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a short time, and were able to better explain their
understanding of electric circuits.
Our protocol analysis of interviews with stu-
dents solving circuit problems brought to light a
number of difficulties students exhibit in both DC
and AC circuit domains (Schwartz, et al., 2000;
Biswas, et al., 2001). The misconceptions appeared
to fall into three general categories: (i) those
specific to particular AC or DC concepts (such
as believing an AC voltage varies in space along
the wire rather than in time), (ii) general difficul-
ties (such as a failure to differentiate concepts, or
incorrect simplifying assumptions when multiple
invariants have to be applied to analyze circuit
behavior), and (iii) lack of basic circuit knowl-
edge, such as when to apply particular invariant
properties and laws of circuit behavior, and in
analyzing the behavior of dynamic elements, such
as capacitors. We created a list of misconceptions
related to understanding AC circuits (Table 1).
cal engineering students. We found that students
had the most difficulty with the invariant principles
underlying dynamic elements, such as capacitors
(45% correct vs. 62% correct on questions not
involving capacitors). Students appeared to have a
better understanding of other invariant principles,
such as Ohm's law, and applied them more cor-
rectly in circuit problems (63%). An analysis of
incorrect answers revealed a significant number
of misconceptions and difficulties (see Figure 1).
Eight of twenty student answers indicated they
possessed a current consumption (or “empty pipe”)
model of current, in which current flows from
the positive side of a voltage source (DC or AC)
sequentially and is consumed by the components.
Five students revealed an “electron flow” model
similar to the current consumption model except
that flow starts from the negative terminal. Three
students revealed a lack of knowledge about the
relationship between power (light bulb wattage)
and resistance, and six students tended to ignore
the role of a capacitor in a circuit altogether. Stu-
dents had the most difficulty with AC capacitor
circuits (or filter circuits). The concepts of power
(via bulbs) and the behavior of capacitors would
thus later become a focus of the fourth phase of
research utilizing an animated circuit simulation.
The context-dependent nature of students'
knowledge of circuit behavior suggests that the
difficulties students have in understanding electri-
cal circuits are directly linked to instruction. Härtel
(1982) believed that many learning difficulties
can be traced to the fact that instruction is done
in a piecemeal fashion, and students are never
taught how to analyze a circuit as a system with
interdependent components and constraints on
behavior. This plus our own observations led us
to develop an invariants-based framework that we
believe experts apply in problem solving tasks,
and we turned to a dynamic assessment approach
(Campione and Brown, 1985, 1987; Bransford, et
al, 1987; Magnusson, Templin, & Boyle, 1997)
that focuses on how to prepare students to learn
through instruction.
Ac/dc concept Inventory
The catalog of student difficulties had performing
circuit analysis formed the basis for the develop-
ment of a set of multiple-choice questions to as-
sess student understanding with larger groups of
students: the AC/DC Concept Inventory (Holton,
Verma, & Biswas, 2008). The questions asked
for qualitative (not quantitative) answers, and
unlike traditional multiple choice tests in which
only the correct answers matter, these questions
have foil responses that are specifically linked to
particular misconceptions our group and others
have identified. The correct answers to our test
questions matter as well, because they are written
to specifically target core invariant principles of
circuit behavior that experts use (see Table 2 be-
low). We can analyze both correct responses and
incorrect responses for information about students'
understanding of invariants, their misconceptions
and other learning difficulties.
We administered a paper and pencil version of
the multiple-choice test to twenty 2nd year electri-
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