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Running Head: COMPLEX SYSTEMS
Fish swim and rocks sit: Understanding structures, behaviors, and functions in a complex system
Cindy E. Hmelo-Silver
Merav Green Pfeffer
Betina A. Malhotra
Correspondence to:
Cindy E. Hmelo-Silver
Rutgers University
10 Seminary Place
New Brunswick, NJ 08901-1183
Email: [email protected]
Acknowledgments:
This research was funded by a Rutgers University Faculty Research Council Grant and an
NSF Early Career grant REC-0133533 to Cindy E. Hmelo-Silver.
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Abstract
Complex systems are pervasive in the world around us. Making sense of a complex system should
require that a person construct a network of concepts and principles about some domain that
represents key (often dynamic) phenomena and their interrelationships. This raises the question of
how expert understanding of complex systems differs from novice understanding. In this study we
examined individuals’ representations of an aquatic system from the perspective of structural
(elements of a system), behavioral (mechanisms), and functional aspects of a system. StructureBehavior-Function (SBF) theory was used as a framework for analysis. The study included
participants from middle school children to preservice teachers to aquarium experts. Individual
interviews were conducted to elicit participants’ mental models of aquaria. Their verbal responses
and pictorial representations were analyzed using an SBF-based coding scheme. The results
indicated that representations ranged from focusing on structures with minimal understanding of
behaviors and functions to representations that included behaviors and functions. Novices’
representations focused on perceptually available, static components of the system, whereas experts
integrated structural, functional, and behavioral elements. This study suggests that the SBF
framework can be one useful formalism for understanding complex systems.
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Fish swim and rocks sit: Understanding structures, behaviors, and functions in a complex system
Complex systems are ubiquitous in nature and the designed world. They can be seen in
phenomena that range from human respiration to fish tanks to home heating and air conditioning
systems. It is difficult to understand complex systems because it requires abstracting thinking that
may challenge current beliefs regarding phenomena. There are several alternative ways of making
sense of such systems, what Collins and Ferguson (1993) have termed “epistemic forms.” For
example, one might look at complex systems from the perspective of a system dynamics model,
aggregate behavior, or structure-behavior function (SBF) analysis.1 SBF seems to be a particularly
promising mode of analysis for this domain because it focuses on causal understandings of the
relationships among different aspects of the system. This is consistent with a great deal of research
on expertise that has demonstrated that experts organized their knowledge around deep principles of
a domain (Chi, 1981; Larkin, 1980; Norman, Trott, Brooks, & Smith, 1994; Wineburg, 1991). This
paper extends the research on expertise to complex systems by presenting a preliminary study that
examined how children, naïve adults, and experts represent their knowledge of an aquarium system.
We conclude with a discussion of using SBF to design instruction.
The characteristics of complex systems make them particularly difficult to understand. They
are comprised of multiple levels of organization that often depend on local interactions (Ferrari &
Chi, 1998; Wilensky & Resnick, 1999). The relationships across these levels are not intuitively
obvious. For example, in learning about ecological systems, one needs to envision how genes,
individuals, populations, and species interrelate. An ecosystem can be viewed from the level of the
individual organism to the level of the environment as a whole (Wilensky & Resnick, 1999). In
1
Collins and Ferguson (1993) refer to this as form and function analysis.
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human biology, phenomena occur at the anatomical, biochemical, and physiological levels. For
example, respiration occurs at a cellular level as well as at the organ system level. The levels are
interdependent with each other. When cells need oxygen, not only does the lung move more deeply
than usual but also the heart may beat faster to get more oxygen to the tissues. In an ecosystem, the
animals provide carbon dioxide needed by the plants for photosynthesis and the plants provide
oxygen needed by fish to utilize energy. A disturbance at one level or component of the system can
easily affect others.
Studies of complex systems demonstrate that understanding focuses on the perceptually
available structures (Gellert, 1962; Hmelo, Holton, & Kolodner, 2000; Mintzes, Trowbridge,
Arnaudin, & Wandersee, 1991; Wood-Robinson, 1995). Invisible, dynamic phenomena pose
considerable barriers to understanding (Feltovich, Coulsen, Spiro, & Dawson-Saunders, 1992). One
reason for this is that processing all the simultaneous events and interactions pose a substantial load
on working memory because of the mental simulation process and rule-based inferences needed to
construct a complete mental model (Graesser, 1999; Narayanan & Hegarty, 1998). Moreover,
making connections among different levels of a complex system places added demands on working
memory. This is particularly true because many systems are characterized by complex causality;
there may be many nonlinear, intermediate steps that intervene between cause and effect (Perkins &
Grotzer, 2000). Finally, complex systems may have emergent properties that are not be fully
predictable from the behavior of individual components (Wilensky & Resnick, 1999).
A review by Perkins and Grotzer (2000) found that students tended towards very simple
causal explanations of complex phenomena. When students reasoned about effects, they missed the
connectedness within the system and the complex causal relationships because they tended to focus
on the structure of systems rather than on the underlying function. In another study, Chi, DeLeeuw,
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Chiu, and LaVancher (1994) asked students to read a passage about the circulatory system. The
functional aspects of the system were implicit and difficult for students to infer. Only students who
engaged in a large amount of self-explanations could make those inferences.
Thinking about emergent phenomena involves the recognition that a system can have
multiple causal factors and these occur at both a micro level and macro level. In two teaching
experiments, Penner (2001) examined students’ understanding of complex systems as they
simulated building a termite nest. Students walked around the room dropping pieces of paper
(corresponding to the materials in termite nests) according to a small set of simple rules and then
made observations about the aggregate patterns that resulted. Students had difficulty in connecting
phenomena occurring at the microlevel with those that occurred at the macrolevel. A second study
used a model of cellular automata (a self contained universe with a small set of simple rules) to
elicit learners’ ways of thinking about emergence (Penner, 2000). Participants were asked to think
about how patterns occur, and how changes in one level of the system can affect other levels.
Participants based their understanding on their existing knowledge and construed phenomena as
resulting from a direct consequence of a single cause. As they explored the cellular automata,
participants became aware of the distinction between the different system levels (macro versus
micro), the static (but not dynamic) properties, and were able to recognize some of the interactions
within levels though they continued to ascribe central causation to the macro level.
Complex systems often involve concepts that can be in conflict with learners’ prior
experience. Resnick and Wilensky (1998) found that most people have what they referred to as a
“centralized mindset,” preferring explanations that assume central control and single causality. This
is consistent with expert-novice comparisons of complex systems thinking (Jacobson, 2001).
Jacobson interviewed undergraduate students and complex systems experts and found that students
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favored simple causality, central control, and predictability. Expert explanations demonstrated
decentralized thinking, multiple causes, and the use of stochastic and equilibration processes. This
suggests that students’ mental models are overly simplistic, often affected by what is perceptually
salient, a common finding in mental model analyses.
In a study conducted by Vosniadou and Brewer, (1992), first, third and fifth grade children
were asked to describe the shape of the earth. Vosniadou and Brewer found that children’s mental
models demonstrated a developmental shift from a perceptually constrained representation to one
that more closely approximated a correct scientific model. Their results suggest that student’s
mental models develop in complexity with exposure to formal instruction that helps students
understand those aspects of phenomena that are not necessarily perceptually salient.
Similarly, understanding a complex system required going beyond the perceptually salient.
Making sense of complex systems requires that a person construct a network of concepts and
principles about some domain that represents key phenomena and the interrelationships among
different levels of the system, whether it is macro to micro or structure to function. Despite the
emergent nature of complex systems, there are deep principles that explain behavior in such systems
and account for the relationships across levels. Research has demonstrated that people can transfer
deep principles of complex systems across domains when examined in the context of simulations
(Goldstone & Sakamoto, in press). Thus, an important research question is how do some of these
deep principles map onto people’s existing understanding and can they provide springboards for
future learning? The findings concerning learners’ intuitive focus on the perceptually available and
observable patterns and simple causal explanations suggest that Structure-Behavior-Function (SBF)
theory may provide a deep principle that is useful for thinking about complex systems. SBF theory
accounts for a complex system’s multiple interrelated levels, and its dynamic nature. This
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framework has been used for explaining and justifying design of physical devices such as electrical
circuits and heat exchangers (Goel et al., 1996; Weld, 1983).
The SBF framework allows effective reasoning about the functional and causal roles played
by structural elements in a system by describing a system’s subcomponents, their purpose in the
system, and the mechanisms that enable their functions. Goel et al (1996) used SBF theory to model
reasoning about a cooling device. More specifically, structures refer to elements of a system (e.g.,
fish, plants, and a filter are some of the elements that comprise an aquarium). Behaviors refer to
how the structures of a system achieve their purpose. These are the interactions or mechanisms that
yield a product, reaction, or outcome (e.g., filters remove waste by trapping large particles,
absorbing chemicals, and converting ammonia into harmless chemicals). Finally, functions refer to
why an element exists within a given system, that is, the purpose of an element in a system (e.g., the
filter removes byproducts from the aquarium). The distinction between behavior and function can
be confusing because of contextual issues. For example, from the perspective of an aquarium
system, fish respiration is a behavior that releases waste products. If we were analyzing the fish as
a system, we might consider respiration as a function and gas exchange and various cellular
reactions as the behavior. Weld (1983) offered a similar analysis concerning the explanations of
physical devices such as a car engine.
In earlier research, Hmelo et al. (2000) showed that the SBF principle was a useful
framework for examining how children understand the respiratory system. They accomplished this
in the context of having middle school students design artificial lungs. The design activities, with
an implicit emphasis on function, helped the students construct an improved understanding of the
function of the respiratory system and think more about behavioral mechanisms, but their
understanding of the behaviors was as likely to be incorrect as correct. This occurred because the
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conceptual tools (the structure-behavior-function models) were not made explicit and there was no
mechanism for the students to test their models and obtain dynamic feedback. In this paper, we
extend this work to an aquarium ecosystem as we examine how well the SBF framework serves as
an epistemic form that captures the differences between expert and novice understanding.
Method
Participants
The participants were 11 seventh grade students from a public suburban middle school, 11
pre-service teachers from a large public university, and eight experts. The experts were individuals
who have been involved in aquatic systems either professionally or recreationally for 10 to 30 years.
The former group (“the biologists”) included established academic researchers who held an
advanced degree in biology. The latter expert group (“the hobbyists”) consisted of individuals who
had maintained numerous aquaria for more than 10 years and were active members of a local
aquarium society. The preservice teachers received course credit for participating in the study, and
the experts were paid for their participation. Only one participant in each of the middle school
student and preservice teacher groups reported having an aquarium at home, and three from each
group reported that they had studied about aquaria.
Procedure
We conducted individual interviews that ranged from 20 to 40 min. All interviews were
tape-recoded and transcribed. Initially, the interviewer presented participants with a piece of paper
that had a three-sided rectangular shape (representing an aquarium), along with color markers. The
participants were asked to draw a picture of “anything you think is in an aquarium” while thinking
out loud. If needed, the interviewer asked the participants for further clarifications as to his/her
drawings. Once participants completed their drawing, the interviewer began asking questions.
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The interviews included open-ended questions and problem solving activities designed to
elicit participants’ knowledge about aquarium systems. Some questions asked about a system’s
structure (e.g., what is in a fish tank?), others elicited knowledge of the functioning of structures in
a system (e.g., what do fish do in an aquarium?), and others inquired about the behavioral
mechanisms of structures in an aquarium (e.g. what happens when a filter breaks?). The participants
were also given a list of items and asked how these related to an aquarium (e.g., air stone, heater,
gravel, etc.). In addition, several what-if problems were posed. In these problems, participants were
asked what would happen if the system was perturbed. For example, one question asked “what do
you think would happen if you decide to add 10 new fish to the 12 guppies already existing in a
twenty gallon tank?”
Coding and analysis
Participants’ transcribed interviews were coded according to an SBF coding scheme for the
presence or absence of a target concept. The coding scheme identified a target list of aquarium
structures and a list of corresponding behaviors and functions. The researchers coded each interview
for evidence of the presence of SBF concepts. For example, any mention of plants (“I am drawing
some fake plants”) or gravel (“there is the sand on the bottom”) was regarded as evidence of a
participant’s representation of plants and/or gravel as a structure. Similarly, a mention of a fish
hiding (“fish come by and they hide in there between the little plants”) or bacterial processes
(“bacteria…changes the ammonia into nitrate and then nitrate into nitrate back into clean water”)
was coded as a behavioral concept. This was coded as a behavior because it refers to a mechanism
for how the cleaning of water (a function) was accomplished. An utterance that mentioned filter
removing byproducts (“ a filter filters out the organic waste”) or light as an energy source for plants
and algae (“live plants, some other organisms need the light to help photosynthesis”) was coded as a
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functional concept. One primary researcher conducted the majority of the coding and a second
independent research assistant coded 20% of the transcripts. Inter-rater agreement conducted on
20% of the interviews was 96.5% for structures, 92.5% for behaviors, and 93% for functions.
Based on a holistic coding of the transcripts, we have identified five progressively more
complex mental models: 1) The Basic Egocentric Model, 2) The Simple Healthy Fish Model, 3)
The Good Tank Model, 4) The Pragmatic Model and 5) The Hierarchical Expert Model. The
lowest level is the Basic Egocentric Model, shown in Figure 1, Participants categorized as holding
this model demonstrated knowledge of a few structures, with little reference to behavior or function.
The relations between the elements in this model were sparse and a depicted an egocentric
perspective and subsequent understanding of the fish tank. The links in the diagram for this model
represent the novices’ perspective that the fish tank exists for his or her viewing entertainment.
Subjects that were coded for having this model made statements like: “Plants are there to look
pretty to me”.
The Simple Healthy Fish Model is diagrammed in Figure 2. This mental model is
characterized by an increase in the number of the structures that the participants identified as well as
a rudimentary understanding of some behaviors and functions in the system. This advance in mental
model reflects the need to keep the fish alive, as reflected in the diagram by the inclusion of time
(T1 and T2). The time element represents an understanding that the system is dynamic and changes
over time. Participants holding this mental model begin to express an understanding that structures
(e.g., a filter) in the fish tank perform behaviors (e.g., cleaning water) that affect the health of the
fish over time (a function). Functions here are more implicit than explicit (e.g. affecting health
rather than a more specific health-related function). For example, participants will note that food
needs to be added to the tank—to keep the fish alive over time. An example of this mental model
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includes: “Plants, oh they grow and, uh, sometimes look pretty too” or “oh yeah you have to add
food too.” In these examples we see the mental model changing away from an egocentric
perspective, but not quite developed into a holistic ‘tank as a system’ perspective.
In the next level model, there is an increase in the amount of associated factual knowledge.
In the Good Tank model, shown in Figure 3, participants begin to demonstrate a more explicit
rudimentary understanding of functions. Participants identify more structures and the relationships
between structures, behaviors, and functions. From this model subjects respond similar to the
following: “ Plants, yeah, well, they look good, the fish might eat um if their alive, and that means
their growing. ” In this model, the fish are no longer the central feature in the tank. In this model
there begins to be the representation of the interconnection of the features of a fish tank that is more
characteristic of the more advanced representations of the fish tank as a model of an ecosystem.
Participants holding this mental model can be characterized as having a basic systemic view of a
fish tank as a small functional ecosystem.
At the next level of understanding of a fish tank expertise is demonstrated through extensive
knowledge of the structures, behaviors and functions and their interrelationships. Analysis of the
connections made in the responses of the subjects reveled two distinctive different expert mental
models: 1) The Pragmatic Model, and 2) The Hierarchical Model (see figures 4 and 5). While both
groups of participants had a rich understanding of the aquarium, their knowledge was structured
differently. The hobbyists were characterized by the Pragmatic model, shown in Figure 4, which
features the driving goal of someone who owns fish tanks in their home—to keep the fish alive, and
thus to maintain a healthy system for example:
OK, real live plants provide a very good uh, visual effect, they provide
good hiding places for the fish, which feel much more at ease in a tank where
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there are a lot of plants: and they uh, help keep the water quality up by absorbing
the wastes from the fish. So if you go with plastic plants you wont have that.
You won’t be able to keep as many fish in the tank, and it will go off chemically
more easily than if you don’t, if you have live plants.
Furthermore, the Pragmatic model included accurate and well thought out biochemical
understanding. The knowledge structures associated with this mental model were practically based
and focused on dynamically maintaining a healthy tank with healthy fish. The distinguishing feature
of this mental model was the compartmentalized elaboration of complex knowledge. This can be
seen best in the diagrammatic representation of this model demonstrating how the elaboration of
deep understanding of the structures, their behaviors and functions has created extensive systemic
understanding. So the mental model of the hobbyist still has as the central feature the function of
keeping the fish alive over time (an evolution from the Simple Healthy Fish model), but includes
elaborate pockets of knowledge centered around various aspects of the tank. So for example, the
hobbyist expert will not only express knowledge of plants and the knowledge that plants
photosynthesize, but they will then explain the entire photosynthetic process as an aside piece of
information that they have acquired as a part of their quest to maintain a healthy tank. Thus their
model is systemic but very much situated in pragmatic concerns.
Hierarchical mental models included deep detailed understanding that was indicative of a
systematic understanding. Experts with hierarchical mental models would answer questions starting
with the larger theoretical framework then proceeding in a systematic fashion through the
discussion of the connections between the structures their behaviors and functions. Hierarchical
mental models are characterized by light at the top of the hierarchy, as the basic driving force that
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provides energy to the aquatic system. These models include biological and chemical mechanisms
as well as integrating structure, behavior, and function as this brief example demonstrates:
Plants in an aquarium are living beings just like the animals that we were talking about and
just like ourselves, and of course living beings again must have oxygen, for respiration, and
must have nutrients to survive and must have an energy source, …But often we use plants
for what it looks like, they’re for decoration, but they’re not, they are there to balance the
aquarium, and by that we mean that these are photosynthetic plants in the sense that they use
the energy of light and they use CO2 and water and small amounts of …potassium, sodium,
phosphate, sulfate, calcium, magnesium, all these elementary materials plus nitrogen from
nitrogen sources, nitrates they can use as nitrogen sources, phosphates they can use as
phosphate souses , and CO2 which is available in the water from the exaltation or release
from the animals or bacteria…
Fish are not the central characters in this model and are one of several interdependent living
entities in the systems. These are generally discussed in taxonomic ordering (vertebrates,
invertebrates, plants, algae). Subordinated to these are the supporting features of the systems such
as heaters, filter, and rocks. System features were discussed as structures, their behavior and their
functions in relation to the aquarium as a system.
Results
Quantitative analyses of SBF
As expected, experts identified more concepts across the SBF framework than the novice
groups (see Table 1). A 2 x 3 mixed ANOVA was conducted to examine the differences between
experts and the two groups of novices in their representation of structures, behaviors, and function.
There was a significant interaction between the level of expertise and SBF concepts (F (4,
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52)=14.30, p< .001). There was no difference among the groups for the numbers of structures
mentioned (F(2, 27)=2.78, p>.05) but there were differences for behaviors and functions (F(2, 27)=
24.58 and 24.19, respectively; p’s<.001). Post-hoc Student-Newman-Keuls tests indicated that the
experts knew more about both functions and behaviors than the middle school students or the
preservice teachers (p<.05), and that the preservice teachers did not differ from the middle school
children. These results indicate that experts have more functional and behavioral understanding of
this complex system whereas novices, regardless of age, have a more structural representation.
Mental Model Analysis
The participants’ mental models were coded from their transcribed protocols and are shown
in Table 2 . Because of the small number of experts, these were collapsed into a single category
however all four hobbyists were coded with the pragmatic model and all 4 biologists were coded in
the hierarchical model. As expected, the distribution of models followed a developmental
progression from more structurally-based models to more functional ones (X2 (8)= 43.203, p< 001).
Qualitative analyses
An examination of the transcripts indicated additional qualitative differences between
experts’ and novices’ understanding. Experts provided more elaborate responses as well as
demonstrating a more integrated understanding that cut across the SBF levels. The experts
consistently used at least two of the three SBF framework elements in their responses. This was
primarily evident in the descriptions of their drawings. All experts mentioned not only the various
structures that can be found in an aquarium, but also discussed the structure’s behaviors and/or
functions. For example, in a description of his aquarium drawing, one expert said:
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…there is usually some kind of substrate, either gravel, sand.. and sometimes you have
rocks and um with certain kinds of fish it’s necessary to have rocks, uh because they like to
breed in the rocks….and other times the rocks are just decorative….
In this example the expert mentions a few structures (gravel, rock) but continues to discuss the
function of the rocks in the aquarium when he mentions that the fish breed in the rocks and that the
rocks have a decorative purpose in the aquarium. The former can be coded as a function of a fish
(fish reproduce) and the latter can be coded as a function of a rock (decoration). A novice
participant responded to the same instructions with the following:
I will draw pebbles on the bottom like rocks and stuff …I know there are rocks and stuff and
then there are plants usually that grow…
This participant mentioned numerous structures but did not offer additional behavioral or functional
information even when probed. This response was limited to structures present in his/her
representation of an aquarium. Integrated expert responses were also evident in the latter part of the
interview where participants were presented with problems. For example, in a response to a
question regarding the difference between a river and a lake fish, one of the experts noted:
The ones in the river that are swimming in strong currents will have to be very strong
swimmers. The one in the lake will have to get its food probably in small areas. They
probably have a small ecosystem where they swim in…some of them have camouflage, ahh
some they are very fast swimmers, some of them have armor on their backs, some of the catfish like they have like armor plating on their backs. So all the fish won’t bother them.
Once again, the expert includes numerous structural and functional differences in his response.
Most novice participants indicated primarily a single structural difference between the two fish that
were related to the fish’s ability to swim in each environment:
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Fish in a river probably uh probably bigger and stronger because they have to fight against
currents sometimes and fish in like a lake is pretty still so they can be like pretty much
anything like small fish, big fish.
Another interesting pattern appeared within our expert group. Upon careful reading of the
interviews, we noticed some differences between the biologists and hobbyists. The biologists
focused on the abstract biological processes and mechanics of the fish tank as a system whereas the
hobbyists focused on concrete aspects relating to maintaining the health of the fish. Both groups had
rich representations but they had different emphases. For example, in a discussion on how fish food
is related to aquarium systems, the biologists provided a more abstract, scientific explanation of the
importance of digestible animal protein and vitamins in a fish’s balanced diet.
… it has to be balanced food containing carbohydrates, fats and proteins and for the younger
ones you wanna more proteins, and for most fish, around 40% protein is very good diet…
So that what we call fish meal is a meal that is produced from fish and bone meal, is a meal
that is produced from bone, and these things go as constituents into fish feed, and so the
provide a nice balanced protein. But in addition you must make sure there is sufficient
vitamins in the fish feed.
The hobbyists talked about feeding schedule, popular food brands, and other food products:
There’s Aquarian or Tetramin or some of the other color flake foods that are very good for a
basic diet. Never over feed them, just feed a little bit and just let them look hungry…you can
get specialized foods for a specific fish. Um, Hikari makes a nice line of foods for guppies,
cichlids, um carnivorous fish. There are pellets you can get that sink or float, uh you can buy
frozen food, frozen brine shrimp is a wonderful basic food for fish, but you can also get
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frozen blood worms, uh Daphnia, all sorts of stuff. Then if your parents, or your spouses, are
willing, you can buy live foods for your fish.
Like the biologist, the hobbyist is making references to the need for high protein when she talks
about live foods and the carnivorous cichlids. However, the hobbyist description is very concrete
and situated in specific fish that need a high protein diet, particular brands of food (“Hikari.
Aquarian, Tetramin”) and the discussion of live foods.
Furthermore, it appears that the biologists were better able to capture the global, dynamic
interdependencies within the system. The hobbyist provided more focused, local explanations
concerning the relationships between and among structures and their associated functions and
behaviors. For example, in a response to questions concerning the function of a filter in an
aquarium, the biologists focused on the properties of a filter as a substrate for bacterial growth and
proceeded to explain the role of bacteria in an aquatic system. Some continued to describe the
relationship between the filtration mechanism and such processes as pH balance in the system (see
Figure 6). The hobbyists indicated that the function of a filter is to remove various wastes or
byproducts from the aquarium and circulate the water in the aquarium (see Figure 7). As in the
food example, the hobbyists understand the relation between waste and pH but they discuss it
situated in the context of how the filter keeps the tank clean.
Discussion
The results of this study clearly indicate that structures are the most cognitively available
level of a complex system for novices. In particular, both the SBF and mental model analyses
demonstrated that those structures that are most perceptually salient are best represented. For the
experts, the behavioral and functional levels serve as the deep principles that organize their
knowledge of the system. Understanding the behaviors and functions of a system indicate a more
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elaborate network of concepts and principles representing key phenomena and their
interrelationships. It was not surprising to see that the experts mentioned functional elements more
than behavioral and structural concepts, as multiple behaviors and structures may combine to
perform various functions. Moreover, functional aspects of the system deal with end results but
behavioral mechanisms deal with dynamic and often invisible processes that are difficult to
represent.
Our qualitative analysis demonstrated the fine differences in the mental representations of
different sorts of experts. We did not consider that an expert's purpose in learning about aquaria
would affect his or her mental representation. Biologists think in global ecosystems terms whereas
hobbyists think in more local terms of what it takes to maintain healthy (and happy, as was noted by
several hobbyists) fish. The hobbyists' understanding is more situated in concrete aspects of the
aquarium. These differences were not expected and are worth further investigation to illuminate the
relationship between one’s goals and the nature of the representation constructed.
In this study we introduced a framework that accounts for the different levels of a complex
system. Breaking down complex systems into structural, behavioral and functional levels may aid
learners in the process of making the implicit functions and behaviors of a system explicit, and may
provide a schema that can be used to understand a number of complex systems. The SBF
framework appears to be a deep principle that maps onto expert ways of knowing about complex
systems. Further work needs to be done to ascertain how general this principle is. Hmelo et al.
(2000) demonstrated that for the respiratory system at least, the SBF principles, implicit in learning
through design activities, have some promise for helping students learn about complex systems.
Our program of research is actively engaged in investigating other systems and exploring how to
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capitalize on the SBF framework as an example of an epistemic form to support learning about
complex systems.
The SBF framework offers a way for learners to look behind the scenes at phenomena that
are not readily perceptually available. Complex systems are an important part of the world that we
live in and, as such, are recognized as a key idea in national science standards (National Research
Council, 1996). Organizing learning around deep principles such as SBF might enable students to
understand new complex systems they encounter (Collins & Ferguson, 1993). Our future work will
investigate how SBF can be used to design instruction. We are taking two approaches to this. The
first test of these ideas will use SBF to structure hypermedia. In this work we will compare the
effects of using structurally organized hypermedia, much like a standard textbook, with a
functionally organized hypermedia. We will examine both browsing patterns and learning
outcomes. Prototype navigation screens are shown in figures 8 and 9. Note that the functionally
organized screen shows examples of functions that are needed to maintain a balanced ecosystem
and the inset is an example of drilling down to the behavioral level. From the behavioral level,
learners could go both to structures and behaviors—eventually going to summary screens that show
how these are related. Our expectation is that the functional organization should support deeper
understanding than the structural organization. Another approach that we plan to explore is the use
of simulation construction kits that would allow functions and behaviors to become “visible”
aspects of systems and open for exploration and discussion. By using SBF as a guiding framework
for learning about complex systems, behavior and functions become salient and learning about
complex systems can become more than the just the sum of the structures.
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Table 1
Means and standard deviation for total number of structures, behaviors, and functions by expertise
group.
Group
Middle
School
PreService
Teachers
Experts
N
Structures
Behaviors
Functions
11
12.27 (1.35)
6.64 (2.98)
8.73 (3.69)
11
11.91 (1.14)
8.18 (2.09)
8.45 (3.17)
8
13.13 (0.64)
15.13 (2.95)
19.00 (4.11)
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Table 2
Percentage of participants classified in each mental model
Group
N
Egocentric
Simple Healthy
Good Tank
Fish
Expert
Middle
School
11
36.4 %
54.5 %
9%
0%
PreService
Teachers
11
18.2%
9.1%
72.7%
0%
Experts
8
0%
0%
0%
100%
24
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Figures
1. Egocentric mental model
2. Simple healthy fish model
3. Good tank model
4. Pragmatic expert mental model
5. Hierarchical expert mental model
6. Biologist understanding of the filter
7. Hobbyist understanding of the filter
8. Prototype structural hypermedia navigation screen
9. Prototype functional hypermedia navigation screen
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