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



322


J. Furtke

the system. During the fifth block all subjects (both the 1- and the O-group)
were to reach and maintain a previously specified goal state.

Results. It was expected that the І-group should be superior to the “observers"
with regard to amount of knowledge as well as to control quality. Also, the
"predictors” should accumulate more knowledge than the "noπ-predictors".
Path-analytical evaluation of the data supported these expectations only
partially: The !-group was indeed better in controlling the system (significant
standardized path coefficient β=0.42, p ≤ 0.10 from I to QSC), but seemed to
know less than the “observers” (β=-0∙30, p ≤ 0.10 from I to QSl). “Predictors”
acquired more Verbalizableknowledge than "non-predictors,'(mean QSI: 1.02
vs. 0.57, F{lJS)=5.50, p ≤0.10). Knowledge about the system was generally a
good predictor of control performance (β=0.41, p ≤ 0.10 from QSI to QSC).
Interestingly, there was a negative relationship between the time spent on the
task and the quality of performance.

Discussion. The results demonstrate the effectiveness of both task
manipulations. Active interventions allow for better system control. However,
this effect is not accompanied by an increase in “extemalizable” knowledge.
Similar dissociations have been reported by Broadbent, FitzGerald, and
Broadbent (1986), Berry and Broadbent (1984, 1987), and Puu-Osterloh
(1987), for a critique see Sanderson (1989). Concerning the second factor,
requiring subjects to predict the next state increases the amount of knowledge
as revealed by QSI. Detailed analyses of the so-called “experimental twins”
- pairs of subjects who had to cope with the same system situations either
actively or passively - indicated a high interindividual variability: there were
no significant correlations between the twins* QSI and QSC scores, thus
showing the importance of person-specific ways of information processing.

Experiment 2: Effects of Eigendynamik

Independent and dependent variables. In this second experiment the effect of
different degrees of “Eigendynamik” was analyzed. Eigendynamik means that
an endogenous variable at time t has an effect on its own state at time t+1
independent of exogenous influences which might add to the effect. These
autonomous system changes represent a central feature of dynamic systems
compared to static ones, where changes can occur only due to active
interventions of an operator. In dynamic tasks, Eigendynamik implies the
existence of forces which are independent from the operator and which have
to foreseen with respect to future goal values of the system. Eigendynamik
requires from the operator to cope with temporal developments, either

Chapter 14 Microworlds Based on Linear Equation Systems

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increasing or decreasing the values of state variables, thus producing the
necessity to think about the system’s next states not only in terms of the
planned interventions, but also in terms of the system’s activity itself.
Eigendynamik can easily be detected in situations where the operator does not
make interventions; but such situations seldom occur because people think
erroneously that they only Ieam about a system by actively influencing it
instead, of looking at its behavior Withoutdisturbances. In case of exogenous
control activities, the separation of endogenous Eigendynamik from
exogenous interventions becomes much harder.

To realize different degrees of "Eigendynamik” within system SINUS,
parameters a and d from Fig. 1 and Eq. (2) to (4) were changed in three steps:
a=l, d=l: a control condition without any Eigendynamik (Condition O); a=l,
d=0.9: one variable with Eigendynamik (Condition 1); a=1.1, d=0.9: two
variables with Eigendynamik (Condition 2). Parameters b=0 and c=0.2 were
held constant Dependent variables were QSC for control performance and
QSI for verbalizable knowledge.

Subjects, material, and procedure. A total of 24 paid males doing their civil
service served as subjects. Under each of the three conditions eight subjects
were run individually. Assuming α=0.10 and "large effects" (f=0.40), the
power l-β proves to be at 0.50 in this case for the main effect (Cohen, 1977).
SINUS was used to simulate the system with the characteristics described
above. The system had to be manipulated during five blocks of seven trials
each. During the first four blocks subjects could freely explore the system.
During the fifth block all subjects were to reach and maintain a previously
specified goal state.

Results. It was expected that with an increase in Eigendynamik the amount of
acquired knowledge as well as the degree of control over the system should
deteriorate. Analysis of variance revealed only a significant effect for QSC
(F(2jd=3.23, p ≤ 0.10; mean QSC for Eigendynamik of 0, 1, and 2 are 3.86,
3.70, and 5.18), but not for QSI (Fft2Ij=I. 12, n.s.). Thus, increasing Eigen-
dynamik leads to a less good control of the system variables, but the causal
dependencies are equally well detected under all Ihreeconditions (but see the
restrictions of this interpretation because of medium power).

Discussion. Eigendynamikhas been previously reported to have an important
effect on the operators’ behavior (see de Keyser, 1990). The results of the
present study show that the degree of knowledge acquisition does not seem to
be influenced by Eigendynamik. In contrast, the control of the system varied
as a function of Eigendynamik. Particularly under the condition of two



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