Probing student understanding of total internal reflection and optical fibers
using Piaget-style interviews conducted both face-to-face and electronically
DJ Wagner1,2, JJ Rivera1, Fran Mateycik1, and Sybillyn Jennings3
Department of Physics, Rensselaer Polytechnic Institute, Troy, NY 12180
2
Department of Physics, Grove City College, Grove City, PA 16127
3
Department of Psychology, Russell Sage College, Troy, NY 12180
1
The Science of Information Technology (ScIT) is a novel course introducing students to
the physics underlying information technologies. We are currently expanding and improving the on-line curricular materials designed for this Rensselaer course to facilitate
their use at other institutions. Our prototype module presents the principles of Reflection,
Refraction, and Optical Fibers. To check whether the materials in this module speak to
students' preconceptions, we interviewed 32 students (with diverse physics experience)
and 2 physics faculty members, probing the participants' understandings of optical fibers
and total internal reflection. 22 pre-instruction interviews, along with 8 post-instruction
interviews, were conducted on-line using a Chat Room. The remaining interviews were
conducted in a traditional face-to-face format. Both interfaces yielded meaningful information about students' conceptual frameworks. In this paper we discuss the conceptual
and methodological findings of our study, and how we are using the results to refine the
curricular materials.
Introduction
Since 1999, 158 students with varied physics
backgrounds (Figure 1) have completed The Science of Information Technology (ScIT) at Rensselaer. This innovative course, that has no science
prerequisite beyond high–school physics, teaches
the scientific principles behind the operation of
computing systems. Five Rensselaer experts who
are researching ways to improve information technologies present “guest lectures” discussing the
current state of specific technologies, along with
their potential for the future.
The course is organized in a topical format
commonly used by our colleagues in the Humanities and Social Sciences but not often found in
Physics courses. Materials are grouped into four
units: Information Transfer, Information Storage,
Information Processing, and Future Information
Technologies. Topics covered in more traditional
physics courses, such as total internal reflection,
the Bohr atom, resistance, and RC circuits, are
combined with topics - less-commonly-covered
but imminently relevant to students’ lives - such as
Fourier transforms as they relate to bandwidth and
8%
13%
8%
Other
Sci.
Engr.,
Phys.
Arch.,
Mgmt.
Computer
Science
17%
EMAC
(Electronic
Arts)
Information
Technology
34%
20%
Figure 1: Percentage of ScIT students
by major
bit-rate, the band structure of semiconductors, p-n
junctions, and magnetoresistance. Quantum effects on microelectronics are also discussed in a
semi-qualitative manner.
Suitable published curricular materials do not
appear to exist, so the original instructor (Wagner)
produced much of the course material. Our cur-
rent NSF-supported project aims to modify and
expand those materials to meet the needs of other
institutions with the goal of fostering instruction
that connects physics with contexts that interest
today’s students [1]. All course materials are webbased and incorporate animations, questions with
randomization, and links to external sites. Transferability of the materials was tested in spring,
2002, when ScIT was taught at Rensselaer by a
different professor. Scores on our learning assessments and attitudinal surveys indicated the
change of professor was successful.
Part of our ongoing development process (see
Figure 2) is to assess student preconceptions,
along with the mental models constructed by
learners, with the goal of addressing those models
in the course materials. The Physics Education
Research (PER) literature is replete with studies of
preconceptions [2], but most studies focus on
commonly-covered topics in mechanics, basic circuits, and occasionally electromagnetism or geometric optics. Few studies have examined how
students approach the topics that form the backbone of ScIT: e.g., total internal reflection (TIR),
propagation of signals, semiconductor physics, or
quantum effects on microelectronics. (An exception is a recent study [3] on student understanding
of quantum physics and conductivity.) In this paper, we present some of our findings about cognitive models of optical fibers and TIR. We also
discuss the successes and limitations of eliciting
this information through electronic interviews.
Methodology
Clinical Interviews have long been regarded
as an effective means of eliciting students’ conceptual frameworks [4-6]. Piaget [4] developed
Conduct Class
(Use Assessment Tools)
Review/Evaluate
the method of critical exploration to see what
thoughts lay behind a child’s initial answer to a
question. Throughout his studies, he and his collaborators expanded and refined this set of techniques [7] to explore the organization of children’s
ideas and reasoning elicited by questioning about
visual displays and material demonstrations, e.g.,
[8]. The principle that underlies the clinical method is “follow the interviewee.” The interviewer is
to reach toward the child’s thinking, whether or
not the response fits the adult’s “expert” understanding. Face-to-face interviewing seems crucial
to this social interaction. The interviewer discerns
the child’s emotional state by reading facial expressions and postures. In contrast, our einterviews relied on language as the sole medium
of communication. We counted on interviewer and
interviewee’s ease with different forms of talk in
the chat room so that they could distinguish and
move back and forth between informal and formal
registers.
In the summer of 2002, we used the traditional
face-to-face format to interview a convenience
sample of 12 volunteers. These pilot participants
included in-service teachers who had studied introductory physics in high school or college, undergraduate physics majors, and physics faculty
members. The interviews were recorded on video
and later transcribed. This widely-accepted process was not an option when interviewing ScIT
students in the spring of 2003, as the interviewer
(Wagner) now works in another state during the
academic year. We therefore tried “e-interviews”,
using the Chat Room tool of WebCT. 22 preinstruction students were interviewed in this manner, and post-instruction e-interviews were conducted with 8 of those 22.
Analyze Data,
Research Others’ Work
Develop Materials
Figure 2: The Materials Development Cycle
Results
Based on both face-to-face interviews and einterviews, we have developed the cognitive progression shown in Figure 3.
Several preinstruction students had no idea what was “optical” about optical fibers. They comprise the pure
“Novice” category [9]. One student falling in this
category described optical fibers as fiber-wrapped
electrical cables with mirrors in the fibers to “maximize the speed of electrons.”
The mental model most commonly expressed
was that mirrors keep light in optical fibers. This
preconception was expected, as those who have
not studied TIR would not connect bouncing light
with refraction. But even some students whose
background included a study of TIR could not
connect the physics effect with optical fibers.
If students could identify the phrase TIR with
optical fibers, they still did not necessarily recognize that TIR is a refractive effect. Finally, those
Novice
No concept of light
carrying signal
Light just needs to
be contained (by,
e.g., dark coating)
Fibers use mirrored
surface or other reflective effect
Use phrase “Total
Internal Reflection”
Recognize that fibers
work through refractive effect
Can explain Total
Internal Reflection in
terms of Snell’s Law
Can explain TIR “to
someone who
doesn’t know what a
sine function is.”
Expert
Figure 3: Progression of Cognition about
Fibers
who could explain how TIR is a consequence of
Snell’s Law generally could not describe TIR as a
physical phenomenon, but were stuck in a mathematical mindset. A senior physics major, when
asked how he would explain TIR to someone who
didn’t know what a sine function is, replied, “I’d
give them the definition of sine, with a right triangle.” Huygens took a similarly mathematical approach in his Treatise on Light [10], perhaps the
earliest published description of TIR.
These 7 cognitive categories appeared in both
the e-interviews and the face-to-face interviews,
suggesting that meaningful information about
mental models can be extracted from the electronic format. Table 1 provides a comparison of the
two formats. E-interviews are convenient, have no
dress code, and reduce transcription time enormously. They also offer a sense of anonymity to
the interviewees. But typing questions and responses uses more time than just speaking would;
students invest more time when the electronic
format is used.
The median length of an einterview was 5 times that of a traditional interview - a tentative conclusion because of the incongruence of the samples. This additional time on
the students’ part may be offset by the convenience and novelty of the electronic format. Several of our students mentioned how “fun” or “interesting” the experience was.
The biggest limitation of the e-interviews
might be the lack of a scratch pad to illustrate ideas. In our next e-interview sequence we will post
a set of drawings on the web that can be accessed
and used for reference by both parties. We may
also explore WebCT’s Whiteboard Tool, which
allows electronic images to be created and viewed
in real time by all participants. We anticipate that
the advent of Tablet PCs [11] will allow interviewers and students to share images drawn with
an electronic pen, but it will be a while before that
promising technology becomes ubiquitous.
Rensselaer students typically have no problem
using Chat Rooms to communicate, but the possibility exists that some students may be uncomfortable using Chat. Anyone, however, who has
taught in a “wired” classroom can attest to the
growing popularity of Instant Messaging and Chat
Rooms. Most traditional college students will
probably be more comfortable in the Chat Room
Table 1: Comparing E-Interviews with Traditional Face-to-Face Interviews
Advantages of E-Interviews
Disadvantages of E-Interviews





Minimal transcription needed!!!
Can be conducted from wherever, whenever,
and however is convenient to participants.
Can hold 2 or 3 interviews simultaneously, typing questions for student 3 while students 1 and
2 are typing their responses.
Typed thoughts often come across more coherently than spoken thoughts.
Apparent anonymity lets students express their
lack of knowledge with less embarrassment.
than the interviewer is! Still, interviewers must
use their knowledge of their own students’ technological comfort level when deciding whether to
conduct e-interviews.
Conclusions and Future Work
Our interviews about optical fibers have provided valuable information about students’ cognitive models concerning optical fibers and total internal reflection. We will modify our instructional
materials to incorporate some of the preconceptions, such as the fiber-optic amusement park toys
many students mentioned in the interviews. We
will also attempt to address explicitly the conceptual difficulties discovered in this study. The diagnostic test will be revised to better distinguish
among the “stages” of conceptual understanding
we have identified. Our work with e-interviews
will continue, and we will consider how to minimize the shortcomings of this format by, for example, referring students to context-dependent
images during the interview process.
Acknowledgements
The RPI portion of this work was supported in
part by NSF CCLI Program under grant # DUE0089399. Special thanks to Leo Schowalter for
providing access to ScIT students and to the rest of
the ScIT advisory committee at Rensselaer for
their guidance and feedback. Much thanks as well
to all the students who participated in the study.
References
[1] All materials are web-based, and many can be
found at the ScIT Development website:
http://www.rpi.edu/dept/phys/ScIT.





Slowness of typing (vs. speech) results in longer time to gain comparable amount of data.
Less personal connection between interviewer
and interviewee.
Students might be multitasking too – not quite a
controlled environment.
Student cannot draw; difficult for instructor to
provide images.
Some students may be uncomfortable using
Chat Room to communicate.
[2] See, for example, E. Redish and L. McDermott, “Resource Letter PER-1: Physics Education
Research,” Am. J. Phys. 67, 755-767 (1999).
[3] Wittmann, Steinberg, and Redish, “Investigating student understanding of quantum physics:
Sponteneous models of conductivity,” Am. J.
Phys., 70, 218-226 (2002).
[4] J. Piaget, The child’s conception of the world,
trans. by J. & A. Tomlinson. (Littlefield, NJ,
1926/1972).
[5] E. Hunt and J. Minstrell, “A Cognitive Approach to the Teaching of Physics,” Classroom
Lessons: Integrating Cognitive Theory and Classroom Practice, ed. by McGilly (MIT Press, 1994).
[6] Lillian C. McDermott, “Bridging the Gap Between Teaching and Learning: The Role of Research,” The Changing Role of Physics Departments in Modern Universities: Proceedings of
ICUPE, ed. by E. F. Redish and J.S. Rigden.
[7] H. Ginsburg, Entering the child’s mind.
(Cambridge, New York, 1996).
[8] J. Piaget, (trans. C. Gattegno & F. Hodgson).
The child’s conception of number. (Norton, New
York, 1941/1965).
[9] M.T.H. Chi, P.J. Feltovich, & R. Glaser, “Categorization and representations of physics problems by experts and novices.” Cognitive Science,
5, 121-152 (1981).
[10] C. Huygens, trans. S. P. Thompson,
TREATISE ON LIGHT: In which are explained the
causes of that which occurs In REFLEXION, & in
REFRACTION And particularly In the strange
REFRACTION OF ICELAND CRYSTAL, (U. of
Chicago Press, Chicago, 1690/1945).
[11] A review of Tablet PCs can be found at www.
tomshardware.com/mobile/20030602/index.html.