of motion. Physics has often been referred to as “the study
of rates”. The language used to describe flows in systems is identical to that used in defining basic
concepts of motion. The ideas of position, rate of change of position (velocity), and rate of change of
velocity (acceleration) can be easily developed through simple models. These models provide
exposure to two of the four basic model structures, linear and quadratic, that CC-STADUS training
focuses on.
Position Current Velocity
oO or
Acceleration
Velocity
These basic linear structures are among the first taught to teachers in the CC-STADUS training.
The linear change in position when velocity is constant and the linear change in velocity when
acceleration is constant are also among the most basic concepts of motion taught in physics. These
models illustrate the ideas in a very simple way, reinforcing the physics and math. Dealing with
position change for an accelerated object is conceptually more difficult. The fact that the distance is
no longer a linear function of time is not easily understood by students. The model shown on the next
page, however, illustrates the reality of the situation. The acceleration constantly changes the
velocity which, in turn, constantly changes the rate at which position changes, The model structure
makes obvious what the algebra does not. Dynamic models such as these provide a visual
reinforcement of the concepts normally introduced algebraically. The structures explain the
relationships of the variables. These models may then be expanded to deal with all the other basic
concepts of motion.
Acceleration
a i i Current Velocity
ie,
Position
Velocity
The alternative physics approach utilizes models illustrating the concepts of impulse, momentum,
and the conservation laws. Effectively, these models introduce physics through Newton's laws of
motion.. The emphasis is less on developing models that are analogues of mathematical relationships
and more on physical concepts. This allows an alternative approach to developing physics in
secondary schools, one usually restricted to college students with advanced mathematical training.
The two models shown below are examples of these basic models. Once again the starting model
structures are linear.
Momentum
Velocity
Mass
Grant participants have developed a broad physics curriculum around both types of models. The
graphical representation of concepts provides an alternative approach to developing an
understanding of basic physics. That, however, does not provide a compelling reason for using
models in physics. Teachers already have several ways of presenting these physics concepts. One
more way, even if very versatile, seems unnecessary. The use of models is only compelling if the
models give students and teachers capabilities the traditional methods do not. These simple models
do provide a good base for models that deal with real problems of interest to students. These
problems are not normally addressed because they cannot be solved using the traditional
mathematical tools at the students’ disposal. Non-constant accelerations (their car!), motion with air
resistance (sky diving), and non-constant mass problems (the flight of a rocket) are all problems that
students ask about. The ability to discuss these and similar problems provides the motivation or
leverage which convinces teachers to bring systems into physics.
=)
Accelerati
= 63
Characteristics
Velocity
Distance
Current Velocity
The simple addition of a graphical converter which makes acceleration dependent on current
velocity turns the basic quadratic model used to describe accelerated motion into one that can
describe the behavior of cars and other objects that have non-constant accelerations. Students can
use popular magazines such as Car and Driver or Road and Track as physics reference materials,
calculating acceleration graphs for various cars. They can even drag race cars against each other.
3
Air Resistance Adjustment
Velocity
Acceleration
Surface area
The same basic model can be modified to deal with air resistance. This is a problem that
frustrates many physics students. They grow weary of problems that always require them to ignore
friction, air resistance, and other factors that are part of real life. Only one secondary text, PSSC
Physics , deals with friction. The approach is confusing, and beyond the reach of most students.
This model allows students to explore the work in that text, as well as other problems. In particular,
the behavior of a sky diver as she falls freely, reaches terminal velocity, pulls her ‘chute and slows to
a new terminal velocity can be studied. More importantly, the differences that changing body
orientation (fetal position, spread-eagle, head down) can not only be talked about conceptually, but
numerically, an impossibility without modeling.
Velocity
Rocket Mass
Fuel use aa
Accel¢ration Altitude
Thrust @
Burn Rate Current Velocity
Force/Impulse/Momentum problems are dealt with extensively in physics. Yet the most interesting
can only be approached conceptually: the flight of a rocket. The algebraic equations taught at the
secondary level do not allow mass and velocity changes to be dealt with simultaneously. Again, the
quadratic modeling structure can be easily adapted, as seen above. This model can even be modified
to use actual thrust data for commercially available model rocket engines, allowing students to
compare experimental and theoretical performance. Once these mechanics/kinematics models have
been used, expansion to electricity, magnetism, and radioactive decay becomes obvious and simple.
Biology presents its own obvious starting points. Regardless of the course emphasis, almost all
secondary biology courses deal with population growth and ecology. Both are excellent leverage
points. Traditional study of these topics has been qualitative. Dynamic models provide a way to
include quantitative work as well. The study of the reproduction of micro-organisms allows the
introduction of the concept of exponential growth. Simple exponential growth models allow students
to explore a wealth of problems discussed in biology. As their experience grows, students or teachers
add complexity, placing different controlling factors in the model. They may also link models that
affect each other. This opens up the possibility of exploring ecosystems. Using simple models
focusing on a single organism and its food supply (an herbivore and the plants it eats) or a simple
predator-prey model (wolf-moose), students can explore the relationship by changing rates,
variables, and population sizes. Ultimately students begin to understand the concept of a biological
system from experimentation with models.
Yeast Population
@ = —¢) 3
Yeast Deaths
Death Rate
The simple population model shown above is a classic starting point for modeling in biology
classes. In this case, it was developed after students had done a long term experiment with yeast
growth. The model was built to reflect actual data. Of course, it is greatly simplified, allowing
unrestricted growth. The real learning begins as students attempt to explain why such growth
cannot happen, and what patterns should occur. The option of exploring these ideas numerically is
the “hook” that often catches teachers. The model below shows a simple modification to the model,
an adjustment in reproduction and deaths due to depletion of nutrients.
‘Yeast Population
re) 63
Reproduction Rate an ®)
Budding Yeast Deaths
Death Rate
Food Shortage
Food Shortage
Food Shortage Trigger
Food Supply
Food consumption
The model can be extended further to look at the effects of waste. This ability to “grow” a model
as student interests, abilities, and questions dictate further enhances the attractiveness of modeling.
Waste per yeast
Waste Products Food per yeast
Toxicity Food Ratio
Reproduction Rate
‘Yeast Deaths
Food Shortage
Food Shortage
Food Shortage Trigger
Food Supply
Food consumption
It is the quantitative nature of this work, as well as the opportunity to experiment, that provides
the motivation for biology teachers to begin using models. Discussion of exponential growth is
compelling when graphs and tables can be easily generated. The structure of an exponential growth
model provides insight to the process, facilitating understanding. The reality that there are limits to
growth can be easily seen working with models. Understanding why and how those limits apply can
be explored with models. They move discussions from the “hand-waving” to the real, because the
variables can be manipulated. As the models are expanded and linked, students can truly explore and
experiment with the interactions of an ecosystem, something simply not possible without dynamic
modeling. For many biology teachers, that capability alone provides sufficient motivation to begin
using systems in their classes.
Chemistry has presented more of a problem. The field seems ideally suited for dynamic models,
with the same emphasis on rates seen in physics. However, successful models have been few. While
some models have been attempted, most are either too complex for easy student use or too narrow in
their focus. For some models, particularly reaction rate models, accurate data is virtually
unobtainable. The only models that have seen substantial use have been heat flow models. While
thermodynamics is certainly an important part of chemistry, thermodynamics models are not strong
motivators, do not provide the leverage needed to broadly attract chemistry teachers. The true
leverage point in this discipline would almost certainly be accurate, easily understood reaction rate
and equilibrium models. Until such models become available, use in chemistry will remain limited.
The Social Sciences are an area where a large amount of successful work has been done using
dynamic models. Introductory work is often based on the same type of exponential
growth/population models used in Biology. Often focused on comparisons between industrial and
third-world nations, these basic models dramatically present information. Many teachers have
become interested in using models in their classes simply through exposure to these models. These
low-complexity models provide all the leverage needed to motivate use. These simple models provide
a basis for discussion that can evolve into very detailed and sophisticated concepts, even with no
further modeling. When the initial systems can be changed to include linked systems and the many
modifiers on systems, including impact of disease, wars, emigration and immigration, a depth of
understanding of the system can be developed that goes far beyond traditional classroom experience.
The possibility of such work, based on simple models, makes social science teachers eager to use
models.
Somalia Pop
3 = 63
‘Somalia Deaths
Somalia Births
‘Somalia Birth Rate Somalia Death Rate
The sequence of models shown here illustrates how even small additions to models can broaden
the scope of discussion in social science classes. The first model is the familiar population model also
used in biology. In this case, it was being used to explore the present and future population problems
of third-world nations. The basic model, run for 100 years, tells a dramatic story. To emphasize
this, two population models are combined and displayed on the same graph and tables, showing the
difference between population growth in an industrialized nation and a third-world nation. Student
responses to this model direct the next step. One option is the addition of two converters to the basic
population model. This allows changes in land availability to be explored, an even more dramatic
development.
Somalia Pop
Somalia Births C) Somalia Deaths
Somalia Birth Rate Somalia Death Rate
O
Land per person
‘Somalia Land Area
Similar modifications allow food availability to be explored as well. The result of all these models
is a wealth of information about the problems faced by third-world nations. It is a powerful starting
point for discussion. In some cases the discussion leads to further models. In others, the extensions
are explored without additional models.
Somalia Pop
63 +} = +63
C) Somalia Deaths
‘Somalia Births
Somalia Birth Rate Somalia Death Rate
O
Minimum average number of calories needed
Total Calories per Person Total Available Food
Somalia Fron Total Meat Calories per Person
QO
O
Total Meat Available
Total Grain Calories per person Total Grains Available
Like physics, much work in mathematics focuses on rates. Concepts from slope through the
second derivative can be easily described by the rates used in systems models. An entry point for
models in mathematics is the use of a motion detector in conjunction with dynamic models of motion.
The motion detector can be used to produce a graphical and a conceptual view of functions from
their rates of change. A model can be introduced to generate the same patterns. The structure of the
model gives clues to the pattern’s causes. The models then allow students to explore problems and
applications that involve the functions. This allows students to use a conceptual perspective, rather
than the traditional methods.
This process can be repeated wherever problems are presented in which the independent variable
is time. Thus, each new topic becomes a potential leverage point where models can be used to
address the topic conceptually before, or in parallel with more traditional treatments. The problems
can be modeled, expanded, and explained by the students, significantly enhancing their experiences
and demonstrating the relevance of mathematical study to other disciplines.
Perhaps the most unusual work done by the CC-STADUS project has been the work done in
literature by Tim Joy and a few others. The whole idea of using systems in literature seems odd to
some. However, the plot of a book is essentially an interplay among characters, in short, a system of
interactions. One of the things literature teachers want students to do is analyze and understand
those interactions and the motivations behind them. They want students to write about them, and
discuss them. The discussion part is the difficult piece. Usually only a few students are truly engaged.
Dynamic models can provide a structure for generating those discussions and involving more
students.
Savage Instincts 3.1 as
Level of Civility Level of Savagery
Regressing
"o
the island
Regress Fractioi
O
Norm Savagery Factor
Using very simple models, like the one shown above, Tim has pioneered work in which students
trace character development through changes in specific traits. Using the authoring level of a
STELLA model, students are presented with a succession of events and quotations from the book.
Students are asked to adjust the change in the level of the trait before the model resumes. This
adjustment is accompanied by written justification based on passages in the text. In the course of
running the complete model students generate a graph of the character’s behavior. These graphs,
like the one shown on the next page, are displayed in class. Students then are asked to explain or
justify their interpretations as displayed in their graphs. The result is an animated, sometimes
passionate discussion. The potential for that level of student involvement serves as a strong
motivator for Literature teachers. It provides enough leverage to involve teachers. Additionally, the
“Savage Instincts/Lord of the Flies” models introduce students to the use of systems at a level that is
accessible to virtually everyone. Discussion and further student modeling bring students more fully
into the understanding of dynamic systems.
@ 1: Level of Civ 2: Level of Say: 3:Norm
1 100.00.
2
3
1
2 50.00:
3
r y 9.00 12,00
Graph 3 Time(Chapters) 5:41PM 5/26/1997
The use of system dynamics in the K-12 environment, and particularly at the secondary level, is
growing at an impressive rate. Advocates compare it to an infection, with the exponential growth
only now in the toe of the curve. If the “infection” is to grow, if it is not to level off, modeling
advocates must emphasize the leverage points as they recruit other users.
References
Forrester, J. W. 1971. Principles of Systems. Portland, OR: Productivity Press.
Kauffman, D. L., Jr. 1980. Systems 1: An Introduction to Systems Thinking. Cambridge, Mass:
Pegasus Communications.
Meadows, D. H., D. L. Meadows, and J. Randers. 1992 Beyond the Limits. Cambridge, Mass:
Pegasus Communications.
Meadows, D. H. 1991. The Global Citizen. Cambridge, Mass: Pegasus Communications.
Richmond, B., and S. Peterson. 1993 STELLA II An Introduction to Systems Thinking. High
Performance Systems, 45 Lyme Road, Hanover, NH 03755, USA.
ee. . 1993. STELLA II Applications. High Performance Systems, 45 Lyme Road, Hanover, NH
03755, USA.
Richmond, B. 1994. Authoring Module. High Performance Systems, 45 Lyme Road, Hanover, NH
03755, USA.
Roberts, N., D. Anderson, R. Deal, M. Garet, and W. Shaffer. 1983. Introduction to Computer
Simulation: A System Dynamics Modeling Approach. Portland, OR: Productivity Press.
Senge, P. M. 1990. The Fifth Discipline. New York: Doubleday.
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