Sandbox SD Models
Catalyzing the Widespread Understanding of Dynamics
Ninad Jagdish" & Andreas Grofler!
‘Radboud University Nijmegen
P.O. box 9108, 6500 HK Nijmegen, The Netherlands
*corresponding author: ninad.jag@ gmail.com, + 31644315682
Abstract
If the dynamically complex systems we live in today are to be managed successfully,
widespread understanding of their dynamics seems essential. In this paper, we present a
framework of desired characteristics for any medium targeting the creation of such
understanding. The framework is used to structure the concept of “Sandbox SD
Models” as a medium for catalyzing the creation of widespread understanding of
dynamics. Sandbox SD models are stand-alone system dynamics models wrapped in
intuitive interfaces without compromising on the critical elements of SD (such as, model
endogeneity, stock and flow representations and the indication of causal linkages). They
are designed with the aim of reducing the effort required to understand system
dynamics and increasing the intuitive interest of users towards doing so. Sandbox
Models are positioned as a stepping stone towards the more extensive use of
conventional stock and flow models. A prototype sandbox based on the Urban
Dynamics model has been developed as an app for touch-screen devices and its key
features are described.
Keywords: microworlds, simulation games, sandbox models, visualization, widespread
understanding of dynamics, intuitive interest
1. Introduction
In today’s globally interconnected world, complex large scale systems are
commonplace. Misperceptions of the dynamics within such systems are considered as a
reason why people fail to manage them well. For successful management of complex
systems, widespread understanding of their dynamics is desirable and needed. The field
of system dynamics (SD) currently provides tools, methods and the conceptual language
that help tackle such dynamically complex problems.
This paper presents a set of desired characteristics of a medium for communicating
system dynamics models. The end goal of this medium is to help catalyze the
widespread understanding of dynamics. The resulting framework of characteristics is
used as the basis to structure the concept Sandbox SD Models.
Sandbox SD models are stand-alone system dynamics models wrapped in intuitive
interfaces without compromising on the critical elements of SD (such as, model
endogeneity, stock and flow representations and the indication of causal linkages). They
are designed with the aim of reducing the effort required to understand system dynamics
and increasing the level of intuitive interest of users towards doing so. The concept is
positioned as a stepping stone towards the more extensive use and understanding of
conventional stock and flow models.
A prototype of a sandbox SD model based on Urban Dynamics (Forrester, 1969) has
been developed in the form of an application for touch screen computers. Key features
of this prototype are described.
2. Review of Literature
Sandbox models are aimed at making system dynamics more accessible to people.
Considerable work has been done towards this goal, especially through the use of
microworlds. A good example is the C-ROADS (and C-Leam) initiative which makes
climate models more user-friendly (Sterman et al., 2012). Literature on system
dynamics microworlds include descriptions of specific microworlds, evaluations of the
performance and learning effect of microworlds, and discussions on microworld design,
usage and utility (Rouwette et al., 2004; Davidsen, 2000).
Morgan (2000) describes various cultural and ethnic factors that need to be taken into
consideration in the design of microworlds. Such consideration of cultural differences in
design is an important component of making microworlds more intuitive. Sandbox
models are associated with an emphasis on improving interface design. Howie et al.
(2000) demonstrate that changes in interface design can play a significant role in
reducing the misperceptions of feedback in users. Jackson et al. (1994) describe the
importance of learner centred design and the use of learning scaffolding to help the user
progress through the learning curve.
The role of pictorial representation of system dynamics models in making them more
accessible has been discussed by Camara et al. (1994). Though their discussion relates
more to an agent-based representation of system dynamics models, the comments on the
possible characteristics and behaviours of images are still relevant. Kim (1989) used
images to represent the processes in a microworld on insurance claims processing.
Claims were represented in the form of envelopes flowing in and out of an
accumulation of outstanding claims. Sterman (2000) notes the importance of matching
the nature of visuals used and the technical ability of the recipients of the model. A lack
of such a match could result in the recipients perceiving the visuals to be either too
complex or too simplistic. Lane (2008) describes the various diagramming conventions
that have become common in the SD field and how they emerged. It is interesting to
note that several of the diagramming conventions that stand as the status-quo today
were not such obvious choices in the past. Black (2013) describes various aspects of
system dynamics visuals that help them serve as boundary objects in participatory
modelling workshops.
Maier & Grofler (2000) create a categorization framework for SD based microworlds.
Warren and Langley (1999) discuss three lines of development that are needed to
exploit the potential of system dynamics in management, namely, linking system
dynamics with established concepts in management, making system dynamics more
accessible to managers, and helping managers through the learning curve by using
simulation tools. Alessi (2000) discusses various characteristics of microworlds and
goes on to describe a way to combine SD modelling software with authoring tools to
create leaming environments. Andersen et al. (1990) note the various issues that
developers of microworlds (gaming interfaces) must contend with. These include the
assumptions regarding the users’ psychology, defining the game’s purpose and
decisions regarding gaming techniques. Kopainsky & Sawicka (2011) measured mental
loads of participants using microworld supported descriptions of a reindeer pasture
management task against those of a control group. The results indicate that microworld
supported descriptions reduce cognitive load and improve performance of the
participants.
Rouwette et al. (2003) reviewed over 200 papers on SD based microworlds and
categorised studies on performance based on model characteristics, simulator
characteristics and player characteristics. It is interesting to note that results on the
relation between these characteristics of microworlds and their performance are often
ambiguous. Certain studies indicate positive effects on performance for a characteristic
while others show mixed or no effects. This may be because empirically evaluating the
performance of microworlds relative to other means of communication is,
methodologically, extremely hard (GroRler, 2001; Davidsen, 2000; Warren & Langley,
1999). The existence of numerous control variables make it difficult to arrive at a
generalised claim about the performance of microworlds (GroRler, 2001).
Outside of efforts reported in academic literature, considerable progress has been made
in making system dynamics more accessible. Documenting the numerous contributions
in this regard is beyond the scope of this paper and thus only a few key examples are
mentioned. The Creative Learning Exchange continues to produce accessible content
and simulations to help students leam about system dynamics. Forio Corporation
provides a platform to build system dynamics based microworlds, create intuitive visual
interfaces around them and access them over the intemet. Strategy Dynamics Ltd is also
engaged in the creation of microworlds that help make understanding dynamics easier.
The electronic book, Beyond Connecting the Dots creates a more visually intuitive and
interactive format for teaching the concepts of system dynamics.
The documented insights and experiences from these efforts, performance evaluation
studies and discussions provide a foundation for the development of sandbox SD
models.
3. A Framework of Desired Characteristics
The framework of desired characteristics for the medium exists at the intersection
between the factors that influence the understanding of dynamics, the factors that
influence the scale of that understanding (i.e. how widespread it is) and design
characteristics of a communication medium (refer Figure 3.1). The methodology used to
derive it is best described as a process of causal factor identification. The method is
similar in nature to abductive inference. In this process, one starts with the end goal and
works backwards to identify the hierarchy of causal factors that influence this goal. We
thus explored the influencing factors and filtered them based on whether they are likely
to be addressable as design characteristics of the communication medium or not. The
final list of factors that is thus obtained forms the framework for a medium that may
help catalyze widespread understanding of dynamics.
Figure 3.1: C ontextualizing the Framework of Desired Characteristics
Framework of
Desired
Characteristics
Figure 3.2 presents this framework of desired characteristics in the form of a causal-
factor map (with the desired characteristics encircled). Existing knowledge from various
fields (such as cognitive science and psychology) were used to identify the desired
characteristics. For example, the need for reducing cognitive load draws upon the
distinction between short term memory (STM) and long term memory (LTM) (Hebb,
1949) and the concept of working memory capacity (Baddeley, 1992; Baddeley, 2003).
Another example is how the idea that leaning involves the transfer of information from
the STM to LTM through the development of schemas was included in the framework.
A schema is a way of categorizing and grouping information so as to make it relevant in
the context of existing knowledge (Swezller, 1994). In other words, the working
memory capacity is employed for utilizing such information and skills when they are
first leamed. Through repetition, a schema develops and the process becomes more
automated to the point where the content (or skill) is considered to have been learned
(Swezller, 1994). Thus the provision of learning scaffolding to aid the development of
schemas and make the content easier to understand is recognized as being essential.
Figure 3.2: The Framework of Desirable Characteristics of the Medium
Widespread
Understanding of
Dynamics
Level of Understanding
of Dynamics
b+
Ratio of Effort
Exerted to Needed +
h ~~
Effort Needed
~~
44
Effort for
understanding
dynamics
Using SD
Conventions
Nurturing
an
Endogenous
Perspective
Learning
through
Experiments
Intuitive
Interest in
the
Medium
a
4 Intuitive Motivation
+ rl
Effort Exerted <— Motivation +
~
Rational Motivation
Effort for processing
information
Reducing
Working
Memory
Load
Learning
Scaffoldings
Appropriate
Visualization
4. The Concept of Sandbox SD Models
Concisely defined, a sandbox SD model is a system dynamics based microworld that
exhibits all the desired characteristics in the framework (refer Figure 3.2). In order to
better describe the concept, for each of the desired characteristics in the framework,
corresponding supportive design elements were identified. These design elements and
the associated desired characteristics they support are listed in Table 4.1.
Assigning a name to this collection of desired characteristics and design elements
makes it easier to perceive and use them as a concept. The name ‘Sandbox SD Models’
has been chosen to reflect the various characteristics exhibited by this medium.
Sandboxes are enclosures filled with sand in which children can play. Found in multiple
cultures across the world, they provide a safe and non-intimidating environment in
which children can to lear about their physical environment by experimentation. The
term “sandbox” in the name symbolizes, simplicity, intuitiveness, learning through
experimentation, and ease of use. The use of the term “model” is used to indicate that
the medium is a computer model. And finally, “SD” points to the fact that the essential
philosophy and visual language used in system dynamics are retained so as to serve as a
stepping stone to conventional stock and flow models.
Table 4.1: Design Elements of Sandbox Models
Desired Characteristic Supporting Sandbox Model Design Element
1 | Intuitively interesting design 1) Use of contemporary interface designs
2) Built for computer form factors that are considered
intuitively interesting
2 | A focus on reducing working 3) Chunking of information
memory load
4) Provides relevant information only when needed
and on demand
3 | Provide learning scaffoldings 5) Use of spiral learning approaches where existing
understanding is used to contextualise and assimilate
new content
Desired Characteristic
Supporting Sandbox Model Design Element
4 | Appropriate visualization
information
6) Balance between the amount of visualization with
the need for reducing cognitive load
7) Use of visuals that are relevant and engaging for
the target user groups
5 | Allow learning by experimentation
8) Use of quantitative SD models allowing for
appropriate changes to its structure and parameters
6 | Nurture an endogenous perspective
9) User inputs at the macro level (as opposed to
specific decisions for each time period)
10) Provision of a visual overview of the system and
its interconnections at an appropriate level of
aggregation
11) Focus on capturing feedback complexity (as
opposed to categorical complexity)
x
Use established SD conventions
12) Retains the visual essence of stock and flow
diagrams used in system dynamics
co
Scalability
13) Built for platforms that support scaling and wide
distribution
5. A Prototype of a Sandbox SD Model
In order to demonstrate the concept of sandbox SD models, a couple of prototypes
based on existing system dynamics models were developed in line with aspects listed in
the preceding table. A prototype based on the Urban Dynamics model (Forrester, 1969)
is described here. Urban Dynamics was selected as it is a large, well-known model
about a topic of universal relevance — the growth and evolution of cities. Figure 5.1
depicts the main stocks and flows in the urban dynamics model. A brief overview of the
Urban Dynamics model is provided here to provide context for the reader. For a more
detailed explanation of the model, the reader is directed to Forrester (1969).
The urban dynamics model divides the city system into three ‘sectors’ — the enterprise
sector, the population (or workforce) sector and the housing sector. The enterprise
sector comprises three kinds of enterprises — new enterprises, mature business and
declining industry. The workforce sector consists of three kinds of workers —
managerial professionals, labor and underemployed workers. The housing sector has
three kinds of houses corresponding to the three worker categories — premium housing
(for managers), worker housing (for labor), and low cost housing (for the
underemployed).
New enterprises are constructed and they decline with time (influenced by the state of
the city) to become mature businesses (refer Figure 5.1). Mature businesses age to
become declining industry and the latter are eventually demolished. Similarly, premium
housing declines to become worker housing, which declines into low-cost housing
which is eventually demolished. Premium housing and worker housing is actively
constructed. However, the model assumes that low-cost housing is only constructed
when a low cost housing program is active.
Each of the flows in the model is influenced by multipliers that are estimated based on
variables from various sectors of the model. A key multiplier in the enterprise sector is
called the ‘enterprise multiplier’. In the workforce sector, ‘arrival multipliers’ and
‘mobility multipliers’ influence the flows of the different workers in and out of the city
and between the three stocks. Housing multipliers influence the construction and
obsolescence of the three types of housing. These multipliers are defined through the
extensive use of table functions and in many instances chains of multipliers are built
into the structure (i.e. a multiplier, which has another multiplier as input, which in turn
has a third multiplier as input). A discussion of these multipliers is out of scope and the
reader is directed to the original book for more details.
Figure 5.1;_Main Stocks and Flows of the Urban Dynamics Model
New Enterprise Mature Business Dectining Industry
fecceteertee: L_] New Enterprise :
Mature Business i
ture Declining Industry
Construction
Decline Demolition
Worker wal Construction
Low Cost Housing Program
Premium Housing Worker flousing Underemployed ousing
| ass iY
| 22]
Premim Housg sesereh eae Worker Housing ‘Slum Housing Demolition
Obsolescence
Manager Birth Rate Labor Birth Rate
UnderEmployed
10
The Urban Dynamics Sandbox is developed as an application that runs on touch-screen
tablets and phones. Simple visuals are used in it to depict stocks and flows. At the core
of the sandbox is the fully replicated code of the original Urban Dynamics model. In
order to achieve this, the Dynamo equations from the Urban Dynamics book were
translated and transferred into a computer language that could be compiled into an app
for touch screen computers.
Figure 5.2 shows how the main stocks, flows and multipliers are visually represented in
the sandbox. A graph panel maps out key stocks and certain variables of the system so
that users have a handle on how the system evolves over time.
A key feature that contributes towards reducing working memory load is the use of
zoom to control the amount of structure visible to the user. The benefit of choosing to
design the sandbox model for touch screen devices is that zooming in and out of content
can be done with an action that is very intuitive — the screen pinch. This ability to easily
control the zoom level has been leveraged to give users a convenient way to take control
of the amount of information they want to see.
When the user is at a low zoom level (i.e. zoomed out) they see a simplified overview of
the system (refer Figure 5.3). As they zoom into the model, more structure and details
emerge. Additional variables and linkages appear and causal links morph to reveal a
more refined structure.
Another feature of the sandbox is the built-in on tap information system. This feature
helps provide users information when relevant and on-demand. The on-tap information
system is activated when a user taps on any of the images that represent a system
element (stock, flow, or variable). Upon being tapped, an information panel appears at
the bottom of the screen covering the graph panel. Figure 5.4 shows two instances of the
on-tap information panel.
11
‘e 5.2: Overview of the Sandbox Model Interface
as ea
manager
12
Figure 5.3: Zoom Level Controlling Visible Information
Greve) Cor)
Gime: 0yrs_)
departure
=" 14,000
perception
time O
on
13
Figure 5.4: On-tap Information System
(Time: 250 yrs J
7,784
Vv u
Time: 250 yrs
perceived
M action
7 “oa
—
esired A
a/\) 77
Tax Ratio Enterprise Multiplier
at (butisnt ) This is a pro-new enterprise multiplier. The higher it’s value, the higher
the desire for new enterprise construction and the lower the values of
y
and businesses in the city ( thousand 8). This latter
Indicated T roughly tiplier so as
divided or
is taken to be 50 S/yr/thousand ).
This multiplier is influenced by the availability of jobs for labor and
UNITS: Unitless managers, the number of labor and managers in the city, the land
fraction occupied and the tax ratio. UNITS: Unitless
A core part of providing learning scaffolding is the use of spiral approaches to learning.
This involves the introduction of new information in context to the information a user
already has so that it can be more easily assimilated. When a user accesses the sandbox
on their device for the first time, they are guided through an introductory tutorial. This
tutorial serves as the main learning scaffolding in the sandbox. The tutorial is designed
to give the user an essential overview of the model structure, its behavior and interface
features. The entire sandbox is not described in complete detail, but rather the user is
provided foundational information based on which they can explore the remainder of
the sandbox and its features. The tutorial is designed to be interactive in nature with the
user having to simulate the system multiple times during its course.
While describing the entire tutorial is out of scope, Figure 5.5. shows four screenshots
from the tutorial as an illustration of the tutorial content.
14
Fi
re 5.5: Select Screenshots of the Tutorial
The sandbox is a simplified, visual
interface to the Urban Dynamics
model by J.W. Forrester.
Let's take a look around!
FY FF Fa
the business sector,
h A o
the people,
.-and their homes
There are three kinds of business units
new enterprises
mature business
declining Industry
Let's simulate the system for 250 years
le
>
o
15
An important aspect of sandbox models — the one that distinguishes them from
animations or still images — is the ability for users to change things in the system and
observe how the simulation is affected. In the Urban Dynamics Sandbox, users are
given access to change the initial values of all the physical stocks in the system. Four
influential policy structures are also built in to the model. These are (a) low cost
housing construction (b) low cost housing demolition (c) an underemployed training
program and (d) declining industry demolition.
These policies are visually integrated into the model structure in the form of on screen
switches that can be toggled even while the system is being simulated (refer figure 5.6).
As the user simulates the system and applies various policy combinations, the graph
panel captures the new behaviour of the system while still displaying the baseline plots.
This allows for a convenient visual reference to how the changes in the system are
influencing its behaviour.
The images used in the sandbox are constructed so as to retain the visual conventions
that are commonly employed in the field of system dynamics. For example, the images
for stocks are contained within rectangular boxes. The flows are represented by thick
arrows while the causal links are represented by distinctly thin arrows. The images for
auxiliary variables are contained within circular outlines.
In order to make it easier for a user to perceive the changes in the system, the size of the
images is linked to their magnitude. When the system is simulated, as the magnitude of
any element (flow, stock, variable) changes, the size of the corresponding image adjusts
accordingly. This allows a user to visually trace the changes as they ripple through the
system, observe how the flows influence the stocks and also make direct visual
comparisons of relative magnitude.
16
Enterprises
Mature
Business
‘rogram
=) @e J
o—@
Under
Employed
Premium
Housing Low cost nous
21000
‘i Key Ratiog] FOO
300000
Low Cost A aS
Housing i =
Z| poe
= a
= 250
oo yeare
aa) =) BS
—- derition
/ LY -_
tnng \\
f 1,200
} \ demalition
pir
perceived
‘mebiity
ZL
= 250
years
17
6. Conclusion
In this paper we presented the concept of Sandbox SD Models—a medium that may aid
the catalyzation of widespread understanding of dynamics. Sandbox models are
designed so as to exhibit characteristics that help overcome known barriers to the
understanding of dynamics. They are conceived and presented as a stepping stone
towards the more extensive use of conventional system dynamics models.
Future work on sandbox models in the short term would focus on extensive prototype
development and usability testing. The real test of the implicit hypothesis—that
sandbox models help understanding of dynamics—will only be obtained by observing
how such models are perceived in multiple cultural and professional contexts.
Apart from sandbox models, one can also identify other “offspring” of the framework of
desired characteristics (Figure 3.2). These offspring result when some of the
characteristics in the framework are selectively not considered. For example, if
“facilitating learning by experimentation” and “providing learning scaffoldings” are not
considered, we arrive at the concept of intuitive visualizations for system dynamics
models. Such visualizations would use similar design elements as described in the
prototype but they would be static images and not interactive software. Visualizations of
this kind may add value in introducing dynamic models in books and posters. If one
only excludes the characteristics of “facilitating learning by experimentation” we arrive
at the offspring of interactive SD visualizations. Interactive SD visualizations would be
similar to the described prototype in all respects except that it will not be a model that
can be simulated. It would thus not allow for parameter changes and policy testing. The
user would be able to unfold the model visually and gradually build up an
understanding of the interconnections and feedback complexity of the system. Such
visualizations would be especially relevant in the communication of large qualitative
SD models.
18
References
Alessi, S. (2000). Designing educational support in system-dynamics-based interactive
learning environments. Simulation & Gaming, 31(2), 178-196.
Andersen, D. F., Chung, I. J., Richardson, G. P., & Stewart, T. R. (1990). Issues in
designing interactive games based on system dynamics models. In Proceedings of the
1990 International System Dynamics Conference, 1, 31-45. Chestnut Hill.
Baddeley, A. (1992). Working memory. Science, 255(5044), 556-559.
Baddeley, A. (2003). Working memory: looking back and looking forward. Nature
reviews neuroscience, 4(10), 829-39.
Black, L. J. (2013). When visuals are boundary objects in system dynamics work. System
Dynamics Review, 29(2), 70-86.
Camara, A. S., Ferreira, F. C., Nobre, E., & Fialho, J. E. (1994). Pictorial modeling of
dynamic systems. System Dynamics Review, 10(4), 361-373.
Davidsen, P. I. (2000). Issues in the design and use of system-dynamics-based interactive
learning environments. Simulation & Gaming, 31(2), 170-177.
Forrester, J. W. (1969). Urban dynamics. Pegasus Communications.
Grofler, A. (2001). Musings about the effectiveness and evaluation of business
simulators. In Proceedings of the 19th International Conference of the System Dynamics
Society, p. 72.
Hebb, D. O. (1949) The Organization of Behavior. New Y ork, NY: Wiley.
Howie, E., Sy, S., Ford, L., & Vicente, K. J. (2000). Human-computer interface design
can reduce misperceptions of feedback. System Dynamics Review, 16(3), 151-171.
Jackson, S. L., Stratford, S. J., Krajcik, J., & Soloway, E. (1994). Making dynamic
modeling accessible to precollege science students. Interactive Learning
Environments, 4(3), 233-257.
Kim, D. (1989) Learning laboratories: Designing a reflective learning environment, in
Milling, P. and E. Zahn (eds.), Computer-Based Management of Complex Systems.
Berlin: Springer, 327-334.
Kopainsky, B., & Sawicka, A. (2011). Simulator-supported descriptions of complex
dynamic problems: experimental results on task performance and system understanding.
System Dynamics Review, 27(2), 142-172.
Lane, D. C. (2008). The emergence and use of diagramming in system dynamics: a
critical account. Systems Research and Behavioral Science, 25(1), 3-23.
19
Maier, F. H., & Grofler, A. (2000). What are we talking about?—A taxonomy of
computer simulations to support leaning. System Dynamics Review, 16(2), 135-148.
Morgan, K. (2000). Cross-cultural considerations for simulation-based learning
environments. Simulation & Gaming, 31(4), 491-508.
Rouwette, E. A., Grofler, A., & Vennix, J. A. (2004). Exploring influencing factors on
rationality: a literature review of dynamic decision-making studies in system
dynamics. Systems Research and Behavioral Science, 21(4), 351-370.
Sterman JD. (2000). Business Dynamics: Systems Thinking and Modeling for a Complex
World. Boston: Irwin/McGraw- Hill.
Sterman, J., Fiddaman, T., Franck, T., Jones, A., McCauley, S., Rice, P., Sawin, E. &
Siegel, L. (2012). Climate interactive: the C-ROADS climate policy model. System
Dynamics Review, 28(3), 295-305.
Swezller, J. (1994). Cognitive load theory, learning difficulty and instructional design.
Learning and Instruction, 4(4), 295-312.
Warren, K., & Langley, P. (1999). The effective communication of system dynamics to
improve insight and learning in management education. Journal of the Operational
Research Society, 50(4). 396-404.
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