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



320


J. Funke

Quantification of structural knowledge requires the following steps: for each
causal specification of a subject one first counts whether it belongs to one of
three classes of knowledge (relational, sign, or numerical; for a similar
classification, see Pldtzner & Sρada, in press) and whether it is correct or
false. Then, for each of the three levels one can determine the “quality of
system identification” (QSI) in terms of the difference between “hits” (HI)
and “false alarms” (FA), weighted by a “guessing” probability (ρ) according
to the following scheme, which closely resembles the discrimination index P,
from the two-high threshold model for recognition memory (see Snodgrass &
Corwin, 1988; the proposed “correction for guessing" dates back to
Woodworth, 1938):

QSI = (l-p) x [HVmax(HI)I-P × [FAZmax(FA)], -p ≤ QSI ≤ (l-p)   (5)

The guessing probability for numerical parameters in a dynamic system could,
for instance, be set to zero. In this case all hits are counted relative to the
maximal number of hits, max(HI). If one sets the guessing probability to 0.5
in the case of sign knowledge (assuming that plus and minus relations are
considered as equally probable by the subject), then errors lead to a reduc-
tion in the QSI index for that level.

The index for structural knowledge, which serves as a dependent variable in
the following experiments, is called “QSI" (“Quality of Identification”). A
high QSI score reveals a good score because of high correspondence between
implemented and assumed causal relations; it results from an additive
combination of the QSI-values for all three knowledge levels. An evaluation
study done by MiiIler (in press) demonstrates considerable reliability and,
thus, sufficient psychometric quality of this index.

Experimental Studies on System Properties2

In the following section three experiments on the role of different system
properties serve to illustrate the approach just outlined. The focus of the
experiments is on the role of active intervention into a system vs. pure
observation (Exp. 1), on the influence of different degrees of Eigendynamik
(Exp. 2), and on the influence of side effects (Exp. 3). For each of the
experiments the presentation includes a description of the independent, as well
as dependent, variables, subjects, material, and procedure, hypotheses and

2 This section follows partly the description of results given in Funke (1992).

Chapter 14 Microworlds Based on Linear Equation Systems

321


result, and a short discussion. Then, in the next section, a general discussion
picks up the interesting results and connects them with results from other
studies.

Experiment 1: Active Intervention vs. Pure Observation

Independent and dependent variables. In this first experiment (for more
details see Funke & Muller, 1988) learning by active interventions was
compared to learning by pure observation of the system’s development
(Factor 1: intervention vs. observation, I vs. O). This factor points to the
question if active regulation is really a necessary precondition for knowledge
acquisition about dynamic systems. If there is reason for the assumption of
different modes of learning (e.g., Berry & Broadbent, 1984, 1987), then
different results forknowledge and performance have to be expected under the
two treatments. In addition to the activity fac lor, the effect of a diagnostic tool
(subjects had to predict the system's next state) was compared to a no-
prediction condition (Factor 2: prediction vs. no prediction, P vs. NP). The
reason for this selection was to test the hypothesis if the diagnostic questions
show interference with the task or if this additional prediction request leads
to a deeper understanding of the system’s structure. The amount of
verbalizable system knowledge subjects had acquired (QSI, as measured by
the “causal diagram” at the end of exploration) and the control quality (QSC,
as measured via the distance of the actual to the specified goal states) served
as dependent variables.

Subjects, material, and procedure. Subjects were 32 college students from
Bonn University who participated in fulfillment of course requirements. Both
factors with two levels each were crossed completely yielding four different
experimental groups. In each of the four conditions eight subjects were run
individually. This allows for detection of “large effects” (f≈0.40, according to
Cohen, 1977) with oc=0.10 and β=0.30 for main effects. In the I- and O-
condition the method of experimental twins was used: Each subject in the O-
condition observed exactly that system data which another subject (the twin)
under the !-condition had produced (yoked-control design). So there was no
difference with respect to the self generated Orobserved information about the
system between the I- and O-conditions.

The Hiicroworld used was SINUS with parameters a=l, b=0, c=0.2, and d=0,9
in Eq. (2), (3), and (4). The system had to be manipulated during five blocks
of seven trials each. During the first four blocks subjects could freely explore



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