Exploring the mutual benefits of collaboration between Concept
Mapping and System Dynamics — a conceptual argumentation and
some puzzles
presented at the
31" International Conference of the System Dynamics Society, Boston, July 21-25
Martin Schaffernicht ' and Barbel Firstenau *
Abstract
Concept maps (CM) are a measure to visually structure topics in the form of two dimensional
networks. CM initiated in educational research and expanded into educational practice. CM are
often used when individuals or groups have to deal with complex subjects from science, economics
and management, hence fields where system dynamics (SD) is also present Proponents of both SD
and CM have developed rigorous methods to analyze and compare such maps respectively
diagrams. We have compared the use, the structure and the analysis methods between CM and SD
and identified conceptual compatibility and some methodical complementarities: SD diagrams of
mental models of dynamic systems (MMDS) can be interpreted as CM and CM analysis methods
for large samples can be brought to MMDS research; also the rigor of SD modeling can become a
vehicle for integrative reconciliation of knowledge and thus SD can become a relevant tool for
educational researchers. We show these aspects on a conceptual level using a simple illustrative
example. We conclude by proposing some relevant research questions.
Keywords: Concept mapping, system dynamics, model comparison, modeling for learning
! Facultad de Ciencias Empresariales, Universidad de Talca (Chile); martin@ utalca.cl
? Fakultat Wirtschaf ten, T he Universitat Dresden (Germany);
baerbel.fuerstenau@ tu-dresden.de
1 Introduction
Concept maps (CM) have been used as a strategy to support leaming and as a measure to represent
knowledge. CM is a recognized area in educational research and applied in subject domains such as
science, economic and business problems and sustainability. Specific methods for CM modeling,
analysis and assessment have been developed. In more recent times measures have been developed
aiming at combining qualitative and quantitative research methods with regard to CM.
Coming from a different background, system dynamics (SD) shares some features with CM: the
intention to help resolving complex problems, the focus on learning, the use of diagramming to
articulate and to structure a problem, and the interest in model comparison as a help for inquiring
learning. At the same time, there are some differences, mainly that SD has a rather specific
modeling language, develops very detailed models and is anchored in the recognition that learning
about dynamically complex situations requires simulation. Also, SD has not yet diffused inside the
educational research field.
In this paper, we want to shed some light on two aspects:
1) Can methods from CM enrich research in SD about how people understand dynamically
complex situations?
2) Can SD enrich or complement CM in educational research where it deals with the
understanding of complex processes in the economy or in the firm?
We analyze the structure of the diagramming languages and find that a SD diagram can in principle
be interpreted as a specific kind of CM; therefore methods for CM analysis and comparison can be
applied to SD models and the first question receives an affirmative answer. We also analyze how
the specificity and the discipline of simulation make SD an interesting tool for educational
researchers using CM, therefore answering the second question with “yes” and arguing that this is
an opportunity to increase the influence of SD in the field of educational research.
The paper is organized as follows. Section 2 briefly introduces CM, its use, the structure of CMs
and methods for analyzing and comparing them. The following section discusses the possibilities to
translate between the different diagram languages; examples of converting from CM to SD
diagrams, as well as of the inverse translation, are given. Section 4 discusses the meaning and
implications of the similarities and differences and proposes fruitful areas of scientific
collaboration.
2 Concept maps
CM are two-dimensional structural representations of a topic consisting of nodes and labeled lines
between the nodes. The nodes represent important concepts; the lines are relations between the
concepts (Nesbit & Adesope, 2006, p. 415; Novak & Carias, 2008, p. 1). Relations are also referred
to as linking phrases, because the lines representing them are labeled with a word. This means that
in one CM there are usually many different relations, each with a different word label to describe it.
Two concepts and a relation form a proposition. A proposition is the basic unit of meaning ina CM
and the smallest unit that can be used to judge the validity of the relation (line) drawn between two
concepts (Ruiz-Primo & Shavelson, 1996, p. 570).
The term concept map was coined by Novak and colleagues (e. g. Novak & Gowin, 1984). CMs
were developed in the framework of a longitudinal study of school children trying to understand if
their cognitive limitations came from genetically determined processes of childhood development
or rather from previous learning in the context of schooling (Novak, 2002; 2005). However,
graphical notations of language, like CM can be traced back to the 1960s, especially the fields of
linguistics and computational linguistics (Sowa, 2008). In the field of psychology, early models of
CM (knowledge networks) were developed by Collins and Quillian (1969), Rumelhart and Norman
(1978), or Minsky (1990). While in the 1960s the models focused on the structure of knowledge
since the 1970s researchers tried in addition to model processes which operate on the structure.
The most important cognitive theories underlying CMs are on the one hand the theory of semantic
networks (e. g. Collins & Quillian, 1969; Dansereau et al., 1979) as in the early psychological
models mentioned above. On the other hand Ausubel’s (1968) learning theory based on assimilation
can be mentioned. Consistent with models of semantic networks CMs as extemal models are
assumed to be structurally consistent with knowledge as internal model. Therefore, concept-
mapping may help students on the one hand to externalize and on the other hand to construct and
elaborate their cognitive structure. Ausubels’s (ec. g. 1968) learning theory focuses on assimilation
as learning process. His theory implies a hierarchical memory structure and explains learning as
subsumption process. Based on Ausubel’s theory, Novak and Gowin (1984) suggest that CMs
should have a hierarchical structure displaying subordinate und superordinate relationships. So-
called crosslinks (links between different sections of the hierarchy) represent integrative connection
between different domains of the hierarchy (Ruiz-Primo & Shavelson, 1996, p. 571). However,
dependent on the respective question, in many studies CMs are used in a more flexible way and do
not have a hierarchical but a network structure.
A couple of other theoretical approaches have been quoted in order to explain the efficacy of CM,
among them dual coding theory (Paivio, 1986) and the learning strategies approach (for an
overview see Nesbit & Adesope, 2006, p. 417ff.). According to dual coding theory verbal and
visuo-spatial information reside in different memories. The memories can be interlinked, and the
links provide additional retrieval options for both kinds of information. In addition, verbal and
visuo-spatial information can be processed in different channels at the same time. This might lead to
deeper and more efficient information processing than working exclusively with verbal data, e. g.
texts. CMs may comprise verbal and visuo-spatial information and thus may enable effective
processing. Closely connected with this line of argumentation is that the format of CMs represents
information in a structured graphic, whereas texts represent information in a linear order. Thus CM
display one concept and all propositions integrating this concept only once, whereas texts may
contain the same concept several times. Thus diagrams may support encoding and comprehension
of information better than text (Larkin & Simon, 1987). Last, but not least CMs can function as
learning strategy, especially as organization or elaboration theory (Weinstein & Mayer, 1986). In
cases students are requested to create or modify CMs they have to group information and by that
actively process information and reach a deep understanding.
CMs are mainly used for two purposes: 1. as instructional tool or learning strategy in order to foster
meaningful leaming, that is to say help students integrating new information with existing prior
knowledge; 2. as measure to assess structured knowledge and knowledge development. Both
purposes can be combined (Horton et al., 1993; Sowa, 2000; Nesbit & Adesope, 2006). Over the
years, CMs are widely used in educational settings, but also for knowledge management purposes
(Novak & Carias, 2008; Novak, 2010; 2011)
In educational research, CMs are often used in order to find out about the effectiveness and quality
of the complex leaning tasks by assessing students’ structured knowledge respectively the
development of their knowledge before and after an intervention. In order to assess the CMs
different approaches can be distinguished. Dependent on the respective aim, they range between
ideographic and nomothetic, qualitative and quantitative, or descriptive and normative analyses. In
the course of ideographic analyses usually the most important features of individual CMs are
verbally described whereas nomothetic analyses aim at comparing all CM of a test sample and then
draw general conclusions. Qualitative approaches aim at referring to features of the content and are
therefore often combined with descriptive approaches. In contrast, quantitative approaches aim at
scoring components of the map or the entire map, such as the number, existence of concepts and/or
propositions, coherence or diameter of the map. The descriptive approach considers maps of test
persons gained in the respective study and describes them qualitatively and/or quantitatively. The
normative approach takes overlaps between students’ maps and a criterion map (e. g. expert’s
reference map) into account (Ruiz-Primo & Shavelson, 1996).
Especially the development of scoring techniques has attracted attention of researchers since the
1990s, both concerning manual scoring and automated computer-supported scoring. Afamasaga-
Fuata’i (2004), for example, used a scoring scheme developed by Novak and Gowin (1984), which
focuses on the structural differentiation (hierarchical depth) and integration (cross-links) between
valid concepts and propositions, according to the guiding theory of learning. Simon and Levin
(2012) report a method which compares and scores CMs in four dimensions: spatial structure (how
well organized is the diagram?), consolidation (the degree of integration expressed by the links
between concepts), focus (prominence of specific concepts inside the CM), and depth and wealth of
ideas. Cafias et al. (2006) developed a topological taxonomy for CMs, which takes into account the
use of single name concepts (over chunks of text, which reveal poor appropriation of the content by
the individual) and structural aspects (concept count, links count, the ramification and the
hierarchical depth. The software CMap Analysis was developed to automate the necessary
computations (Cafias & Reiska, 2010); it is currently used by researchers (Derbentseva, 2012).
Some limitations of existing scoring measures can he identified. Often, qualitative and quantitative
measures are not related. Quantitative indicators like number of propositions do not legitimate
researchers to draw inferences on the quality of knowledge. In turn, qualitative measures, e. g. the
frequency of special propositions, lose sight of the semantics. Therefore, the work already done can
be improved by using models and measures strongly combining qualitative and quantitative
research tradition. With the help of those measures congruencies and differences between individual
maps of a test sample or between individual maps and a criterion map can be judged both
qualitatively and quantitatively. In the course of the analyses the semantic information of the maps,
that is to say the propositions and their interrelationships (i. e. the content structure), is kept and
does not disappear behind scoring indicators. For that purpose all maps of a sample can be
represented, evaluated and statistically assessed by only one, e. g. a modal network. A modal
network contains those propositions named commonly and most frequently by the test persons
(Oldenbiirger et al., 1992). Besides this descriptive approach, congruencies and differences between
all individual maps and a criterion map, e. g. an experts' map of the contents can be identified, in
order to follow a normative approach. The reliability and the degree of representativeness of modal
map and criterion map can be judged by the internal consistency of a congruence scale measuring
the overlap between maps. The internal consistency is indicated by Cronbach’s a, and the
congruence scale should have a high intemal consistency (reliability). The calculations are based on
a person x proposition matrix (Firstenau et al., 2009; 2012b). The results allow defining more
content valid and concrete starting points for more effectively improving teaching-learning
processes.
This method has been applied in a number of cases related to starting a company (Fiirstenau et al.,
2009) or based on management simulation games (Ryssel & Firstenau, 2011). It has also been used
to assess the advantages of CM over alternative means of knowledge articulation (Fiirstenau et al.,
2010; 2012a).
There have been attempts at using other comparison methods, especially the Pathfinder networks
(Torres Carvalho et al., 2012); however, such methods, which do not distinguish between different
link types, cannot be applied on CM without losing relevant information.
3 Concept maps and system dynamics diagrams
3.1 Symbols and usage
The purpose and background of system dynamics (SD) is helping decision makers to design better
decision policies by providing a simulation-based testing environment (Forrester, 2007). It assumes
that (social) systems are dynamic in nature and driven by feedback loops — logically closed paths of
causation. Such loops consist of accumulation variables (“stocks”) and flow rates adding to or
draining from stocks (Forrester, 1969). The structure of such a system can further be divided into
the “physics” — that which is going on independently of the decision maker — and the decision
policies by which the decision maker tries to influence the system’s behavior over time. Such
policies are expressed as sets of intermediate steps between stocks and flow rates, and so-called
auxiliary variables help to express them clearly.
Stocks, flow rates and auxiliaries conform differential equations which enable to simulate the thus
modeled system. Originally, system diagrams were only used to communicate the causal structure
of simulation models, but with the advent of graphical user interfaces for personal computers, new
software products allowed to formulate system models by developing “stock-and-flow” diagrams
(Schaffernicht, 2009). Later on, the simplified symbolic language of “causal loop” diagrams
focused attention on the causal loops, partly be leaving out the difference between the types of
variables (Lane, 2008). Together, stock-and-flow diagrams (SFD) and causal loop diagrams (CLD)
have become a standard toolset for the qualitative formulation SD models, even though SD also
includes quantitative work based on equations (Lane, 2008; Schaffernicht, 2010). “Hybrid”
diagrams (HD) combine the advantages of both diagram types by inserting causal link polarity and
loops into SFD (Sterman, 2000), but do not add new symbols.
From its very conception, SD is based upon the assumption that most relevant knowledge about a
social system is in the minds of those who live and act inside them (Forrester, 1961); therefore the
“mental database”, as well as the challenges of eliciting and improving it — learning — have been
main topics in SD (Morecroft and Sterman, 1994). The intention to elicit and improve knowledge as
well as the use of diagrams constitutes a bridge between SD and CM, despite other differences.
3.2 Corresponding components
Diagrams of the three types - CLD, SFD and HD - can easily be converted into a CM, as the
following tables illustrate.
CLD CM
Variable Concept
Positive causal link without delay Relation of type ,,+
Positive causal link with delay Relation of type ,,+ D*
Negative causal link without delay Relation of type ,,-“
Negative causal link with delay Relation of type ,,- D“
Table I: converting a CLD intoa CM
As shown in Table I, a CLD maps into one concept and four relationship types. A CLD has only
one type of variable, but the causal links can have two different polarities and an optional delay
mark, which gives four possible linking-phrases to build propositions like “motivation -+> effort”.
SFD CM
Stock variable Concept of type “stock”
Flow variable Concept of type “flow”
Intermediate variable (auxiliary, | Concept of type “intermediate”
converter)
Information flow Relation ,,is-used-by*
Table II: converting a SF D intoa CM
Table II associates CM components to each component of a SFD. SFD distinguish three types of
variables, but instead of several types of causal links the only type of relations are information
flows (thin arrows); one can think of an illustrative label like “is used by”.
HD CM
Stock variable Concept of type “stock”
Flow variable Concept of type “flow”
Intermediate variable (auxiliary, | Concept of type “intermediate”
converter)
Positive causal link without delay Relation of type ,,+“
Positive causal link with delay Relation of type + D*
Negative causal link without delay Relation of type ,,-“
Negative causal link with delay Relation of type ,,- D*
Table III: converting a HD into a CM
Last not least, Table III shows how HD are converted into a CM; they combine the SFD variable
types with the CLDs’ causal links, and therefore constitute the most differentiated symbolic
language of SD.
It is immediately clear that any SD diagram can easily be “translated” into a CM, and any story
implied by the propositions can be interpreted as the meaning of the mental model articulated in the
diagram. This ease is explained by the fact that by allowing for any kind of concept and any kind of
relationship, the “language” of CM does not impose specific types of concepts or relationships. On
the other hand, SD does only allow the specific types of variables and links which have been
presented above. On top of this specificity, SD has a set of rules limiting the syntactically allowed
connections; for instance, only a flow rate can influence a stock, and therefore causal links from
stock to stock or from auxiliary to stock are prohibited. Another important epistemic rule is that
only stocks can be directly observed; therefore it is syntactically wrong to posit a causal link from a
flow rate to an auxiliary or another flow rate.
Such restrictions do not have a counterpart in CM. It follows that one can construct a CM
containing concepts which are not variables (but “objects”), and therefore not all syntactically well-
developed CM can be translated into a SD diagram.
The comparatively strict syntactical rules in SD, together with a larger set of symbols (for
expressing more specific meanings), is not an end in itself: it has the purpose to focus the modeler’s
mind on important aspects of a dynamic system and to help him. In this context, let us recall that
one of the systems thinking skills held in high esteem in the SD community is “operational
thinking”, meaning that the recount we develop of a dynamical phenomenon should reveal how the
studied behavior pattern is created (Richmond, 1993). While the term “systems thinking” as used
inside the SD community sadly collides with its general interpretation, it has received a growing
amount of attention and has its own stream of publication (see Maani & Maharaj, 2004 and
Sweeney & Sterman, 2007), A detailed discussion of these skills and habits is beyond the scope of
this paper — some details can be found in the appendix. However, SD reasoning analyzes problems
or systems such as to generate comprehension of all causal mechanisms required to endogenously
reproduce and then influence the dynamic system. The symbolic language and the meanings it
supposes (and obliges to use) are thought as a help for inquiry.
We should then suspect that the development of SD-diagrams would lead to unearthing operational
details of the analyzed phenomenon, together with a conceptual boundary which includes the
relevant factors and privileges an endogenous explanation. Since CM does not become so specific,
typical SD-diagrams should reveal more of those aspects than CM.
As far as this supposition holds true, SD diagramming and modeling would be a good candidate for
the type of learning envisaged by Novak, and thus an attractive complementary approach to
knowledge articulation and structuring.
We will now discuss some illustrative examples meant to reveal this potential complementarity.
3.3 Some illustrative examples
We will now discuss some illustrative examples taken from the context of the growth and collapse
of the original Easter Island population; this is a well-known case which has been treated in SD
education (Fisher, 2007; for another example see the systems wiki 3. At the Lewis & Clark College 4
the same subject has been explored using CM.
The first example (Figure 1) translates a SF diagram inspired by Fisher’s (2007) exercise into a CM.
There are two stocks — Population and Trees. Population changes due to the births and the deaths
flows, while Trees only diminish due to the consumption flow, which uses (is determined by)the
Population size. On the other hand, the deaths (flow) depend on Population, but also on the number
of Trees (passing by available trees per person, sufficiency of trees and the death rate.
3 http://www.systemswiki.org/index.php?title=Mysteries of Easter Island (3/12/2013)
“ http://www.Iclark.edu/
oO Hybrid Diagram
birth rate Ne
Births
D consumption per
te) f
Jconsumption
deaths Trees
B2
+
+
DQ deathrate available trees
yy per person
desired sufficiency of trees iw
number or
trees per
person
G
+o
birth rate
consumption
per person
\
\ |
|
i
|
death rate
per person
Sf
ry |
sufficiency of trees
desired number
available trees i
per person
Concept Map
Figure 1: translating a HD intoa CM
This CM has three types of concepts: stocks are represented by rectangles, flows by rounded
rectangles and intermediate variables are just words. The linking sentences are simple “+” and “-“.
The diagram can be transformed into the list of propositions displayed in Table IV:
Propositions
First concept (cause) Linking phrase ‘Second concept (effect)
Population + deaths
sufficiency of trees death rate
Trees + available trees per person
deaths Population
death rate + deaths
consumption per person + consumption
birth rate + births
births available trees per person
Population + consumption
births + Population
desired number of trees per person sufficiency of trees
available trees per person + sufficiency of trees
consumption Trees
Population + Births
Table IV: the set of propositions
Even though the CM language does not have a symbol for feedback loops (which do not play a
specific conceptual role), such loops can be detected and conceptualized as chains of propositions.
It is also interesting to note that a propositions’ list like the one shown in Table IV above contains
the same information as an adjacency matrix, which would be created for each relation and would
have the following content. The following Table V represents the corresponding adjacency matrix:
[Adjacency matrix
5
:
© a
8 315
8/S/8] elec
gs) |o| jelele|z]a]2
8) o/2/2|2/2/8/8/§/§
aleselsls/slE/3| 2/2/38
é|5/5|s5|5/al2{s5|8/ sie
Population 1 1 -1 1
births
birth rate 1
deaths aA
death rate 1
available trees per person 1
sufficiency of trees af.
desired number of trees per person 1
Iconsumption per person 1
i 1
Trees 1
Table V: adjacency representation of the model
Since we have a case with 11 variables, the matrix has a 11 X 11 structure. By default, all the
matrix elements are equal to zero. When there is a causal link from a variable a to another variable
b, then the element for row a and column b is set to a non-zero value. We have used a “1” to
represent positive polarity, and a “-1” to express negative polarity. For instance, the first proposition
from above — “Population + deaths” is now represented by the “1” in row 1, column 4. The “-1” in
row 1, column 6 represents the third proposition in Table IV.
This means that the loop detection methods based on the exploitation of an adjacency matrix can
also operate on the CM. In our case, the loops are shown in the following Table VI:
Loo y
Ri | + births: Population
B Population | consumption Trees available trees per person (sufficiency of trees [death rate deaths
B Population [available trees per person [sufficiency of trees |death rate deaths
B Population [deaths
Table VI: the feedback loops as proposition chains
If we can translate a HD without losing relevant information, the same can be done with CLDs and
SFDs. Thus mathematical methods developed for CMs and the proposition sets (like the one
displayed in Table IV — especially the computations for constructing a reference net (model) and
then using statistical processing to compare large sets of models — are applicable to SD models and
mental models of dynamic systems (MMDS). We could even bypass the graphical translation and
transform a MMDS’ adjacency matrix directly into a propositions’ list (which we have already done
in an exploratory case).
In conclusion, it is argued here that SD educators and researchers interested in the learning of SD
can benefit from collaboration with educational researchers from the CM field.
Tuming now to the transformation of a CM to a SD diagram, let us analyze a CM available from the
Lewis & Clark College’, which also focuses on why the Easter Island original population collapsed.
It tums out that this is not possible without taking design decisions at several points, because either
a concept or a linking phrase cannot be directly represented in a SD diagram.
In the case of the CM shown in the following Figure 2, the Easter Island Population is clearly a
central concept, and it is reduced by four factors: slave trade, diseases (which are increased by
slave trade), diminished agricultural capabilities and ecosystem collapse. The two latter problems
are caused by soil fertility/health which is reduced by the deforestation of the coconut palm. At the
same time, the Easter Island Population builds Statues which results in the deforestation.
Since the concepts in this CM are of undefined type, the translator has to take a series of decisions
in order to create a corresponding Hybrid Diagram. In this case, Easter Island Population and
Statues are the obvious stocks; however, Disease — understood as the number of sick people — and
Slave trade — as dumber of sequestered people- are interpreted as stocks, too, as are Agricultural
capabilities. Of course, this means that diminished agricultural capabilities is split up in a stock and
the diminished part is put as an outflow.
> http://enviro.Iclark.edu:8002/rid=1235441584719_ 936506269_114/Easter%20Island.cmap (3/12/2013)
Concept Map
Slave Trade
introduces
reduces
Easter Island Population
=
4 (ecosystem collapse ) Agricultural capabilities
builds ee
causes
a
results in
ise
Easter Island
Population oe)
ecosystem (82
functionality Agricultural
A, capabilities
Bl
soil fertility /health
Z| Coconut
palms
deforestation
Hybrid Diagram
+
builds
Q
Figure 2: translating a CM intoa HD
In a similar manner, the deforestation of the coconut palm is split into a Coconut palm stock and a
deforestation flow. Additionally, the linking phrases increases, reduces and builds are represented
as flow variables.
It is noteworthy how many operational details were implicit in the CM and are only articulated
because we have to decide if a concept is a stock or a flow variable, and then comply to the rule that
stocks can only be influenced by flow variables. By imposing stricter rules and restrictions on the
13
modeler, SD leads him or her to articulate his or her understanding of the situation in a way which
automatically corrects ideas which could not work in the represented situation. On top of this, the
modeler is held to recognize the feedback loops, which leads to the discovery that the population
collapse was self-inflicted.
The re-translation into a CM and comparison with the original CM illustrates the gain in relevant
aspects:
Concept Map
Slave Trade
introduces
reduces
Easter Island Population
Diminished
PA (ecosystem collapse ) Agricultural capabilities
builds f
results in
functionality +
—!
Hybrid Diagram -> Concept Map
Figure 3: translating a CM intoa CLD
Visual inspection reveals that the translated HD has more components, and there are three types of
concepts (implicitly treating the recognition of the different types of variables as superordinate
learning). This also shows in the propositions table, where we have replaced the linking words
reduces with “-“ and builds, causes, results in and introduces by “+”.
[Propositions of the original CM
#]
[Propositions of the reconstructed CI
3 7
#
a
I
‘sol erty health
phrase [Second
1 ‘deforestation of coconut palm 1 bald States
2_ | Diminished Agricultural capabities Easter Island Population 2 Coconut palms + sol fertity 7 heath
3 Disease) = Easter Island Population 3 deforestation’ Coconut palms
4 Easter Island Population + Statues 4 | ecosystem functonalty - reduction
5 ecosystem collapse: Easter Island Population 5 soll fertility / health + diminished
6 Slave trade = Easter Island Population é <iminished ‘Agyicultial capebilies
7 ‘soll fertlty / health + ‘ecosystem collapse 7 |_ Agricultural capabiles - reduction
8 Soil fertility / healt + Diminished Agricultural capabilities a soll fertility / health + ecosy stem functionality
9 Statues + “deforestation of coconut palm 9 | Easter island Population + build
10 Slave tade + Disease 10 reduction + Easter Island Populaton
1 Slave tade + increase
2 Diseases + reduction
13 Slave tade + reduction
4 Statues + deforestation
15 inerease + Diseases:
Table VII: comparison of propositions
The Hybrid Diagram converted into CM not only has more details; most of the propositions of the
original CM have become a chain or propositions:
Original CM | Reconstructed CM
1
3,2
7,10
12, 10
9,1
4,10
13, 10
5,6
8
clolslolalalelr
14,3
10
11, 15
Table VIII: corresponding propositions
This is a trace of what individuals are led to do when developing a HD, but not those who develop a
CM: if one has to decide if a concept is a stock or another type of variable, then one also has to
identify the relevant flows. This remains implicit in CM, and therefore the structure of the situation
has more operational clearness in a HD.
4 Discussion
Section 3 has shown two areas where the SD field can advance by collaborating with researchers
from the CM field. First, since a SD diagram is supposed to express knowledge about a dynamic
problem and can be translated into a CM without losing relevant information, the methods used to
analyze and compare CM are applicable to SD diagrams. This is a methodological statement which
should be considered by those using SD to trigger and support leaming. Specifically the
interpretation of causal links and chains of causal links as propositions and chains of propositions
creates a link with the educational research field. This is of high relevance for methodological
aspects of research concerning mental models of dynamic systems. This is a kind of mental models
under research in SD (Groesser & Schaffernicht, 2012; Schaffernicht and Groesser, 2011). Also,
initial steps towards taking into account paths (sequences of causal links) in the analysis of such
mental models are under way (Schaffernicht & Groesser, 2013).
As we have argued in the second part, using SD diagramming and its miles facilitates the
development of operationally accurate diagrams; as far as one accepts that such diagrams represent
knowledge and that developing them also develops our knowledge, this means that whenever the
focus question involves a dynamic system, SD will be an enrichment for the CM field, and its
advantages should be detectable with the same analysis methods.
Both aspects seem to point at a new field of scientific collaboration for the advancement of
knowledge about how we learn about and know dynamic systems. Two research questions shall be
proposed here:
1) Can the methods for analyzing CMs qualitatively and quantitatively applied to the analysis
of MMDS? Is it, for example, possible to apply the modal map and the criterion map
(reference map) approach developed in CM to SD, and consequently define modal MMDs
or a reference MMDS based upon expert opinions for MMDS and teaching cases? And
would it be possible to assess the quality of individual MMDS by applying this approach?
2) Does the development of SD diagrams and models improve the quality of concept maps,
where dynamical phenomena are studied? Are there more operational details? Are there
more feedback loops? Are the explanations provided by the diagrams more endogenous?
Conclusions
In this conceptual inquiry, we have asked if there are compatibilities and complementarities
between CM and SD. We have then shown that the representational tools are compatible: any SD
diagram can be interpreted and represented as a CM. However, specific additional rules are required
if one wants to develop a CM which can be interpreted and represented as a SD diagram. As shown,
this has the benefit of facilitating the development of more operationally accurate knowledge and
representations. SD diagrams from experiments with large numbers of individuals can — and shall —
be analyzed using CM methods to improve our understanding of how people learn about dynamic
systems.
This is, of course, only a conceptual contribution with methodological implications. Only practical
investigations will reveal more information about the fruitfulness of this line of work for both
communities. Thus we conclude by inviting researchers to take up the research questions and report
back from their endeavors.
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Appendix: systems thinking
According to Richmond (1993):
1.
Dynamic thinking: “Dynamic thinking is the ability to see and deduce behavior patterns
rather than focusing on, and seeking to predict, events. It's thinking about phenomena as
resulting from ongoing circular processes unfolding through time rather than as belonging
to a set of factors.” (p. 122)
System-as-cause thinking (closed-loop thinking): “When exercising closed-loop thinking,
people will look to the loops themselves (i.e., the circular cause-effect relations) as being
responsible for generating the behavior patterns exhibited by a system. This is in contrast to
holding some set of external forces responsible: external forces tend to be viewed as
precipitators rather than as causes.” (p. 124)
Forest thinking (generic thinking): “Just as most people are captivated by events, they are
generally locked into thinking in terms of specifics” (p. 124)
Structural thinking: “Structural thinking is one of the most disciplined of the systems
thinking tracks. It's here that people must think in terms of units of measure, or dimensions.
Physical conservation laws are rigorously adhered to in this domain. The distinction
between a stock and a flow is emphasized.” (p. 125).
Operational thinking: “Thinking operationally means thinking in terms of how things really
work—not how they theoretically work, or how one might fashion a bit of algebra capable
of generating realistic-looking output.” (p. 127)
Continuum thinking: reasoning in terms of continuous processes rather than discrete events.
Scientific thinking: striving for quantification rather than precise measurement. Developing
hypothesis and being rigorous about testing them.
Habits of minde
The
systems thinker’s habits of mind according to Linda Booth Sweeney
(http://www. lindaboothsweeney .net/thinking/habits)
1.
Sees the Whole: sees the world in terms of interrelated “wholes” or systems, rather than as
single events, or snapshots;
Looks for Connections: assumes that nothing stands in isolation; and so tends to look for
connections among nature, ourselves, people, problems, and events;
Pays Attention to Boundaries: “goes wide” (uses peripheral vision) to check the boundaries
drawn around problems, knowing that systems are nested and how you define the system is
critical to what you consider and don’t consider;
Changes Perspective: changes perspective to increase understanding, knowing that what we
see depends on where we are in the system;
Looks for Stocks: knows that hidden accumulations (of knowledge, carbon dioxide, debt,
and so on) can create delays and inertia;
Challenges Mental Models: challenges one’s own assumptions about how the world works
(our mental models) — and looks for how they may limit thinking;
Anticipates Unintended Consequences: anticipates unintended consequences by tracing
loops of cause and effect and always asking “what happens next?”
21
B
=
12.
Habits
Looks for Change over Time: sees today’s events as a result of past trends and a harbinger
of future ones;
Sees Self as Part of the System: looks for influences from within the system, focusing less
on blame and more on how the structure (or set of interrelationships) may be influencing
behavior;
. Embraces Ambiguity: holds the tension of paradox and ambiguity, without trying to resolve
it quickly;
. Finds Leverage: knows that solutions may be far away from problems and looks for areas
of leverage, where a small change can have a large impact on the whole system,
Watches for Win/Lose Attitudes: is wary of “win/lose” mindsets, knowing they usually
makes matters worse in situations of high interdependence.
of mind according to the Waters Foundation (http://watersfoundation.org/systems-
thinking/habits-of-a-systems-thinkery):
Ne
© 90
12,
Big picture: Seeks to understand the big picture
Change over time: Observes how elements within systems change over time, generating
patterns and trends
Systems’ structure: Recognizes that a system’s structure generates its behavior
Interdependencies: Identifies the circular nature of complex cause and effect relationships
Changes perspectives: Changes perspectives to increase understanding
Assumptions: Surfaces and tests assumptions
Considers issue fully: Considers an issue fully and resists the urge to come to a quick
conclusion
Mental models: Considers how mental models affect current reality and the future
Leverage: Uses understanding of system structure to identify possible leverage actions
Short term / long term consequences: Considers both short and long term consequences of
actions
. Unintended consequences: Finds where unintended consequences emerge
Time delays: Recognizes the impact of time delays when exploring cause and effect
relationships
Successive approximation: Checks results and changes actions if needed
22
