Research in Engineering Education Symposium 2011 - rees2009

Universidad Politécnica de Madrid (UPM) Página 46 de 957
of the potentials was greater than the other or that they were of equal magnitude. In task
(b), not only was there a larger number of nonblank answers given on both parts of this
task (about 250 in each case), but also the fraction of correct answers was substantially
greater, as close to 50% of the students gave a completely correct answer in the two cases.
From these results we infer that students even at this stage have considerable difficulty
interpreting a voltage source in a circuit diagram in terms of a mathematical statement of
a potential difference between two points in the diagram. Furthermore, these results
indicate that comparable questions about currents are answered by a substantially greater
fraction of students. This seems to confirm our claim that of the two concepts, voltage and
current, voltage is the one that proves more difficult for most students (Kautz, 2011).
Task (c) was again answered more or less correctly by about 30% of the students, while
about 15% stated that inserting an additional source between the specified points was not
possible. A surprisingly large fraction of students (slightly more than 20%) stated that the
value of the added source either had to be greater or that it had to be less than that of the
existing source. While we could not gain much insight into the students’ reasoning from
their answers, we suspect that students felt that one of the sources had to be, in some
sense, “stronger” than the other. It is possible that students were trying to imagine the
behavior of real batteries as they answered this question. We are hoping to get a better
understanding of student reasoning about this issue through interviews with individual
students.
Questions on applicability of model assumptions
Quiz question: In another quiz question, the students were shown the circuit diagram in
Figure 2, in which a battery was connected to a parallel circuit consisting of one branch
with two light bulbs and another with a single bulb. All bulbs were given to be identical
and the connecting wires were to be considered ideally conducting (as is the general
assumption for lines in a circuit diagram). However, two statements were made about
possible limitations to the usual idealizations implicit in the model: (i) It was stated as
unknown whether the battery could or could not be considered an ideal voltage source. (ii)
The I-U characteristic of the bulbs was stated as “unknown”. As part of the problem
description, outcomes of two measurements were given to the students: The current
through bulb B (the lower bulb in the series circuit) was given as IB = 0.3 A; the current
through bulb C (the one in the single-bulb branch on the right) as IC = 0.5 A. The students
were then given the following three tasks: (a) to determine the current IA through bulb A,
(b) to determine the voltage UA across bulb A relative to that across bulb C, and (c) to
decide whether either of two statements could be inferred from the given data: Statement
X, that the battery behaved as a non-ideal voltage source (i.e. that it had a non-vanishing
internal resistance, or Ri > 0), or statement Y, that the I-U characteristic of the bulbs is
nonlinear (i.e. that current and voltage are not proportional).
The current readings given to the students in this question were realistic values for
miniature incandescent bulbs but did not correspond to the values obtained if equal
resistances for the three bulbs were assumed. One purpose of the first two tasks, however,
Proceedings of Research in Engineering Education Symposium 2011
Madrid, 4 th - 7 th October 2011