Children’s Misconceptions as Barriers to Learning
Stock-and-Flow Modeling
Oren Zuckerman and Mitchel Resnick
MIT Media Laboratory
20 Ames Street E15-020, Cambridge MA 02139 USA
{orenz, mres} @ media.mit.edu
ABSTRACT
Research has shown that people have difficulties understanding dynamic behavior. In an attempt
to better understand the nature of these difficulties, we have developed a new modeling tool and
conducted an exploratory study with young children. The modeling tool, called System Blocks, is
a set of communicating plastic boxes with embedded computation that facilitates hands-on
modeling and simulation of stock & flow structures. In the study, 5" grade students were asked to
perform several assignments with System Blocks, dealing with concepts such as rates,
accumulation, net-flow, and positive feedback. Our initial findings suggest there are common
patterns in the way children think about dynamic behavior, which might account for some of the
difficulties children as well as adults have when faced with dynamic behavior in general and
stock & flow models in particular. These patterns include a tendency to prefer: quantity over
process (stock over flow), sequential processes over simultaneous processes, and inflow over
outflow.
INTRODUCTION
Research has shown that people’s understanding of systems behavior is extremely poor (Booth-
Sweeney & Sterman, 2000; Dorner, 1989; Resnick, 1994; Sterman, 1994). Booth-Sweeney &
Sterman showed that business school students have a poor level of understanding of stock & flow
relationships and time delays. Dorner used computer simulations in his experiments and showed
how poorly people perform when dealing with real life problems with interdependent features. He
argued that people rely on a primary mechanism of “extrapolating from the moment” when
dealing with temporal patterns. Resnick showed how people assume centralized control for
patterns they see in the world, when in fact many phenomena are self-organizing, coordinated
without a coordinator. Sterman listed the different barriers to learning that organizations face,
including misperception of feedback, flawed cognitive maps of causal relations, and more.
Sterman recommendations for improving the learning process include: eliciting participants’
knowledge, using simulation tools, and improving scientific reasoning skills.
Existing stock & flow simulation tools such as Stella (isee systems) and Vensim (Ventana
Systems) are easy to use, but not easy enough to enable novices to model without training.
Building on the body of work in constructionist research (Piaget, 1972; Papert 1980, 1991; Kafai
and Resnick, 1996), the approach we took is to make dynamic processes visible and manipulable
through physical interaction. Towards that end, we have developed System Blocks, a new hands-
on modeling and simulation tool (Zuckerman & Resnick 2003). System Blocks were designed to
provide an easier introduction to systems modeling and simulation. The blocks are physical, with
knobs that enable real-time interaction with a running simulation. The dynamic behavior is
represented using different mediums, including moving lights, sound, and a line graph. Special
attention was given to create an “equation-less” modeling process, to prevent possible barriers to
learning equations might cause.
Figure 1. System Blocks simulating water flow through a bathtub
We conducted an exploratory study with ten 5" grade students. These students used System
Blocks to interact with core system concepts. We conducted one-on-one interviews with the
students while they used System Blocks to model and simulate systems that relate to their own
lives. We observed how the 5" grade students show tendency towards sequential processes, and
how the interactive simulation and the visibility of the simulated processes enabled them to
recognize the simultaneous activity. In the same way, we observed how they interact and adapt
their theories about concepts such as inflow, outflow, stock, net-flow, and positive feedback.
Based on our study we report on several misconceptions and tendencies, with regards to young
children’s understanding of systems concepts. In addition, we suggest two preliminary
conclusions: (1) Multi-sensory representation of a system simulation can help children understand
key systems concepts; for example, sound helped the children recognize rate-of-change in an
accumulation process. (2) An iterative process of modeling and simulation, performed by the
children themselves, might help children revise their current conception of dynamic behavior and
help them adapt new theories based on their simulation experience.
Our findings are based on an exploratory study and a small sample. Nevertheless, the patterns we
observed can be helpful pointers to some of the difficulties children and adults might have when
trying to learn about the behavior of systems. Further study should be conducted to examine the
nature of these tendencies and to further suggest practical strategies that can help people develop
richer understanding of systems concepts.
EXTENDED EXAMPLE
Consider the dynamic system modeled in Figure 2. Children participate in a “cookies store”
activity at school, where they bake and sell cookies to school’s students. Some students bake the
cookies at the school kitchen and pass them to a cookies basket, while other students sell the
cookies to other students.
stock block
inflow block “ys outflow block
inflow outflow
variable variable
Figure 2. System Blocks simulating a “cookies store” example
This system behavior can be modeled using System Blocks (see Figure 2). The inflow block
represents the “baking cookies” rate, the stock block represents the “number of cookies in
basket”, and the outflow block represents the “selling cookies” rate. When this model is
simulated, students can play different scenarios and see how the system reacts.
For example, increasing the inflow rate by turning the dial on the inflow variable block (baking
more cookies) will increase the stock (number of cookies in basket). Increasing the outflow rate
by turning dial on the outflow variable block (selling more cookies) will decrease the stock
(number of cookies in basket). Further tinkering with System Blocks enables students to quickly
get to the next step, analyzing net-flow dynamics: If the inflow is set to a higher rate than the
outflow, the stock will increase; If the outflow is set to a higher rate than the inflow, the stock
will decrease; finally, if the inflow and outflow are set to exactly the same rate, the stock level
will not change and the system will remain in a state of dynamic equilibrium. In our cookies store
example, dynamic equilibrium means the number of cookies in the basket stays constant, while
cookies are being baked and sold all the time.
The above scenario represents a generic system structure. Other simplified real-life examples that
can fit this structure are a bank account balance, amount of homework left to do, pollution level
in the atmosphere, and amount of calories in the body, to name a few.
If a stock represents “amount of calories in the body”, then the inflow is “consuming calories” or
“eating”, and the outflow is “exercising”. A person familiar with this generic structure would
know that in order to decrease the amount of calories in the body and maintain a new balance one
must pay attention to the inflow and outflow at the same time, and not focus only on one of them.
Building on this simple generic structure, consider the following next step: the students that bake
the cookies want to make sure the cookies basket is always full. They watch the number of
cookies in the basket, and they bake new cookies if this number decreases. This scenario
describes a goal-seeking system. The goal is to keep the “actual number of cookies in basket” as
close as possible to the “desired number of cookies in basket”. The students are an integral part of
the system. They monitor the goal (number of cookies in basket) and adjust the inflow (baking
more cookies) based on the gap between the actual stock level and the desired level. In our study
we have not modeled the time delay it takes to bake the cookies (“baking time”). System Blocks
can model this time delay in the same way as any other stock & flow modeling tool, by adding an
additional stock block for “number of cookies in oven” with a “cooking time” outflow.
METHOD AND DATA ANALYSIS
We conducted our empirical study with 5" grade students at 2 different schools: the Carlisle
Public School in Carlisle, MA and the Baldwin Public School in Cambridge, MA (see Table 1).
The goals of the study were to evaluate System Blocks as a new modeling and simulation tool, to
surface any misconceptions children might hold about dynamic behavior, and to investigate the
potential of an interactive simulation environment as a method to overcome these
misconceptions.
Our research approach was a qualitative one. We used a clinical interviews approach where an
interviewer presents brief, standard tasks to the students, and then probes the students’
understanding based upon their response to the tasks.
The two groups of 5" grade students differ in their prior instruction in systems concepts. The
Carlisle Public School is part of the “Waters Foundation” program, where systems thinking
concepts are introduced and used starting at elementary school. The Baldwin Public School
students had no prior instruction in systems concepts.
Grade level | School socio- Prior instruction in Number of
name economic | systems concepts participants
status
5" grade Carlisle | High Prior instruction. Part of | 5 students
the “Waters
Foundation” program.
Familiarity with Stocks
and Flows and Behavior
Over Time Graphs.
5" grade Baldwin | Mixed No prior instruction. 5 students
Table 1: Overview of schools where study was performed
The 5" grade interviews were conducted in 2 one-on-one sessions of 45 minutes each. The
interviews incorporated a standard set of probes but they were loosely structured and designed to
follow up on what the students said. The main activities in each interview were: (1) mapping of
picture cards onto a simple inflow-stock-outflow structure. (2) Simulating the model and
analyzing net-flow dynamics using moving lights and sound. (3) Analyzing net-flow dynamics
using real-time line graph. (4) Analyzing models with simple positive-feedback loop. All sessions
were videotaped for later analysis.
Table 3 lists some of the picture cards examples used during the sessions (both with and without
positive feedback).
Inflow Stock Outflow
flow into bathtub water level in bathtub flow out from bathtub
am «
getting money spending money
baking cookies
number of cookies made
eating cookies
number of sick people
interest in characters
people join the trend
number of people in the trend
people leave the trend
Table 2: Examples of picture cards used during the sessions
OBSERVATIONS
The students reacted positively towards System Blocks as a modeling interface:
“T like the blocks much more than working on the computer. With the computer, you click buttons
and insert numbers and then a window opens and you see the result. With the blocks, I can see
the flow, I can change this dial and see the lights move faster.”
“I think the lights and the sound are very helpful. Also the graph is helpful, but I like the sound
better. Starting with the lights, and then hearing the sound, and then seeing the graph worked
great.”
The simulation capabilities of System Blocks were essential to the students’ iterative cycle of
having a theory, testing it out, and revising the theory. This process of testing and revising
confronted students with their own misconceptions time after time, and was effective in helping
them use their own senses and observations to come up with a new theory. They did it quickly. It
appeared as if they had no problem changing their theories. This is a core benefit of System
Blocks. A simulation that can be operated by the student alone is critical to help students revise
their theories when they fail. Without a simulation tool, student could hold to their false theories,
or drop them but adopt new false theories. In my activities with the students I repeatedly observed
how System Blocks gives them a framework to test and revise their theories.
During the sessions I asked the students to generate their own examples. I asked them to think of
examples that match the system structure we simulated of inflow, stock, and outflow. In addition,
l asked them to pick examples that relate to their own lives. Table 3 lists the examples generated
by the Carlisle students, and table 4 the ones generated by the Baldwin students. Table 5 lists
selected pictures of the Baldwin students’ examples.
Student’s Inflow Stock Outflow
gender
Male 1 Reading over a Books read -
week no outflow
Male 2 How many minutes | Pages I have already -
I read a day read no outflow
Female | Getting books from | # of books I have Returning
library books
Female 2 Speed Iam running | Total number of MinI | -
ran. no outflow
Later changed to:
Total yards
Male 3 Responsibility of Total chances of me Grandma’s
me caring for my getting another pet health status
current pets
Table 3: Carlisle 5" graders personal examples for real-life systems
Student Inflow Stock Outflow
Male 1 Getting a basketball | Practice How good you
are
Male 2 When I win games | How much I won -
no outflow
Female | Putting book in the | Bookshelf is filled Children take
shelf the books
Female 2 How much I dance | How much! get tired | How I feel
after
Male 3 Buying a LEGO set | Putting it together Finish and
play with it
Table 4: Baldwin 5" graders personal examples for real-life systems
Inflow Stock Outflow
Things Yatnle tes | How anaty | ann Wings Wed calnne do ev,
ore “ a Wy
A
KE
vu
J
Ge a Bade tal
SS
<Q a 4
Ss x
oa er ce
ee
_ How gehyy ave
ocekshelf GS ‘a
oO
bookshelf i's
Si Heal,
take the 7
booles -—
3
Table 5: Examples of drawings made by the Baldwin school students
Throughout the sessions we observed several misconceptions and tendencies students held about
dynamic behavior in general and systems concepts in particular. Our observations are based on an
exploratory study with a small sample, but nevertheless, the patterns observed might serve as
helpful pointers to some of the difficulties people have when trying to learn about
systems concepts. There were surprising differences in the type of tendencies between the
students with and without prior instruction. System Blocks were effective in surfacing those
tendencies with both groups of students.
= Sequentially over Simultaneously: a tendency to think in a narrative way (beginning, middle,
and end), A causes B then B causes C. Thinking about processes as if they happen one-at-a-
time, rather than simultaneously. Occurred more with the Baldwin students (the group with
no prior instruction).
= Quantity Over Process: a tendency to favor quantity (something that can be counted) over
process (an activity). When mapping real-life examples to Stock & Flow models, students
that had this problem mixed the inflow (activity, process) with the stock (amount of
something, quantity). Occurred more with the Carlisle students (the group with prior
instruction).
= Inflow Over Outflow: a tendency to give higher priority to the inflow rather than the outflow.
When dealing with a problem, students with this tendency preferred to increase or decrease
the inflow and did not pay enough attention to the outflow. Occurred more with the Carlisle
students (the ones with prior instruction). When analyzing line graphs, students with this
tendency connected the slope of the graph to the inflow, and completely ignored the influence
of the outflow (the slope represents the net-flow, which is the difference between the inflow
and the outflow). Occurred more with the Carlisle students (the group with prior instruction).
= Minor differences will not make a difference: When minor differences exist between an
inflow and an outflow, students ignored the change these differences would create over time,
and assume the system would stay in balance or not change. No differences observed between
the two student groups.
= Linear vs. curved: students did not pay enough attention to the curvature of line graphs. They
focused more on the direction of the graph (going up or down), and not so much on the
curvature. From mathematical (and real-life implications) point of view, there is a major
difference between linear and curved growth (or decay). This problem night be addressed by
improving the way line graphs are presented to students. Teachers can pay more attention to
line curvature, using computer-generated graphs when possible, and emphasize the difference
between straight and curved graphs. Occurred more with the Carlisle students (the group with
prior instruction).
DISCUSSION
Our findings are based on an exploratory study and a small sample, and should be regarded as
such. We have showed that using System Blocks, both students with or without prior instruction
in systems were capable of performing Stock & Flow modeling, simulation and analysis. Students
were able to correctly map different real-life examples into Stock & Flow structures, and when
errors were made, the interactive nature of System Blocks helped the students revise their models
by themselves. In addition, students were able to map their own personal experiences to Stock &
Flow structure. System Blocks were most effective in helping students understand the net-flow
dynamics concept (that emphasizes simultaneous processes).
With regards to positive feedback, our observations suggest that 5" grade students are capable of
learning feedback concepts (Zuckerman 2004). Further research should be done to prepare the
relevant educational scaffolding to support learning of feedback concepts at a younger age.
Summarizing the misconceptions and tendencies, it seems that students with prior system
thinking instruction had a tendency to favor inflow over outflow and quantity over process. On
the other hand, they were faster to “shake off” the tendency for sequentially over simultaneously.
It seems that System Blocks might help to decrease the number of misconceptions with regards to
net-flow dynamics and graph curvature, if used when these concepts are introduced to students
for the first time.
System Blocks offer a delicate integration of tangible, physical representation and abstract,
dynamic behavior. The blocks are tangible, but represent abstract entities. The picture cards serve
as an intuitive way to create analogies, mapping the abstract entities with real-life examples. The
students had no problem shifting between different domains in a matter of minutes - from
physical examples such as water flowing and cookies baked to emotional examples such as level
of anger to social networks examples such as trends and diseases. In the same way that children
build a castle from LEGO or wooden blocks and pretend it is a castle, they can pretend a box is a
bathtub and blinking lights are flow of water.
In the interviews we played a key role as the facilitator, and could have directly influence the
students’ performance. We challenged the students and at the same time might have guided them.
It is not clear if a student working independently can yield the same results. In a classroom
environment, teachers would play the role of the facilitator. Teachers have a great deal of
knowledge about their students’ character, style of learning, and behavior in a group setting.
Further study should be done to evaluate how effective System Blocks can be in a small group
setting with a teacher as the facilitator, working with the proper educational materials.
In this paper we showed how System Blocks provide students an opportunity to confront their
misconceptions about dynamic behavior through a hands-on, interactive process of modeling and
simulation. Many factors can be the cause for students’ misconceptions and tendencies, including
prior instruction, prior life experiences, the design of System Blocks interface or the specific
examples we have used in our interviews. Nevertheless, our exploratory study suggests that one-
on-one interaction with a student using an interactive simulation tool such as System Blocks can
help students confront their current conceptions about dynamic behavior, and provide students an
opportunity to revise their mental models towards a deeper understanding of systems concepts.
ACKNOWLEDGMENTS
We would like to thank: Saeed Arida for the blocks’ physical design. Ji Zhang, Timothy Brantley,
and Brian Silverman for software and hardware support. Carlisle’s and Baldwin’s 5" grade
students. Carlisle’s SD mentors Rob Quaden and Alan Ticotsky. Baldwin’s Technology
Specialist Espedito Rivera.
This research could not have been done without the generous support of the LEGO Company, the
MIT Media Lab’s Center for Bits and Atoms (NSF CCR-0122419), Things That Think and
Digital Life consortia.
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