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1993). In a sense the students are enacting the role
of the table and can sense that they have to push
up harder if more topics are added.
With more complex and simulated physical
systems, however, determining how to facilitate
such participation is more difficult. Most com-
puter-based simulations are symbolic simula-
tions, encapsulated representations of an external
physical system such as an electric circuit. In
contrast, experiential simulations are simulations
in which the user or learner is a functional ele-
ment, or agent, in the situation or system being
modeled. An example of this is Model U.N., in
which students from various schools take on roles
of different countries in pretend meetings of the
United Nations. The question I pursued though is
can students learn by participating in simulations
of complex physical systems as well as social
systems. Does enacting the physical and temporal
constraints that operate within a system help one
understand the behavior of the system as a whole?
one of the most difficult concepts for undergradu-
ate students to learn, and is also very difficult to
represent visually or explain verbally to students.
Most students may only memorize a formula or
a shortcut and never understand how or why a
capacitor exhibits this impedance, or how this
impedance characteristic is useful for designing
or troubleshooting circuits (such as radio tuners),
or how it is related to other invariant constraints
on circuit behavior such as Kirchoff's laws or
Ohm's law.
Imagine there is an interface to a circuit simu-
lation that allows you to directly vary the voltage
applied to a circuit, and the circuit responds in
real-time. You could alternate the voltage from
positive to negative just like an AC voltage source
does, with zero voltage being the middle, or rest-
ing point. Imagine also that you could both feel
the resistance of the circuit (Ohm's law), and see
resistance in the form of reduced current flow. A
circuit with high resistance would resist your ap-
plying voltage, and a circuit with low resistance
would be easy to apply voltage. The flow of charge
(current) through the circuit would also be visually
depicted as an animation, to redundantly specify
current and resistance.
A force-feedback steering joystick or steering
wheel (commonly available as interfaces for com-
puter games and simulations) may help students
embody and understand the constraints of an AC
voltage source. One may move the joystick or
wheel to the right to increase the voltage positively,
and to the left for negative voltages. Instead of
setting the frequency of an AC voltage source
by entering a numeric value or moving a slider
control, students enact a change in frequency by
changing how fast they move the steering wheel
from side to side. The force feedback compo-
nent allows one to make the joystick or steering
wheel harder to move if there is a higher circuit
resistance (or impedance), and easier for lower
resistance. In the aforementioned AC capacitor
circuit, the law governing how a capacitor's
impedance varies inversely with frequency can
Enactive Modeling Interface
for a Circuit Simulation
We applied the enactive modeling strategy to the
design of an animated simulation of electrical
circuit behavior. As mentioned before, electricity
is one of the most difficult subjects for students
to understand, and there are a great deal of mis-
conceptions about circuit behavior. Particularly
difficult are behaviors that change over time, as
in alternating current (AC) circuits. In an AC
circuit, the voltage changes very quickly, often
switching from positive to negative values. Further
complicating matters, some circuit elements such
as capacitors and inductors respond differently
based on the rate of change in voltage or current.
A capacitor in an alternating current (AC) electri-
cal circuit exhibits qualities similar to a resistor,
a virtual impedance, but unlike a resistor, the
impedance of a capacitor varies inversely with
the frequency of the AC voltage source. This law
of circuit behavior has consistently proved to be
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