Research in Engineering Education Symposium 2011 - rees2009

Universidad Politécnica de Madrid (UPM) Página 44 de 957
example, enhance their belief that voltage and current in an ideal source are always in
phase (Kautz, 2011). Interestingly, it appears as if in this case it is not a lack of connection
between model and real-world objects that causes difficulties for many students, as
suggested by Carstensen et al. (2005) in the context of a lab activity on transient behavior
of electric circuits. Instead, students may make too close a connection between the
graphical representation of the mathematical formalism and the real-world objects to
which they (perhaps incorrectly) ascribe certain properties.
In this paper, we present further evidence that even after instruction (1) many students
have very basic difficulties with electric potential; (2) that they often do not recognize that
the content they are expected to learn constitutes a theoretical model with certain rules
and assumptions; and (3) that they fail to appreciate that these assumptions may be
satisfied to varying degree in a real-life apparatus.
Modeling aspects of circuit analysis
A large part of introductory science and engineering instruction can be thought of as the
teaching of conceptual and quantitative models of natural and technological phenomena.
About twenty years ago, David Hestenes (1992) argued, that “to understand science is to
know how scientific models are constructed and validated. The main objective of science
instruction should therefore be to teach the modeling game.” In engineering education, this
view may not be completely shared, but for students to recognize that the course content
largely consists of such models may be necessary for their functional understanding of the
material.
The formalism of DC and AC circuit analysis, as it is taught in the first and second semester
of several engineering bachelor programs at Hamburg University of Technology, consists
of a set of rules that relate measurable physical quantities that can be ascribed to certain
physical elements with specified properties. In this linear circuit model, the rules are
Kirchhoff’s circuit laws regarding currents (KCL) and voltages (KVL), whereas Ohm’s law
and its generalization (U = I·Z) for reactive elements specifies the properties of the
elements resistance, inductance, and capacitance. The remaining elements are ideallyconducting
connecting wires (U = 0), and voltage or current sources (U = const., and I =
const., respectively). While it is mentioned early on that incandescent light bulbs do not
obey Ohm’s law, a discussion of non-linear elements usually only takes place in the second
semester of the course.
Context of study
Our study on student understanding of electric circuit concepts involved students in
various first-year electrical engineering courses at two institutions in Hamburg, Germany,
as well as students in an electronics laboratory course at an institution in the United
States. The data presented in this paper were all obtained in the first semester of two yearlong
courses for mechanical and naval engineering students (TUHH-ME) or for general
and electrical engineering students (TUHH-EE) at our home institution in Germany.
Proceedings of Research in Engineering Education Symposium 2011
Madrid, 4 th - 7 th October 2011