MICROWORLDS BASED ON LINEAR EQUATION SYSTEMS: A NEW APPROACH TO COMPLEX PROBLEM SOLVING AND EXPERIMENTAL RESULTS

Z Funke

General Experimental Procedure

In our experiments, subjects pass through at least two phases. In the first
phase, the knowledge acquisition phase, subjects can explore the system and
its behavior as they like (learning by exploration; see also Moray, Lootsteen,
& Pajak, 1986; Shragcr & KLahr, 1986). They can take actions (i.e., make an
intervention on one or more of the exogenous variables) and observe the
resulting effects in the endogenous variables. Figure 2 shows how the SINUS
microworld is presented to subjects.

Press "space bar" Io select an intervention, choose a value
and then press "return”

Figure 2: Screen display of the numerical version of DYNAMIS when presenting
system SINUS after four week (= trials) on the first block. The upper part
shows the state of the three endogenous variables, the lower part shows past
interventions.

Exploration is possible within four blocks following one after the other. Each
block consists of a certain number of trials (referred to as “weeks "in the cover
story) which all depend on each other. From one block to another the system
is reset to the same starting values. From time to time we measure the
knowledge that has been acquired so far by asking subjects for a graphical
representation of their structural knowledge (“causal diagrams”). In the
second phase, called knowledge application phase, the subject has to reach a
defined system state and try to maintain the variable values as close as
possible to the values defined as goal states. In this phase, we measure the

Chapter 14 Micro worlds Based on Linear Equation Systems

quality of the operator’s control by assessing the distance between the current
and the goal values for all endogenous variables.

Some comments on measuring structural knowledge and system performance
seem necessary at this point because this is central to our studies. A review on
techniques for knowledge assessment can be found in Kluwe (1988). Also,
Rouse and Morris (1986) discuss some of the diagnostic problems in more
detail.

Measuresfor qualify of identification and control

Starting with control performance quality, the goal is to determine how well
a given goal state is approximated by the operator’s interventions. The
classical approach requires the measurement of the deviation from the target
system state in terms of the root mean squares criterion (RMS). This indicator
reflects the mean deviation, independent of sign. The weights of individual
deviations become increasingly higher the farther away they are from the
target state. A good discussion of the frequently used RMS criterion can be
found in Poulton (1973) and Bbsser (1983).

Our solution for this problem is a logarithmic transformation of the goal
deviation. This transformation leads to an evaluation of distances which is
from our point of view more efficient: larger distances are no longer weighted
more heavily. Rather, they are considered less important by this
transformation because of an assumed decrease in measurement reliability
with increasing goal distance. The transformation, thus, reduces the error
variance that increases as a function of the operator’s distance to the goal
state.

In the experimental section the variable “QSC” refers to this kind of
dependent variable ("Quality of System Control”). A low QSC score
representsa good score because it results from low discrepancies between goal
values and the values subjects reached on the endogenous variables through
their control behavior.

Measuring the structural knowledge an operator has acquired about a system
also requires some kind of distance Orsimilarity measurement. In this case the
distance exists between the structural relations hypothesized by subjects and
those implemented in the system. For this purpose, the subject marks on a
sheet (or in some versions directly on the screen) the assumed causal
relationships at certain points in time (either at the end of each trial or at the
end of a block of trials). This results in a subjective causal structure similar to
the real one shown in Fig. 1.

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