Stock-Flow-T hinking and Reading stock-flow-related G raphs:
An Empirical Investigation in Dynamic T hinking A bilities
Giinther Ossimitz
University of Klagenfurt, Austria
Department of Mathematics Education
Universitatsstr. 65
A-9020 Klagenfurt A ustria/Europe
phone: +43-463-2700-3132
fax: +43-463-2700-3199
ossimitz@ bigfoot.com
http://quenther.ossimitz.at
Preliminary Version January 2001
Prepared for the 2001 System Dynamics Conference, Atlanta, Georgia
Stock-Flow-Thinking and Reading stock-flow-related Graphs:
An Empirical Investigation in Dynamic Thinking A bilities
Giinther Ossimitz
University of Klagenfurt, Austria
Department of Mathematics Education
ossimitz@ bigfoot.com
ABSTRACT
This paper reports on an empirical study of the ability of university students to discern
between stocks and flows, and as such is a sequel to the "Bathtub Dynamics" - study of
Sweeney and Sterman (Sweeney/Sterman 2000). The 154 subjects were given six different
tasks. Some of the tasks required the ability to read and interpret time-graphs, others did not.
Two of the tasks were taken directly from the Sweeney/Sterman (2000) study.
The findings of this study were alarming. On the first task, which dealt with the difference
between federal budgetary deficit (a net-flow) and public debt (a stock), the mean perfor-
mance of the candidates was approximately on the same level as if they had flipped a coin for
each answer. Generally the study showed severe deficits in the ability to discern between
stocks and flows. These deficits did not depend upon whether the tasks required the
candidates to read or to draw graphs or not. Graphs showing the development of flows over
time were interpreted by many subjects as if these were graphs of stocks.
In almost all tasks the females scored significantly poorer than the males. At the present
stage of investigation I have no reasonable explanation for this massive gender bias. Further
research might help to reveal something of this mystery.
A number of extreme correlations between different criteria concerning the performance of
the bathtub tasks (which have been taken from Sweeney/Sterman) suggest that there might
exist a core ability which triggers all other stock-flow-thinking capabilities: this is the ability
to grasp that a positive net-flow results in an increase of the corresponding stock.
The study revealed serious deficits in stock-flow-thinking, which urgently need an
educational "therapy". It is a major challenge for systems-oriented education to design and
evaluate appropriate courses.
1 Stock-Flow-T hinking
Discerning between stocks and flows is not only important for System
Dynamics (SD) modelling (see Forrester 1961, Richmond 1993, Sterman 2000),
but, can be considered a genuine component of Systems Thinking (ST) abilities,
too!. This is argued in some detail by Sweeney/Sterman (2000) or Ossimitz
000 pp 52ff), who identifies four basic ST dimensions:
Thinking in Interrelated Structures ("Vvernetztes Denken").
Dynamic Thinking, which means a thinking which is not restricted to
grasping just snapshots of a situation, but takes into account evolution over
time.
Thinking in Models, which means that any systems thinker should be aware
that he or she is always dealing with a model of a complex situation, which
is usually massively simplified compared with the "actual" situation.
Systemic Action, which means the practical ability of steering systems.
I will refer to the ability to discern between stocks and flows as "Stock-Flow-
Thinking". Stock-Flow-T hinking is an important aspect of both the "Dynamic-
Thinking" and "Thinking in Models" dimension of ST.
Stock-Flow-Thinking is a natural ability for any SD modeler and actually the
ability to make models by distinguishing between stocks and correlating flows is
in the very core of the SD modeling technique. Nevertheless the basic difference
between stocks and flows is very important outside SD modeling, too. Let me
give two examples taken from economic life:
Public debt vs. federal deficit:
In Austria, the public debt has become a serious problem over the last 30 years.
Although one of the wealthiest nations in the world, this small nation with 8
million inhabitants accumulated a public debt of about 200 billion Euro up to the
year 2000.” Nevertheless it is not the public debt, but just the federal deficit, i.e.
the annual increase in public debt, which has been considered in the public
political debate in Austria. Politicians claimed a decrease of federal deficit from
say six billion Euro in the year 1996 to four billion Euro in the year 1997 as a
"budgetary consolidation". In fact, nothing has been consolidated, the public
debt increased in both years together by another ten billion Euro.
! Different aspects of systems thinking are discussed in some detail in Dorner (1996), Draper (1993), Forrester
(1994), Frensch/Funke (1995), Gould (1993), Gomez/Probst (1997), Richardson (1991), Richmond (1991,
1993), Senge (1990) or Vester (1999). For a comparative overview concerning different uses of the term
"systems thinking" see Ossimitz (2000, pp 9-62).
? This is about half the total public debt all 52 states of the whole A frican continent - which has a 100 times the
population of Austria - had at the beginning of year 2000.
3
Balance sheet vs. profit-and-loss-statement:
I occasionally ask business administration students in my lectures about the
difference between the figures in a balance sheet and the corresponding profit-
loss-statement. Of course they know which figures are to be found in each of
these sheets, but they find it very difficult to say why these data are organized in
two different sheets and are not combined in a single sheet. Almost no one
recognizes that the figures in a balance sheet refer to a point of time, e.g. Dec
31 2000, whereas the figures in a profit-and-loss-statement refer to a time
period, e.g. the whole year 2000. This means the balance sheet contains only
stocks, the profit-and-loss-statement just flows.
2 The Sweeney/Sterman (2000) Study
My own study was motivated by John D. Sterman's plenary presentation of the
Sweeney/Sterman (2000) paper at the 2000 SD Conference in Bergen, Norway.
There John Sterman presented primarily the results of two "bathtub dynamics"
tasks, which were presented with two different cover-stories (the literal filling of
a bathtub, see Fig. 1, and a more abstract cash-flow.).
1. Consider the bathtub shown below. Water flows in ata certain rate, and exits through
the drain at another rate:
=
The graph below shows the hypothetical behavior of the inflow and outflow rates for
the bathtub. From that information, draw the behavior of the quantity of water in the
tub on the second graph below.
Assume the initial quantity in the tub (at time zero) is 100 liters.
100
Inflow
/
75
g Outflow
€
2 's0: acaitiecncue| sami aera eae Cov
i
j
~ 25 4
0
) 2 4 6 8 FU) 12 14 16
Time (Minutes)
200
i wo 4
pb
Pw: |
° Z 7 € a w i w
‘Time (Minutes)
Fig. 1. Original "Bathtub-Task 1" from Sweeney/Sterman (2000)
Sterman stressed in his plenary presentation that the results of the (highly
educated) MIT-students were rather poor. Sweeney and Sterman had identified
seven criteria which were then used to evaluate each drawing. Table 1 gives the
percentage of correct answers according to the different criteria.
Swweney/Sterman Ossimitz
N=95 N=154
31]When the inflow exceeds the outflow, the stock is rising 0,87 0,42
32 |When the outflow exceeds the inflow, the stock is falling 0,86 0,43
33 |The stock should not show any discontinuous jumps (it is piecewise continuous) 0,96 0,64
34 |The peaks and troughs of the stock occur when the net flow crosses zero. 0,89 0,56
35 [During each segment the net flow is constant so the stock must rise (fall) linearly. 0,84 0,38
36 |The slope of the stock during each segment is +/- 25 units/time period. 0,73 0,26
37 |The quantity added to (removed from) the stock during each segment is 100 0,68 0,27
lunits, so the stock peaks at 200 units and falls to a minimum of 100 units.
Mean for all items 0,83 0,42
Table 1 Performance on the Bathtub Task 1.
In my own study there were 154 subjects, divided into three groups:
- 104 students at the beginning of their business administration studies at
Klagenfurt University (Masters degree). Their age was mostly 19-21.
- 25 students (from different Viennese universities and various depart-
ments) just before playing the beer-game. Their age varied from 20 - 30.
- 25 students of environmental systems studies at the beginning of a
systems modeling course at the University of Graz. Their age varied from
19 - 24.
About 60% of the 154 subjects of my study had just finished their secondary
school education at age 18 or 19. The rest were students of higher semesters at
university, but without a university degree.
In general, the results of the bathtub - tasks in my own study were considerably
poorer than those of the MIT study. For a more detailed discussion see 4.3 and
4A,
3 My own Study
The Sweeney/Sterman (2000) study did not disclose whether the observed prob-
lems of the subjects were due to deficits in stock-flow-thinking or due to deficits
in the ability of reading and interpreting graphs. So I tried to create some addi-
tional tasks which should help to discern between these issues. My own study
contained six tasks:
Federal Deficit vs National Debt (FD ND-Task)
Arrivals and departures in the Alpenhotel (ADA-Task)
Bathtub Task 1 (from Sweeney/Sterman 2000, see Fig. 1) (BT 1-Task)
Bathtub Task 2 (from Sweeney/Sterman 2000)? (BT 2-Task)
Filling of an Oiltank (FO-Task)
Filling and emptying of a Bathtub (FEB-Task)
(1
(2
(3
(4
(5
(6
The Federal Deficit vs. National Debt Task (FD ND) intended to test whether the
subjects were aware of the difference between national debt (as a stock) and
federal deficit (as a net flow). No graphs were involved in this task.
The Arrivals and Departures in the Alpenhotel Task (ADA - see Fig. 2) was
designed to check the ability of the subjects to read and interpret a graph
showing the number of guests arriving and departing on a daily basis. In this
graph two flows were given, and qualitative answers concerning the stocks
behind the flows had to be answered.
Arrivals and Departures in the Alpenhotel 18.12. - 10.1.
fe FX } a
ee ‘ita
q
§
18.Dez 25.Dez 01J an 08.) an
Fig. 2: Arrivals and Departures at the Alpenhotel (ADA)
3 In this task the inflow followed a sawtooth wave, decreasing and increasing linearly between +100 and 0.
7
The bathtub tasks BT1 and BT2 should help to compare the achievements of the
subjects of my own study with those of the Sweeney/Sterman study. The
subjects were given exactly the same tasks as by Sweeney/Sterman (2000)*.
The Oiltank-Filling-Task (OF - see Fig. 3) was designed to interpret a flow
graph which is even simpler than the Bathtub task BT 1. The inflow of oil starts
at t=1 instantly with a rate of 200 Litres/Minute and stops at t=16. The questions
should indicate the ability of the subjects to interpret the graph correctly.
Filling of an Oil-Tank
300
=== Inflow
g 200
2
E 100
0
0 5 10 15 20
Time (minutes)
Fig. 3: Oiltank-Filling-Task (OF)
The Filling and Emptying of a Bathtub Task (FEB) was intended to check the
ability to create a graph of the amount of water in a bathtub according to a story
given in a reading text. This was designed to help to identify stock-flow-think-
ing capabilities without interference from the subjects' ability in interpreting
graphs.
4 Basic Results
The study was undertaken with 154 students (62 female, 92 male). Most of the
volunteers were born between 1979 and 1981 (=aged about 20 years at the time
of the investigation in autumn 2000). Sixty of the subjects stated subjectively
that they had excellent or good experience in reading and interpreting graphs,
“| translated the text into German; the graphics were simply copied from Sweeney/Sterman without alteration. In
the text the terms "inflow" and "outflow" were translated as "Zufluss" and "Abfluss".
8
only eleven voulunteers thought that their ability to deal with graphs was poor or
very poor. About half of the persons stated that their mathematics grade at the
final "Matura"? exam was excellent or good, which is higher than the average of
all mathematics grades at Matura exams in Austria.
The last preliminary question "Have you ever heard about stocks
("Bestandsmassen") and flows ("Bewegungsmassen’) in statistics?" received the
answer "no" from 83% of the test candidates.
4.1 The Federal Deficit vs National Debt - Task (FDND)
The aim of the FDND task was mainly to reveal how the subjects were able to
discern between National Debt as a stock and Federal Budgetary Deficit as the
corresponding net flow.
Ina land called Fantasia the amount, by which the federal expenses exeed the
federal income in one year is called the "Federal Budget Deficit". In 1998 the
Federal Budget Deficit in Fantasia was 60 Billion Dollars, one year later it was
40 Billion Dollars. Please check which of the following statements are either
right, wrong or not answerable! If you are not sure, please check don't know!
Fig. 4 Cover-Story for the FDND task
The following table shows the distribution of the answers to the individual
questions®,
Tight wrong] notans) | dont
werable know
10 | In the year 1999 20 Billion Dollars of public debt have been paid back 28% 68% 3%
(m: 76% / f: 56%)
11 | The Minister of Finance could reduce the public debt from 1998 to1999 by a third. 53% 36% 8% 3%
(45% / 24%)
12 | If the Minister of Finance in Fantasia is able to reduce the federal budget deficit to zero 19% 62% 13% 6%
Dollars, (a balanced budget), then Fantasia does not have any more debt. (70% / 52%)
7 7 ; - 7
13 | The public debt in Fantasia grew both in 1998 and in 1999. eo 29% 19% 6%
14 | If the Minister of Finance in Fantasia is able to reduce the federal budget deficit to zero 1% 52% 21% %
Dollars, (to budget balanced), then Fantasia has reached its highest public debt ever. (24% / 6%)
15 | A decrease in federal budget deficit implies automatically a decrease in the public debt. 48% 42% % 6%
(55% / 23%)
Table 2: Performance on the FDND task
The percentages in the second rows in the shaded cells give the percentage of
correct answers among the male (left) and female (right) subjects. Any of the
5 The Austrian "Matura' is equivalent to the German "Abitur exam. It finishes secondary education after 12" or
13" class and qualifies for any university study in Austria. Its level is somewhere between the US high-school-
degree and a first college degree.
° The boxes marked grey represent the correct answers. For item 10 both answers "wrong" and "not answerable"
were considered correct.
9
indicated differences is significant on a 5% level’, the bold printed values are
significant on a 1% error level.
The average performance on each item was less than 45%! To make clear how
disastrous this result is we should remind ourselves of the following: If I had
instructed 70% of 154 complete ignoramuses to throw a coin to choose by
chance between "right" and "wrong" and the other 30% to roll some dice to
choose with equal chance one of the three answers "right", "wrong" or "not
answerable", the expected average performance of this club of idiots flipping
coins and rolling dice would also be 45%!
Out of the 45% performance the males consistently scored significantly higher
than the females. We will see that this is true also for most of the other tasks.
For me this finding is a big surprise. It definitely cannot be explained simply by
saying that the female subjects are generally inferior to their male colleagues.
The average math grades at the Matura of the female students was 1,9 (ona
scale of 1(best) - 4(worst), whereas the men scored just 1,97 on average. Most
of the students attended my own lessons after the test and also here I did not find
that the females were inferior in their achievements compared to the males.
Although I have considerable experience in empirical studies in a broad variety
of educational issues, this is actually the very first time that some significant
difference in the performance between the sexes appeared.
4.2 Arrivals and departures in the Alpenhotel - task (ADA)
In the ADA-task the candidates were given an inflow and an outflow (arrivals
and departures) of hotel guests as a graph (Fig. 2). The main goal of this task
was to see whether the subjects can infer the stock of guests from these flows.
The task was constructed in such a way that in the first period from Dec 18"
until Dec 27" every day the number of guests arriving was higher than the
number of guests departing. For the rest of the time the opposite was true. So
from Dec 18" until 27" the number of guests was rising and from Dec 28" until
Jan 10" the number of guests was decreasing. So the maximum number of
guests was in the hotel on the night from Dec 27" to Dec 28". In questions 21
and 22 this fact was addressed. The results were disastrous.
21) How can the graphic be used to discern (in an fast and elegant way, without
any tedious calculations, but just by looking at the graph!) when the most guests
were in the hotel? Explain how you might manage this.
7 The hypothesis that both sexes have the same percentage of correct answers was tested using a Chi-Square
independence test.
10
Only 16% of the subjects gave an answer which could be interpreted as
something like "where the two lines intersect". 27% of the answers could be put
in a group where the subject stated at least that the arrivals and departures had to
be compared and the difference between these values is somehow relevant. 10%
gave plainly the wrong answer "where the number of arrivals is maximum".
Most of the verbal answers to this item were messy and hard to interpret.
22) On which day were the maximum number of guests in the Hotel ?]
This item was correctly answered by just 24% (m: 34%, f: 10%) of the subjects®.
60% (m: 48% f: 74%) of the answers were Dec 22™ or one day before or after
that day, which is the peak of the arrivals. Another 9% of the subjects took the
peak of the departures (Jan 6" +1 day) as their answer.
Item 23 (On which day was the maximum number of departures?) was correctly
answered by virtually all subjects. Just 4% picked Jan 7" or 5", while 3 out of
154 persons gave a completely wrong answer.
The comparision between the answers to items 22 and 23 allows the interpreta-
tion that subjects tend to interpret a graph as a graph of stocks, even if it is actu-
ally a graph of flows. To read the maximum from a curve in a graph seems to be
a trivial task, if we ignore the minor problems of some subjects to read the hori-
zontal time axis (which is a bit uncommon in this example) precisely. In item 22
a highly significant difference between the genders can again be observed.
5 Any of the answers Dec 27", Dec 28" or "the night from Dec 27" to 28" was counted as correct.
11
4.3 Bathtub Task 1 (taken from Sweeney/Sterman 2000) - (BT 1, see Fig. 1)
The bathtub tasks were taken with permission from the Sweeney/Sterman study.
The main results in Table 2 show that the performance was considerably poorer
than in Sweeney/Sterman (2000).
Swweney/ Ossimitz
Sterman
31]When the inflow exceeds the outflow, the stock is rising 0,87 0,42 (m: 0,53 / f:0,24)
32 When the outflow exceeds the inflow, the stock is falling 0,86 0,43 (m: 0,55 / f:0,24)
33]The stock should not show any discontinuous jumps (it is piecewise continouos) 0,96 0,64 (m: 0,72 / 0,53)
34 |The peaks and troughs of the stock occur when the net flow crosses zero. 0,89 0,56 (m: 0,66 / f:0,40)
35 |During each segment the net flow is constant so the stock must rise (fall) linearly. 0,84 0,38 (m: 0,52 / f:0,18)
36 |The slope of the stock during each segment is +/- 25 units/time period. 0,73 0,26 (m: 0,37 / f:0,10)
37 |The quantity added to (removed from) the stock during each segment is 100 0,68 0,27 (m: 0,37 / f:0,11)
lunits, so the stock peaks at 200 units and falls to a minimum of 100 units.
Mean for all items 0,83 0,42 (m: 0,53 / f:0,26)
Table 3: Performance on the BT 1
As in the other tasks, also in the BT task the responses of the female subjects are
significantly weaker than the responses of the males: The average performance
of the male subjects was 53%, about twice as high as that of the female subjects.
The criteria 31 to 37 are far from being independent of each other. On the
contrary: the criteria 31 and 32 resp. 36 and 37 are so highly correlated with
each other that each pair 31/32 and 36/37 can essentially be considered as a
single variable. In both cases only a few outliers prevent a perfect correlation.
Another very strong correlation is between the criteria 31/32 and 35: only 3
persons who miss criterion 31 succeed in criterion 35; just 8 of 95 persons who
miss criterion 35 are successful in criterion 31.
For other pairs of criteria the correlation was just "one-sided": e.g. those who
failed in criterion 31 trivially had no chance of succeeding in criterion 36. Out of
the 64 who succeeded in 31, 40 were also successful concerning criterion 36.
When comparing criteria 31 and 33 we have a somewhat different "one-sided"
situation: of the 64 subjects who succeeded in criterion 31 only 2 failed in crite-
rion 33. Very similar to the correlation between 31 and 33 is the correlation
between 31 and 34.
What can be learned from the interrelations between the criteria? The most basic
fact is that the ability to master criterion 31 "when the net flow is positive, then
the stock increases" (and its counterpart 32) is crucial for the whole set of other
criteria. Whoever fails on criterion 31, will most probably fail on all the others,
too. It seems noteworthy to me that criterion 31/32 is not a quantitative, but
° The percentages would have been slightly better if the 16 of 154 subjects who have given no answer to the BT1
task at all had been discarded.
12
essentially a qualitative criterion: it argues just with the sign of the net flow and
the resulting monotony of the stock. We can say that criterion 31/32 is the most
fundamental and elementary aspect of any stock-flow relation. In other words, if
this aspect is not understood properly, it is legitimate to say that the stock-flow-
relationship is not understood at all. On the other hand, for those who do
understand the difference between stocks and flows, criterion 31/32 is absolutely
evident.
The main didactic conclusion that can be drawn from this analysis is very
straightforward: teaching the fact that a positive net-flow induces an increase in
the stock and vice versa might be the most fundamental lever for acquiring a
practical knowledge of stock-flow relationships.
4.4 Bathtub Task 2 (from Sweeney/Sterman 2000)'° - BT2
The BT2 task is structurally very similar to the BT 1 task. The linear change of
the flow induces a non-linear (actually parabolic) change of the stock. This
makes this task considerably harder than BT 1. This can be easily seen when the
figures of table 4 are compared with those of table 3.
Swweney/ Ossimitz
Sterman N=79 N=154
41/)When the inflow exceeds the outflow, the stock is rising 0,46 0,25 (m: 0,38 / f:0,06)
42 |When the outflow exceeds the inflow, the stock is falling 0,41 0,23 (m: 0,36 / f:0,03)
43 |The stock should not show any discontinuous jumps (itis piecewise continouos) 0,99 0,71 (m: 0,74 / £:0,66)
44 |The peaks and troughs of the stock occur when the net flow crosses zero. 0,41 0,23 (m: 0,36 / f:0,03)
45 |The slope of the stock at any time is the net rate. 0,25 0,10 (m: 0,13 / f:0,06)
46 |The quantity added to (removed from) the stock during each segment of 2 time
units is 50 units. The stock therefore peaks at 150 units and reaches a minimum 0,34 0,14 (m: 0,37 / £:0,10)
of 50 units.
Mean for all items 0,48 0,28 (m: 0,39 / f:0,16)
Table 4: Performance on the BT 2
Concerning the gender-specific differences, the gap between the performance of
the male and femals subjects was even bigger for the BT 2 task. Items 42 and 44
were extreme: almost all of the persons who succeded on these criteria were
male!
Asin BT1 task, the criteria of the BT2 task are highly correlated. The basic
pattern is the same as in the BT 1 task:
- Items 41 and 42 are in almost perfect correlation
10 Tn this task the inflow followed a sawtooth wave, decreasing and increasing linearly between +100 and 0.
13
A subject who fails on criterion 41/42 most probably fails all the other
criteria, too.
4.5 Filling of an Oiltank (FO)
The FO task consisted of two parts. In the first part the discontinuities in the
graph should be explained. Two of three persons confirmed that such a graph
might be realistic, 25% of all subjects thought it might be not. Their arguments
differed highly in content and quality, so that it was very hard to group them.
About 9% of all persons made the point that the vertical discontinuity of the
graph would mean that the valves of the filling device had to open instant-
aneously. 6% argued that such an instant change in flow is impossible. Another
5% of all test-candidates argued explicitly in a way which made it clear that they
thought that the graph resembles the stock of oil in the tank.
The variety of answers to item 51 made one thing clear: there are numerous
ways that the graph could be understood in a different way than was intended by
me. One of the crucial aspects was the precise meaning of the word "filling".
Some subjects inferred(rr-r?) from the facts that the graph was titled "Filling of
an Oil-Tank" and that the time-axis was labeled from 0 - 20 minutes, that the
filling lasted for 20 minutes, since the "whole graph" was titled "Filling of an
Oil-Tank". Some of them argued that in the first and last four minutes the whole
thing was just connected, which has to be counted technically as "filling" time,
but no oil was flowing. Others argued that in the first and last four minutes the
thick inflow-line is just a trifle above the horizontal zero line, so that a minimum
of flow took place during these periods. I was baffled by how many different
plausible interpretations could be given for the same graph! These ambiguities
have to be taken into account when interpreting items 53, 55 and 56.
The following table gives the percentages of answers for all items'’.
Check the appropriate boxes!
Tight wrong not don't know
answerable
52 | The oiltank has been filled 200 cm high with oil. 8% 38% 47% 3%
53 | The filling lasted 16 minutes. 21% 71% 4% 1%
54 | Altogether 200 Liters have been filled in 18% 76% 4% 1%
(m: 83% f: 66%)
55 | After 16 Minutes 200 litres have been let out of the tank. 14% 68% 13% 3%
56 | The filling lasted 15 minutes. 68% 27% 2% 1%
57 | The oiltank’s capacity is 200 litres maximum. 4% 14% 16% 4%
58 | After 16 minutes there were 3000 litres more in the tank than before. 64% 22% 3% 1%
(m: 74% f: 50%)
Table 5: FO - Task (correct answers are shadowed)
' The balance to 100% did not respond.
14
The performance on the OF-task was clearly better than on any other task of my
study. For any item the percentage of correct answers was about 64 - 85%."
For items 53 and 56 I did not highlight a "correct" answer, because of the
different possible meanings of the word "filling", which has crucial influence
upon the question of which answer is correct. An analysis of the cross-tabulation
of the answers to these two items revealed some interesting details. No less than
14 out of 154 persons checked both assertions 53 and 56 as "wrong". Those
could be from the fraction who believes that the whole filling lasted for 20
minutes. But even more astonishingly 9 persons actually checked both assertions
as "true". Maybe they interpreted the statement "lasted 15 minutes" as "lasted at
least 15 minutes" and not as "lasted exactly 15 minutes".
The results of the FO - Task were less gender-specific than for the other tasks.
A highly significant difference’® could be observed just for the percentage of
correct scores on item 58 (m: 74%, f: 50%); another significant difference!*
could be found for the distribution of correct answers for item 54.
T also tried to find some correlations between the performance of the FO - Task
and the ADA - Task. Both tasks are based on the correct interpretation of a flow
graph. At the present state of my investigations no positive correlations can be
reported. The only anomalies I found were rather strange. When comparing the
scores of items 22 ("On which day are most guests in the Alpenhotel?") and 64 it
turned out that 36 of the 38 persons who gave the definitively wrong answer Jan
6" (or Jan 5" or 7") to item 22 answered item 64 correctly as "wrong"; the other
two gave the answer "not answerable" to item 64.
In short, I can summarize that the FO task results seem to be somewhat
independent of the results of the other tasks.
4.6 Filling and Emptying of a Bathtub (FEB)
The FEB task should test the ability of the subjects to transpose a story about the
filling and emptying of a bathtub into a graph of the amount of water over time.
The following table gives an overview of the results.
"? For Items 52 and 55 both answers "wrong" and "not answerable" were generously counted as correct.
'S Error-Level for Chi-Square: better than 1%.
\ Error-Level for Chi-Square: between 1 and 5 Percent.
15
FEB-Task scores abs all male female
Correct solution 44 29% 38,0% 145%
[Almost correct, minor inaccuracies 39° 25% 27.2% 22,6%
In the first 4 minutes the amount of water was considered to be constant, otherwise correct 10 6% 6,5% 6,5%
Partial solution or serious errors, but somehow plausible in the overall picture 19 12% 98% 161%
Very severe errors, very poor solution or just a minor part of the graph sketched 36 23% 15,2% 35,5%
No solution 6 4% 33% 48%
N= 154 100% 100,0% — 100,0%
Table 5: FEB-Task
In the FEB task slightly more than half of all the answers were correct or at least
almost correct. We again see a significant gender trend: among the correct solu-
tions male subjects are overrepresented, while in the category of the poorest so-
lutions the women are overrepresented.
An interesting question was whether the performance on the FEB task is some-
how correlated with some other score. First of all I could find a positive correla-
tion between the self- estimation of the subjects about their ability to deal with
graphs and with the performance on the FEB - Task. Of the nine persons who
estimated themselves as very good in dealing with graphs, four did indeed
provide a perfect solution to the FEB-Task. Similarly four of the six subjects
who estimated their knowledge concerning graphs as very poor were scored in
the poorest category on the FEB task.
A comparision between the FEB-Task and the BDND and ADA - Tasks
revealed some partial trends, but no result with statistical significance. A curious
detail is that almost all subjects who chose the wrong answer Jan 6" on item 22
performed well or very well on the FEB Task.
The cross-tabulation of the FEB-Scores with the "basic" criterions 31 and 41
"when the inflow exceeds the outflow, the stock is rising" of the BT1 and BT2
tasks brought significant results. The subjects who fulfilled criterion 31 were
significantly better’ in their performance of the FEB-Task. The correlation
between the criterion 41 and the FEB-Scores was highly significant on the 1%-
level. This gives some indication about a certain relationship between the BT
and BEF tasks.
5 Further investigations
At the present stage of the evaluation of the results only a few of the many
possible correlations between the test items have been checked for significance.
One of the very clear findings of this survey is the massive gender-bias of the
'S The error-level is only slightly below 5%.
16
results. I sincerely must admit that I have no explanation and not even a serious
hypothesis about the reasons for this finding.
Another interesting result emerges from the high correlation between several
criteria of the BT 1 and BT2 tasks. These correlations indicate that there might
be a fundamental aspect of stock-flow-thinking, which is a prerequisite for more
elaborate stock-flow-thinking capabilities. This fundamental aspect is the ability
to grasp that in a stock-flow-context the stock with one inflow and one outflow
is increasing when the inflow is bigger than the outflow (or the net flow is
positive, to put it in another way). Some findings indicate that this might be a
key criterion for discriminating between a stock-flow- thinker and a non-stock-
flow-thinker.
The present study raises a number of puzzling questions and indicates the need
for further investigations. The most serious issue is the fact that the practical
abilities in stock-flow-thinking and in interpreting graphs among students at
different Austrian Universities are shockingly poor. The situation among the
Austrian students is much severer than that of the highly educated MIT-students,
which Sweeney and Sterman described as being "on a poor level"
(Sweeney/Sterman 2000).
I hope that a closer investigation of the material of this study can reveal some
additional clues about how to deal with this problem in education. It is my
intention to develop within the next months a "Stock-Flow-Thinking Crash
Course", which is designed to overcome within a few hours of instruction the
deficits that have been shown in the Sweeney/Sterman and in my own study.
The crash-course should be applicable for a very broad audience; without many
technical requirements in mathematics, computer science or SD modelling.
I plan to evaluate the efficiency of this crash course in a pre-test - post-test
design. The pre-test should take place one or two months before the course; the
post-test at least two months after the course. In this way I hope to gain some
insights into the long-term efficiency of the course.
17
References
Dorner, Dietrich (1996): The Logic of Failure. (dt. Die Logik des Misslingens.) New
Y ork: Metropolitan Books/Henry Holt
Draper, Frank (1993): A proposed sequence for developing systems thinking skills A
proposed sequence for developing systems thinking in a grades 4 - 12 curriculum.
System Dynamics Review 9(2), 207-214.
URL: ftp://www.clexchange.org/documents/system-ed/S E 1993-01AP roposedS equence.pdf
Forrester, Jay W. (1961): Industrial Dynamics. Cambridge, MIT Press
Forrester, Jay W. (1994): System Dynamics, Systems thinking and Soft OR. System
Dynamics Review 10(2)
Frensch, Peter A./ Joachim Funke (eds) (1995): Complex Problem Solving - The
European Perspective. Mahwah: Lawrence Erlbaum Associates, Inc.
Gould, J. (ed) (1993): Systems Thinking in Education. Systems Thinking Review
(special issue)
Gomez, Peter / Gilbert J. Probst (1997): Die Praxis des ganzheitlichen Problemldsens:
vernetzt denken, unternehmerisch handeln, personlich tberzeugen. Bern: Paul Haupt
Ossimitz, Gunther (2000): Entwicklung systemischen Denkens. Munchen: Profil
Verlag
Richardson, George (1991): Feedback Thought in Social Science and Systems Theory.
Philadelphia: University of Pennsylvania Press
Richmond, Barry (1991): Systems Thinking: Four Key Questions. Lyme: HPS Inc.
Richmond, Barry (1993): Systems Thinking: Critical Thinking Skills for the 1990ies
and beyond. System Dynamics Review 9(2), 113 - 133.
Senge, Peter (1990): The Fifth Discipline: The Art and Practice of the Learning
Organization. New Y ork: Doubleday.
Sweeney, Linda Booth / John D. Sterman (2000): Bathtub Dynamics: Preliminary
Results of a Systems Thinking Inventory
Sterman, John D. (2000): Business Dynamics. Systems Thinking and Modeling for a
Complex World. New Y ork: Irwin/McGraw- Hill
Vester, Frederic (1999): Die Kunst, vernetzt zu denken. Stuttgart: DVA
18
Appendix A: Original testing form (translated)
19
4 min
1 Code Name:
2 Year of Birth: 3 Sex: male O female O
4 How well do you think you are able to read and understand graphs?
very well average very poorly
(6) (6) ) 6) (6)
5 Mathematics grade at "Matura"-exam 1- 2- 3- 4- no grade
6 In Statistics Classes, have you ever heard anything about stocks
(Bestandsmassen) versus flows (Bewegungsmassen)? Y es O NoO
If yes, please explain the difference between stocks and flows.
1)
Ina land called Fantasia the amount, by which the federal expenses exeed the
federal income in one year is called the "Federal Budget Deficit". In 1998 the
Federal Budget Deficit in Fantasia was 60 Billion Dollars, one year later it was
40 Billion Dollars. Please check which of the following statements are either
right, wrong or not answerable! If you are not sure, please check don't know!
Tight | wrong Tot
answerable
don't
know
10 | In the year 1999 20 Billion Dollars of public debt were paid back
11 |The Minister of Finance could reduce the public debt from 1998 to1999
by a third.
12. | If the Minister of Finance in Fantasia is able to reduce the federal budget
deficit to zero Dollars, (a balanced budget), then Fantasia does not have
any more debt.
13__|The public debt in Fantasia grew both in 1998 and in 1999.
14 _|If the Minister of Finance in Fantasia is able to reduce the federal budget
deficit to zero Dollars, (to budget balanced), then Fantasia has reached
its highest public debt ever.
15 |A decrease in federal budget deficit implies automatically a decrease in
the public debt.
20
2) 2 min
Arrivals and Departures in the Alpenhotel 18.12. - 10.1.
18.Dez 25.Dez 01J an 08.) an
The Alpenhotel opens for its Christmas season on Dec. 18" and closes on
January the 10". The graphic above shows for each day the number of arriving
(light squares) and departing (dark circles) guests. Please answer the following
questions:
21) How can the graphic be used to discern (in an fast and elegant way, without
any tedious calculations, but just by looking at the graph!) when the most guests
were in the hotel? Explain how you might manage this.
22) On which day were the maximum number of guests in the Hotel?
25) According to which criterion might you discern whether on a certain day the
number of guests is increasing or decreasing?
21
4)** (4min) Consider the bathtub shown below. Water flows in at a certain
rate, and exits through the drain at another rate:
———
The graph below shows the hypothetical behavior of the inflow and outflow
rates for the bathtub. From that information, draw the behavior of the
quantity of water in the tub on the second graph below.
Assume the initial quantity in the tub (at time zero) is 100 liters.
100 . . 1 1 1 1 1
~
a
Flows
(Liters /Minute)
a
o
N
a
) 2 4 6 8 10 12 14 16
Time (Minutes)
‘Quantity in Bathtub
a
Time (Minutes)
1 This is exactly the same as bathtub task 1 of the Sweeney/Sterman.(2000) study.
22
5)"” (4min) Consider the bathtub shown below. Water flows in at a certain rate,
and exits through the drain at another rate:
———
The graph below shows the hypothetical behavior of the inflow and outflow
rates for the bathtub. From that information, draw the behavior of the
quantity of water in the tub on the second graph below.
Assume the initial quantity in the tub (at time zero) is 100 liters.
100
Inflow
Time (minutes)
in Bathtub
4
a
i)
(liters)
So
i=)
Quaniti
wo
=)
‘) 2 4 6 8° to’ 2° ia” t6
Time (minutes)
'” This is exactly the same as bathtub task 2 of the Sweeney/Sterman (2000) study.
23
5) (4min)
The following graph describes the filling of an oil-tank:
Filling of an Oiltank
300
=== inflow
4 200
&
i
3 100
0
0 5 10 15 20
Time (Minutes)
Please answer the following questions:
51) Are the discontinuities in the graph of the function at time 1 resp. 16
reasonably explainable? Y es O NoO
If yes, how?
If no, why not?
Which of the following statements are true, false or not answerable?
Check the appropriate boxes!
right] wrong not
answerable
don't
know
52__| The oiltank has been filled 200 cm high with oil.
53__| The filling lasted 16 minutes.
54 | Altogether 200 litres have been filled in.
55__|After 16 minutes 200 litres have been let out of the tank.
56 |The filling lasted 15 minutes.
57__| The oiltank's capacity is 200 Liters maximum.
58 _|After 16 minutes there were 3000 liters more in the tank than before.
24
6) (3 min)
At 7:00pm exactly Mr. Maier starts to fill his (empty) bathtub. The inflow is
constant at 14 liters/min. At exactly 7:04pm Mr. Maier notices that the outflow
of his bathtub has been left open and he closes it. Through the open outflow
exactly 9 Litres/min leave the bathtub. At excatly 7:09 Mr. Maier closes the
inflow and enjoys his bath until 7:15pm. At exactly 7:15 he opens the outflow
and lets all the water flow out.
Amount of Water in the Bathtub
100
Litres Water
an
oo
Time (min)
61) Give in the above graphic an approximate sketch how the amount of water
in the Bathtub will develop over the time!
25
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