Interviews with Upper-Level
Undergraduates about Plane Waves
Andrew J. Berger
The Institute of Optics, University of Rochester, Rochester NY
andrew.berger@rochester.edu
Goal: to investigate how students reconcile conceptual and mathematical
representations of electric field plane waves
Methods: 7 recorded 30-45 minute interviews; all students had completed an upper-level
electromagnetic theory course in which plane waves were used extensively
Educ. Res. Pract. 13(3), 172-178 (2013)]
4: How do the two
representations work
together to teach about
plane waves?
Sequence of prompts:
1: How would you explain
electric field plane waves to a
student a year behind you?
(interviewee talks and
sketches on whiteboard after
each prompt)
3-phase single-interview technique
with multiple representations
(3PSIT-MR) [Linenberger and Bretz, Chem.
2: How could you use this
cartoon in your explanation?
3: How could you use this
math expression in your
explanation?
5: How does the math
expression dictate planes?
Unexpected finding: initial responses to this question ignored an essential part of the request.
Most students either didn’t mention
Experts would recognize that
Discussion
and
future
directions
planes or didn’t mention the math.
both parts are essential.
All students gave insufficient answers.
Difficulty with the math expression—especially the dot
Four types of insufficient answers were produced by multiple students:
product? Or not recognizing the standards for answering
(2)
No
math:
invoking
such a question? Probably varies by student.
(1) No planes: focus on 1-D
other
planes
(e.g.
plane
sinusoids [3 students]
Suggests difficulty blending conceptual and formal
(3)
No
connection:
of polarization, realmathematical reasoning—something associated with
Pointed
to
dot
product
imaginary plane) [3]
expertise [Hull et al., Phys. Rev. ST Phys. Educ. Res. 9 010105 (2013)].
but unable to suggest
why it implies planes [3]
Insufficient answers despite many students starting
off
interview
with
correct
conceptual
statements
(4) Wrong connection:
about
planes
being
iso-phase
surfaces.
“Amplitude E is
0
Figure 1: student sketchwork showing many
one-dimensional sine waves but little
indication of planes.
Figure 2: sketch of a plane defined by
two possible linear polarizations of
the electric field (not dictated by the
math expression).
constant, therefore
there are planes.” [2]
HAJIM SCHOOL OF ENGINEERING & APPLIED SCIENCES
UNIVERSITY of ROCHESTER
Future: heighten awareness of expert standards for
answering such questions prior to interview.
Thanks to Profs. Scott Franklin and Ben Zwickl and the entire
SMERC group at RIT for mentoring, advice, and feedback.
supported by
NSF RIGEE grant EEC-