An Experiment Using The Hexagon Technique With
Semiquantitative Computer Modelling
Arion de Castro Kurtz dos Santos
Departamento de Fisica - Projeto PROFECOMP
Fundacao Universidade Federal do Rio Grande - FURG - Brazil
arion@ calvin.ocfis.furg.br
Fabio Ferrentini Sampaio
Nucleo de Computagao Eletronica
Universidade Federal do Rio de Janeiro - UFRJ - Brazil
ffs@nce.ufy).br
Laércio Ferracioli
Laboratorio de Tecnologias Interativas A plicadas a Modelagem Cognitiva
Departamento de Fisica
Universidade Federal do Espirito Santo - UFES - Brazil
laercio@ npd.ufes.br - laercio@ cce.ufes.br
ABSTRACT
This paper reports a small experiment carried out with Master’ s degree students about the
development of semiquantitative models first using the VISQ modelling system and
STELLA afterwards. The conception, elaboration and representation of the models
included a conceptual phase using the hexagon technique (idons - combination of idea and
icon). A classical model, for coupled non-linear feedback loops, presented by Forrester
(1990), was used as a parameter to define the activity and as a validation criteria. Results
suggest that it seems recommendable to take students through a phase of developing the
conceptual model with idons, before working with the computer (VISQ). Despite the fact
that the model developed with STELLA is very simple when compared to Forrester’s,
results show that the students were able to construct a flux diagram taking into account the
VISQ model which was previously developed.
KEY WORDS: Computer, Modelling, Model, Semiquantitative, Idons, Hexagon,VISQ,
STELLA.
Paper partially financed by CAPES, CNPq, FAPERGS and FACITEC/ES
INTRODUCTION
This work is about the use of computer modelling systems in Science Education (Kurtz Dos
Santos, C., 1992). Each of the authors of this article is carrying out work in this area with
their research groups in different Brazilian Public Universities. In the end of 1998 there
was a Research Seminar (II Seminar about Modelling and Representations in the
Teaching-Leaming Process) at the Laboratory of Applied Interactive Technologies to the
Cognitive Modelling, at the Federal University of Espirito Santo (Brazil). Amongst the
different activities of the Seminar, there was a short course on Principles of Systems in
which the students had the opportunity to work with semiquantitative modelling using
VISQ modelling system (Kurtz Dos Santos, C., 1995; Kurtz Dos Santos. C. et al., 1997)
and (later) STELLA environment (Richmond, B. et al., 1987). The conception, elaboration
and representation of the models had a conceptual phase using the technique of hexagons
(Hodgson, A.m., 1994).
The association of Computer Science and Education has generated new strategies for
teaching and learning, making headway with teachers, students and school. A relatively
recent strategy of working with computers in education has been through Dynamic System
that is based on the representation of ideas with causal diagrams (Roberts, N. et al., 1983)
and its conversion to flow diagrams (Roberts, N. et al., 1983; Forrester, J. W., 1990;
Kurtz dos Santos, A. C., 1995) to be used in quantitative computer modelling system such
as STELLA. A semiquantitative computer modelling system called VISQ was developed
based on the same principles. It uses the mathematics of neural networks to allow the
animation of causal diagrams directly on the computer screen, with no need of using
numbers.
VISQ programme can be considered as a tool for leaning, making new ways of interaction
with school contents possible, such as learning through the interpretation of simultaneous
graphs, or through the discussion about the dynamic behavior of the elements during
simulation, which would be - perhaps - impossible with pencil and paper.
There are two possible ways of working with modelling systems that are based on System
Dynamics. The first one is through exploratory activities where the user explores a model
or a representation of a teacher or researcher previously placed in the modelling system. In
this case, the user interacts with simulations and is limited to the manipulation of
parameters. According to Mandinach, and B. & Cline, H. F. (1994) the manipulation of
parameters in existing models promotes basic research abilities such as the understanding
of causality and variations, and can directly influence the acquisition of content
knowledge, demanding a lower level of knowledge of the user. The other way is through
expressive activities, where the user presents or exposes her/his vision or mental model of
the situation that is being modelled. According to Mandinach, and B. & Cline, H. F. (1994)
model building promotes more general problem solving abilities and transference of these
abilities to other research areas.
This article presents results of a small introductory expressive actvity, where a small
group of students develop models, using three tools: the hexagons, for the systemic
thought, VISQ, for semiquantitative modelling and STELLA for the quantitative modelling
for a situation already presented in the literature (Forrester’ s one). In this study our
intention was to find some evidences about the effect of the use of a tool over its
predecessor and about the modelling process facilitation. The results presented here are
certainly modest, not generalizable, but they point to possible enlargement of the research
in future works.
2. VISQ - A SEMIQUANTITATIVE MODELLING SYSTEM
In this section we will make a brief introduction to the VISQ environment and its functions.
VISQ is a semiquantitative modelling system in which the mathematics is hidden from the
user, with no need of entering numbers, which means, it is suitable to be used by students
of elementary levels.
VISQ - an acronym for Interacting variables in a semiquantitative way - (Kurtz Dos
Santos, C., 1995; Kurtz Dos Santos. C. et al., 1997) was developed in cT (Sherwood, B. &
the Sherwood, J. N., 1989) and can be used in IBM 486 (and superior) PC compatible and '
Macintosh Quadra 605 '. It uses the mathematics of neural networks to animate causal
diagrams on the computer screen. The system supplies a systematic interpretation to any
causal diagram, allowing the creation of semiquantitative models without taking into
consideration the content, in natural as well as human sciences.
The neural network mathematics of VISQ works considering that each pair X > *Y (X
affects Y positively. See Figure 01) means that a change in the vertical level of Y is caused
by the semiquantitative state or vertical level of X. In other words, X is the rate of change
inY.
x ¥ lL.
Co—oe-
Figura 01 - X affects Y in a positive way, in VISQ, with its corresponding graphical
output of Y against time. Note that Y increases until it stabilizes due to the squashing
function used by the system. The horizontal line corresponds to the normal (resting) level
and coincides with the time axis.
A positive pair as presented in Figure 1 would he described by the following equation
dy |. _y2 i
meth? x -lp*Y)
where k and p are constants, limiting the levels of the involved variables to a variation
between -1 and 1. Notice that the level of Y will eventually damp with the time. Thus, the
causal diagrams or networks, will always evolve for a stationary state - equilibrium. A
person analyzing a causal diagram made with pencil and paper will be able to foresee
diverse dynamic behaviours as possible (viable) solutions. In VISQ, a causal diagram, will
have a unique interpretation.
Although, a model in VISQ will be able to contain many boxes representing variables with
negative and positive links between them, the mathematics is hidden from the user.
2.1 VISQ Functions
Through a direct manipulation interface, users can construct and simulate models that
represent causal relations between entities of the world to be modelled. The result of the
simulation is presented to the user in an interactive way (step by step) through the
animation of objects presented on the computer screen. The main window of VISQ presents
a tool bar that shows a set of all basic functions of the programme through icons (Figure
02).
CIOOSBRX MEW Ew
fae a
Lj © Ow A Xf bl ie) ae
Figura 02 - VISQ main window showing the tool bar and a model
CI - Represents a variable or a constant in the model.
© O. They represent the types of causal links (positive and negative) that connect the
boxes. The links can have different weights as shown in table 01. A link can be more
intense than others in the same model.
Links [Low Medium [High
Postve © @) ic)
[Negative S) ‘© S
Table 01 - Positive and minus weights of the links.
- The lens icon allows the change of names of a selected variable, as well as the
writing of a hypertext document containing information about the variables and “hot
words” to other variables.
- The hammer is used when it is desired to isolate a variable, allowing the observation
of the model without it.
- Icon X has two functions: to delete a box ora link and to reset the model values.
M. The Graph icon allows the observation of time evolution of any variable and its phase
diagram against another one. It is also possible to obtain up to six graphical outputs of
different variables at the same time using different colors for each variable.
- The pistol icon allows to simulate the model and to present the graphical window.
8] - The hand icon stops the simulation of a model and a graph presentation.
- The Sliders icon allows to change the speed, the damping, the time interval and the
scales of the graphs.
- The box and arrow icon supplies the semiquantitative initial values of dependent and
independent variables of a model. This function can be used by placing the pointer
directly on the vertical bar of the boxes and dragging it to the desired position.
Boxes and links can be dragged and rearranged on the screen, according to the user
discretion, using the pointer and pressing mouse down.
3- THE TECHNIQUE OF HEXAGONS APPLIED TO SYSTEMS THINKING
In this section we briefly present the Hexagon technique which has been used for modellers
working with enterprise modelling. In the present work, this technique was used by
students in a training phase, previous to the semiquantitative modelling phase with VISQ.
Hodgson (1994) proposes a bridge between the generalistic thinking of decision makers
and the specialized thinking of modellers, using the grouping of hexagons that allows the
combination of an idea and an icon - what he called idon. The core idea of this method
would be the semantic unit - the atomic object of thought. According to some authors, the
construction of conceptual maps with idons (Novak & Gowin, 1984) is the process of
making tacit models visible and available for the analysis of any person. The hexagons add
dimensions of flexibility and speed to the constant rearranging that happens when the
creative thought is made visible. The method proposed by Hodgson focuses on the
development of the conceptual model, during the modelling process. Although the
hexagons originally proposed are magnetic and plastic, the hexagons used in this study
were made of cardboard paper fixed on a flannel board for the development of the
conceptual model.
The method makes it possible to think about new hexagons representing events, processes,
objects or groups of concepts corresponding to variables that would be lacking to make the
conceptual model more complete.
The use of the hexagon technique can be questioned by more experienced modellers
(Hodgson, 1994). However, it is being used by people who do not have any experience on
modelling, but only an expertise in his/her field of work ora naive knowledge he/she wants
to elicitate.
In the present study, a particular situation was presented through a short text to the students
(See Section 6). Based on the content of the text and their own knowledge about the
situation the students were asked to develop their models with idons. The class was
divided into groups which worked for about 30 minutes. Afterwards, each group was
invited to present and comment the final model developed with the hexagons to the large
group.
4. The Problem
In this section we present the situation used for the development of the models and the
sequence of modelling proposed in the study.
A situation governed by coupled non linear feedback links, studied by Forrester (1990,
originally 1971) and presented in figure 03 was used in order to test the hypothesis of the
use of the hexagrams grouping as a method to facilitate the construction of models in the
computational modelling environment VISQ and STELLA. For doing so, we proposed the
sequence of modelling presented below:
System Thinkin, Semiquantitative Quantitative
Reasoning Reasoning
—_ _»+
IDONS VIsQ STELLA
In this case, the method of the hexagons - considered static when compared to
computational animations - would be the first step for the construction of the computational
model before using VISQ and STELLA which are dynamic. Thus, in this design, VISQ is
seen as a predecessor of the quantitative modelling with STELLA. The association of the
idons with VISQ would appear as facilitator of the modelling process and it would allow a
better knowledge on the system/process that will be modelled in a quantitative way. It is
important to point out that there has been no systematic study about the bridge between the
SEMIQUANTITATIVE REASONING and QUANTITATIVE REASONING regarding
computational modelling so far.
Thus, such methodology was applied in the proposed activity, enabling each group of
students to develop a conceptual model with idons for the same situation, which was
followed by the construction of a model in VISQ and the construction of a model in
STELLA.
The situation chosen to be modelled was very intuitive, consisting of the idea of acompany
that possesses its team of salesmen and, eventually, expands it depending on its production,
that is, on the solicitation of its products by the customers. However, there is a delay
between the solicitation and the delivery of the product, which is noticed by the customer.
Depending on the delay, the customer can seek for another company, an attitude that
would reflect in the salesmen recruiting.
The computational model developed by Forrester (1990) (Figure 03), here adapted for the
computational modelling environment STELLA corresponding to the situation, was
completely unknown to the students.
TIME FOR DELIVERY DELAY RECOGNITION TDDR
DELIVERY DELAY RECOGNIZED DDR
(-)
CHANGE IN DELIVERY DELAY ARCOGNIZED CDDR
SALESMEN S
SALESMEN HIRED SH ALES EFFECTIVENESS SE
(-)
DELIVERY DELAY IMPENDING DDI
ORDERS BOOKED OB
(+)
SALESMEN AD| UST TIME SAT
DeLyéRy RATE OR
(-)
omen
ORDERS ENTERED OE ORDERS COMPLETED OC
BACKLOG BL,
INDICATED SALESMEN IS
BUDGET 8
SALESMAN SALARY SS REVENUE TO SALES RS
Figure 03 - STELLA version of the model presented by Forrester (1971)
As shown in the model of Figure 03 the growth of the sales that is eventually suppressed
by the saturation of the production frequently happens through a system of relationships.
In this model, the positive link of the left controls the number of salesmen. The link on the
right is a second order negative one. The two levels in the largest negative link are Backlog
(BL) (not yet attended) and Delivery Delay Recognized (DDR), that is related to the
custumer’s perception of the delay. Inside both links on the left and on the right, there are
negative subordinate first order feedback link. The system consists of five feedback links -
a larger positive, a larger negative, and three smaller negative. The loops represented with
large (+) and (-), in Figure 03, correspond, respectively, to the larger positive and negative
links.
A detailed description of the model can be obtained in Forrester (1990). In the present
article, we will just present a qualitative description of the links, though in the Appendix a
complete version of the models equations in STELLA can be found.
Next, we present some information for a better understanding of the Forrester ‘s model
presented in Figure 03.
5. Understanding A Little More About the Forrester’s Model
In this section we briefly present the description of the main larger positive and negative
feedback links, aiming at the best understanding of the model in Figure 03, which is being
used as reference in this study.
5. 1. The Positive Link
In the positive link, a fraction RS of the capital of the solicitations is available in the budget
to pay expenses with the Salesmen. The suitable Salesmen are those that could be sustained
by the budget. Salesmen (S) are contracted (or dismissed) to adjust the current value of the
number of Salesmen in direction to the number of Indicated Salesmen (IS). When the
salesman sells more than enough to pay its own expenses, an expansion of the force of
sales takes place.
The orders booked depend on the number of salesmen and of the sales effectiveness. The
effectiveness of sales is a variable that depends on the time that the customer has to wait for
the delivery of the product.
The budget for the salesman's monthly expenses is computed of the Orders Booked
multiplied by the effective monetary units by unit of the product.
The Indicated salesmen are computed by the division of the monthly budget by the monthly
expense with each salesman.
Salesmen and Salesmen hired form a small negative feedback link. The Salesmen hired
rate adjusts the Salesmen in direction of the number of Indicated Salesmen (IS) that can
be sustained by the budget. The goal Indicated Salesmen (IS) comes from outside of the
negative link but it is a variable created by the positive link. It is the difference between
Indicated Salesmen and Salesmen (current), that motivates the hiring of more Salesmen.
5. 2. The Negative Link
In the largest negative link of the right, the orders that enter are placed in a group of not
filled solicitations that is decreased by the completed solicitations. The division between
the Backlog (BL) and the Delivery Rate (DR) supplies the Delivery Delay Impending
(DDI). Delivery delay here means that there was not time enough of such delay being
recognized and interfering in the market desire of purchase. A temporary delay intervenes
before the delivery delay is recognized. The sales effectiveness depends on the recognition
of the delay in the delivery of the product in such a way that a small delay will facilitate
the sale of the product while a larger delay will make it difficult.
The delivery rate depends on the group of solicitations to represent the fact that the
production capacity is limited.
The negative link as a whole tends to adjust the order rate to the maximum delivery rate
(production capacity), whenever the force of sales is large enough to support the total
production. If the order rate is larger than the maximum delivery rate, the group of
solicitations will increase.
Inasmuch as the work demanded in each machine tends not to increase anymore, the
delivery rate does not increase in proportion with the group of solicitations. An order rate
larger than the delivery rate will only cause an increase in the group of solicitations without
any growth in the delivery rate.
Out of the group of solicitations and of the delivery rate it is possible to deduce the “true”
delay in the solicitations. But this is not generally known by the customer. Even after being
aware of the delay in the delivery, the customer usually takes some time to redirect the
search for other company. However, there is a time delay between the delay of factory
delivery and the moment in that this affects the customer's readiness to request. The
Delivery Delay Recognized (DDR) is represented as a delayed version of the Delivery
Delay Impending (DDI). The delay is created in two steps, first the rate in which the
Change in Delivery Delay is Recognized (CDDR), and then the Delivery Delay
Recognition (DDR). Notice that the way Forrester works with delay is not intuitive and
demands a great modelling expertise.
If the goods were available for immediate delivery, each salesman in one month would
manage to sell, on the average, an amount that would be determined by characteristics such
as price, quality, readiness, adaptation to the customer's need, the maker's reputation, and
sales ability. But when the customer realizes that he/she should wait for the delivery, more
and more customers refuse to buy the goods, then reducing the average of the sales
effectiveness.
6. Research Methodology
In this section we present the research methodology showing how the activities were
carried out and making clear the data collection dynamics.
Physics and Computer Education Post-graduate students of Espirito Santo and Rio de
Janeiro Federal Universities, respectively, were asked to split themselves naturally into four
working groups. This paper focuses on the results of one of the groups only, describing the
development of a conceptual model using hexagons, and the modelling with VISQ
followed by STELLA. Our aim was to observe possible effects of using one tool compared
to the one used before in terms of facilitating the modelling process.
The following text (original in Portuguese) was used to present a situation to be modelled
with hexagons:
“ A company has a number of Salesmen which is increased according to production, or
demand of products made by clients. Nevertheless, there is a delay between the order of
the product and its delivery, noticed by the client. Depending on the delay, the client may
even look for another supplier, jeopardizing the hiring of new Salesmen”.
The development of a conceptual model makes it possible to think about the main events,
objects, processes, concepts to be translated into variables and then establish the possible
interactions present in the studied situation. The translation of the conceptual model into a
semiquantitative one makes it possible, through simulation, to intuit about tendencies of
expected dynamic behaviours and possible mathematical relations among variables. The
construction of a quantitative model, with STELLA, presupposes a rigorous study which
will be based on an iterative process involving the conceptual and semiquantitative
representations to the understanding of the passage which moves from semiquantitative to
quantitative reasoning.
The groups were asked to work during a certain time and try to reach an agreement on their
conceptual model with hexagons. Afterwards, the models were presented with the help of a
flannel board on which cardboard paper hexagons were fixed. Each group explained the
structure and entities of the conceptual model to the large group. All the detailed recordos
about the models presented were kept.
In the following activity, students were asked to develop a semiquantitative model using
VISQ corresponding to the previous model with hexagons, which had just been presented
to the large group. Students worked during a certain period of time, discussing within small
groups and saving computer versions of their models in VISQ which were given to the
researchers.
During VISQ model construction process, all groups were encouraged, in every
developmental phase, to ask for coloured superposed graphs of the main variables of the
model. It is important to point out that VISQ allows the simultaneous observation of up to
six variables of a model at the same graphical window. Based on the graphical analysis
students improved the structure of the model.
We believe that the superposition of coloured graphs of variables and the consequent
improvement of the model structure, as shown in the graphical analysis, as well as the fact
that no mathematical knowledge is needed to use VISQ, are aspects that add support to the
use of computers in Education, in our case the VISQ programme, and show advantages
over the use of hexagons or other static methods of representation.
Following the activities with idons and VISQ, students were asked to develop a model in
STELLA corresponding to the one constructed with VISQ. The groups spent some time
mapping in STELLA. The attribution of numbers and algebraic equations for running
models, giving back numerical and graphical output, showed to be extremely difficult in
STELLA. According to Kurtz dos Santos, A. C. (1992) STELLA metaphor is very
demanding in terms of world conceptions, which influences the idea students have about
variables. Differently from V1SQ, that allows students to freely choose entities, STELLA
structure works like a straight jacket, forcing students to use the idea or conception of rates
of change, which means that in order to model with STELLA an entity must be thought as
arate or a level. When the student is not familiar with such conceptions, he/she is not able
to express himself/herself successfully with the tool. Aware of the difficulties in using
STELLA, we searched for some evidences on the process of moving from modelling in
VISQ to modelling in STELLA, considering the coherence of STELLA diagram in relation
to models developed before with idons and VISQ. The computer versions of models
developed in STELLA were saved and given to the researchers.
7, Results of the Modelling Research Methodology to the Proposed Situation
In this section we present the models developed by students and the corresponding
discussion about its characteristics.
7. 1, Development of conceptual model with hexagons
The studied group was composed of three students and spent about 30 minutes for reaching
an agreement about the conceptual model which would be translated into idons and whose
representation by hexagons is showed in figure 04.
Education | Patience
Persuasion
Production
Bureaucracy
Quality of Modem
product. equipment
Quality of | Process of
employee
Lack of Extemal
material factors
Lack infra -
estructure
Figure 04 - Conceptual Model with Hexagons made by a Group of Students.
Kind of
service
Clients need
Economic
conjuncture
The conceptual model is composed of six blocks of hexagrams or hives that represent the
groups of related concepts. We can identify groups related to six concepts:
Group representing the Salesmen;
Group composed by a single hexagon representing the profit;
Group related to solicitations;
Group of the largest hive which represents the product or process of production;
Group representing the delay, to the right of the largest hive and
Group related to the external world, on the left of the largest hive.
Pe CoS
According to the discussion about Forrester’ s model presented in figure 03, STELLA
model has the following fundamental blocks: one related to the Salesmen, one to the group
of solicitations and another more sophisticated one representing the delay. Thus, it can be
noticed that the intuitive conceptual model developed by the students includes a range of
concepts needed for a later quantitative modelling with STELLA.
Although the students did not draw arrows showing the relationships amongst hexagons of
distinct hives, it was possible to observe the elicitation of such relations during the oral
presentation of the conceptual models.
7, 2. Modelling with VISQ
Figure 05, shows the group’s VISQ model which corresponds to the conceptual model
presented in figure 04.
Opcoes _ MODELO T3
Solicitation Bureaucracy
KL-——©
oo
e—) =
Lack infraegtructure
Extefhal factors
Figure 05 - VISQ model which corresponds to the conceptual model developed by
the studied group.
A detailed study of the intuitive conceptual models and VISQ semiquantitative models
shows that, apart from the hive composed by the hexagons <kind of service>, <clients
need> and <economic conjuncture>, interpreted as related to links with the external world,
there is a topological preservation of the conceptual models with hexagons and of VISQ
semiquantitative model. This result seems to reveal that the conceptual model guided the
development of VISQ semiquantitative model in some way.
For better understanding of VISQ model structure presented in figure 05, the spacial
correspondence between this model and the conceptual one with hexagons presented in
figure 04 was broken and the VISQ semiquantitative model was rearranged as presented in
figure 06.
Opcoes _MODELO [3
Solicitation
(+) Lack of material
tL
Extemal factors
rl Hl Lack infraegrrmcture
Modern equipments
Figure 06 - Rearranged VISQ model to better understanding its structure.
This new arrangement makes it possible to observe that the model does not contain any
feedback loop: it is basically composed of chains, e. g. {modern equipments| > |production|
> |quantity of Salesmen| > |profit|, and the pairs, e. g. flack of material| > |delay|.
Another observation is that there are 08 (eight) independent variables which are not
affected by others: |quality of Salesmenl, |lack of material, lack of infrastructure|, |external
factors|, [modem equipments|, [process of production|, |quantity of employees|,
fbureaucracy|. We can say that the model in general was rich in variables but poor in
structure, due to the absence of feedback.
In figure 04 conceptual model, besides the concept <Salesmen> qualities such as
<intellect>, <friendly>, <patience>, <persuasion> and <education> were also considered.
These five hexagons were considered in VISQ as a single variable: |quality of Salesmen|.
The hexagons <quality of employee>, <process of selection> and <project of qualification>
appeared in VISQ as a single variable |quantity of employees| . The justification for that
would be that the employees are hired through a process of selection and have their
qualification guided by the company’s project.
The hexagons <raw material>, <quality of product> and <process of production> were
grouped in a single variable in VISQ: [process of production|. The kind of raw material
used is related to the quality of the product and everything is part of the production process.
The remaining hexagons correspond exactly to the final variables in VISQ.
While running the model of figure 05 aiming at distincting initial semiquantitative values of
independent variables (vertical levels of boxes), students verified that it showed coherence
in terms of dynamic behaviour of the main variables. For example, when a company was
considered efficient the delay dropped, resulting in a higher production rate in more profit.
We can say that the obtained semiquantitative behaviour was partly in accordance with the
more sofisticated behaviour in STELLA, which can be considered a way of validating the
work done by the students.
7.3. Modelling with STELLA
See in figure 07 the model developed by the studied group for the situation in figure 05.
Time Delay Profits
Number of Salesmen
Costs
Figure 07 - STELLA model developed by the studied group.
Comparing the model in figure 03 to the ones in figures 04 and 06 we verify a similarity
between them. Comparing to figure 07 we see that the topology was partly destroyed. The
topology was preserved in only three links (‘production’ > ‘number of Salesmen’,
‘production’ > ‘delay’ and ‘production’ > ‘profit’). There are three new variables which
do not appear in VISQ model (‘clients’, ‘crises’ and ‘costs’). There are four new links that
do not exist in VISQ model, embodying those variables. A positive aspect was the
inversion in the direction of causality in STELLA, from ‘solicitation’ to ‘production’ and
not from ‘production’ to ‘solicitation’, inappropriately represented in VISQ model, what
makes evident a refinement of the students’ reasoning motivated probably by STELLA
methaphor.
In modelling with STELLA students took the VISQ model in figure 05 based on the idons
in figure 04 as working basis. In figure 07 STELLA model the conversors ‘number of
salesmen’, ‘profit’ and ‘delay’ correspond exactly to the hexagons in figure 04 and the
variables in figure 05. The conversor ‘costs’ refers to the process of production and does
not appear explicitly in any hexagon. The rate ‘solicitation’ and the level ‘production’
correspond to hexagons of distinct groups in figure 04 and to variables in figure 05. The
conversor ‘clients’ does not appear either in figure 04 nor in figure 05 and was used in
figure 07 as a determinant factor of ‘solicitations’ and as affected by ‘crisis’. There is a
coherence in STELLA diagram in terms of the models with idons and in VISQ taking into
account that the ‘clients’ lead to ‘solicitations’ (input rate) that will increase the
‘production’ (which is a level). ‘Production’ decreases due to ‘crisis’ (output rate). ‘Crisis’
affects the ‘clients’ and the ‘production’ changes the ‘number of salesmen’ and ‘profit’.
It seems that the process of moving from modelling in VISQ to modelling in STELLA
cannot be taken for granted and probably demands complementary activities to be given to
the students. Once the intuitive conceptual model already has the groups of concepts
necessary for a future quantitative modelling with STELLA, the passage from VISQ to
STELLA presupposes a careful reduction of variables and the placing of the remaining
ones inside STELLA metaphor. This appears to be the main factor responsible for the
insipid character of the developed model (in figure 07) and the consequent destruction of
the intuitive original topology.
8. Conclusion
Taking into account that this activity was exploratory and introductory, with a small
number of students, the results shall not be generalised, and only point to some tendencies
that need to be further explored in future research.
We can say that, in the present study, the conceptual modelling with idons helped the
students to define a specific topology to the model that would be constructed in VISQ. The
model with idons allowed students to work intuitively with conceptual before they could be
considered variables. In working with VISQ some hexagons were carefully reduced and
groups of hexagons were added in a single variable. Results suggest that it seems
recommendable to take students through a phase of developing a conceptual model with
idons, before working with the computer (VISQ).
Forrester’ s work was used as a parameter to define an activity and as a criterion for model
validation. Given the sophistication of such model, we were not expecting students to be
able of developing a similar model with STELLA. We understand that the attempt of
modelling in STELLA, having VISQ model as a basis, even only as a mapping of rates and
levels, was worth it. The model or map developed in STELLA by the studied group was of
avery insipid character compared to the model in figure 03, but had some relation with the
model with idons in figure 04 and with VISQ model in figure 05. The too demanding
STELLA metaphor may have destroyed the intuitive original topology, but there was still a
correspondence between hexagons and STELLA variables.
Thus, for the sequence presented at the beginning of the article
za Semiquantitative Quantitative
System Thinking Reasoning Reasoning
_— —_
IDONS VISQ STELLA
We can say that there is enough evidence to say that the thinking through idons is an
interesting tool to be used before VISQ.
Nevertheless, more research is needed to determine in which way the development of
semiquantitative models in VISQ can help the development of quantitative models in
STELLA. There is an indication that maybe it is possible to develop a flux diagram in
STELLA having a VISQ model as basis, but the question of STELLA model quantification
could not be developed in such study.
Readers interested in STELLA will find more information about it, as well as a demo
version of STELLA Research 6.0 in http://www.hps-inc.com/new/version6.htm .
9. Acknowledgements
This paper was partially financed by CNPq, CAPES, FAPERGS and
FACITEC/CMTC/PMV - Fundo de Apoio a Ciéncia e Tecnologia do Conselho Municipal
de Ciéncia e Tecnologia do Municipio de Vitoria, ES.
10. Bibliography
Forrester, J. W. (1990) Principles of Systems, Productivity Press, Portland, Oregon.
Hodgson, A.M. (1994) Hexagons for Systems Thinking. In MORECROFT J. D. W. &
STERMAN, J. D. (eds) Modelling for Learning Organizations, Productivity Press,
Portland, Oregon.
Kurtz dos Santos, A. C. (1992) Computational Modellign in Science Education: A Study of
Students’ Ability to Manage some Different A pproaches to Modelling, Unpublished
PhD Thesis, Institute of Education, University of London.
Kurtz dos Santos, A. C. (1995) Introdugao 4 Modelagem Computacional na Educacao.
Editora da FURG, Rio Grande.
Kurtz dos Santos, A. C., Thielo, M. R. & Kleer, A. A. (1997) Students modelling
environmental issues. J ournal of Computer Assisted Learning, Vol. 13, N°1, March.
Mandinach, E. B. & Cline, H. F. (1994) Classroom Dynamics - Implementing a
Technology-Based Learning Environment. Lawrence. Erlbaum Associates,
Publishers, Hillsdale, New Jersey.
Novack, J. D. & Gowin, D. B. (1983) Learning How to Lean. Cambridge: Cambridge
University Press.
Richmond, B. et al. (1987) An Academic User's Guide to STELLA. High Performance
System, Inc. Lyme.
Roberts, N. et al. (1983) Introduction to Computer Simulation - a System Dynamics
Modelling Approach. Addison Wesley, New Y ork.
Sherwood, B. A. & Sherwood, J. N. (1989) cT Version 2. 0. Falcon Software Inc.
Wentworth, N. H.
Appendix: STELLA model equations
BACKLOG BL(t)=BACKLOG BL(t- dt) +(ORDERS ENTERED OE -
ORDERS COMPLETED OC) * dt
INIT BACKLOG _BL =8000
INFLOWS:
ORDERS_ENTERED_OE =ORDERS BOOKED OB
OUTFLOWS:
ORDERS COMPLETED OC =DELIVERY RATE DR
DELIVERY DELAY RECOGNIZED DDRi(t) =
DELIVERY DELAY RECOGNIZED _DDR(t- dt) +
(CHANGE_IN DELIVERY DELAY RECOGNIZED _CDDR)* dt
INIT DELIVERY DELAY RECOGNIZED_DDR =2
INFLOWS:
CHANGE IN DELIVERY DELAY RECOGNIZED CDDR=
(1/TIME_FOR DELIVERY DELAY RECOGNITION TDDR)*(DELIVERY_DELAY_
IMPENDING DDI-DELIVERY DELAY RECOGNIZED DDR)
SALESMEN S(t) =SALESMEN _S(t- dt) +(SALESMEN_HIRED_SH) * dt
INIT SALESMEN_S =10
INFLOWS:
SALESMEN _HIRED_SH =
(1/SALESMEN ADJUST TIME SAT)*(INDICATED_SALESMEN IS-SALESMEN S)
BUDGET _B =ORDERS BOOKED OB*REVENUE TO SALES RS
DELIVERY DELAY IMPENDING DDI=BACKLOG BL/DELIVERY RATE DR
INDICATED SALESMEN IS =BUDGET_B/SALESMAN SALARY SS
ORDERS BOOKED_OB =SALESMEN_S*SALES EFFECTIVENESS SE
REVENUE TO SALES RS =10
SALESMAN SALARY SS =2000
SALESMEN ADJUST TIME SAT =20
TIME FOR DELIVERY DELAY RECOGNITION TDDR =6
DELIVERY RATE DR =GRAPH(BACKLOG BL)
(0.00, 0.00), (10000, 5000), (20000, 10000), (30000, 13500), (40000, 16000), (50000,
17500), (60000, 18500), (70000, 19000), (80000, 19500), (90000, 19575), (100000, 20000)
SALES EFFECTIVENESS SE =GRAPH(DELIVERY DELAY RECOGNIZED DDR)
(0.00, 400), (0.5, 400), (1.00, 385), (1.50, 370), (2.00, 350), (2.50, 320), (3.00, 289), (3.50,
250), (4.00, 209), (4.50, 178), (5.00, 150), (5.50, 120), (6.00, 100)
CC BY-NC-SA 4.0