During an investigation of student understanding of physical optics, we found that some serious difficulties that students have with this topic may be due, at least in part, to a lack of understanding of the nature of light as an electromagnetic wave. We therefore decided to look carefully at how students interpret the diagrammatic and mathematical formalism commonly used to represent a plane EM wave. The results of this research have guided the development and modification of tutorials that address some of the difficulties that we identified. These instructional materials are an example of how, within a relatively short time allotment, a curriculum developed on the basis of research can help students relate the concepts and formal representations associated with EM waves to physical phenomena.
REFERENCES
1.
K. Wosilait, “Research as a guide for the development of tutorials to improve student understanding of geometrical and physical optics,” Ph.D. dissertation, Department of Physics, University of Washington, 1996 (unpublished).
2.
B. S. Ambrose, “Investigation of student understanding of the wave-like properties of light and matter,” Ph.D. dissertation, Department of Physics, University of Washington, 1999 (unpublished).
3.
B. S.
Ambrose
, P. S.
Shaffer
, R. N.
Steinbergr
, and L. C.
McDermott
, “An investigation of student understanding of single-slit diffraction and double-slit interference
,” Am. J. Phys.
67
, 146
–155
(1999
).4.
K. Wosilait, P. R. L. Heron, P. S. Shaffer, and L. C. McDermott, “Addressing student difficulties in applying a wave model to the interference and diffraction of light,” accepted for publication in Physics Education Research, a Supplement to the American Journal of Physics.
5.
In an earlier study, we had examined the ability of students to relate the formal representations used in geometrical optics to physical phenomena. See
F. M.
Goldberg
and L. C.
McDermott
, “Student difficulties in understanding image formation by a plane mirror
,” Phys. Teach.
24
, 472
–480
(1986
) andF. M.
Goldberg
and L. C.
McDermott
, “An investigation of student understanding of the real image formed by a converging lens or concave mirror
,” Am. J. Phys.
55
, 108
–119
(1987
).6.
For a report of another study in which the Physics Education Group examined the ability of students to make connections among concepts, their formal representations, and the real world, see
M. L.
Rosenquist
and L. C.
McDermott
, “A conceptual approach to teaching kinematics
,” Am. J. Phys.
55
, 407
–415
(1987
) andL. C.
McDermott
, M. L.
Rosenquist
, and E.
van Zee
, “Student difficulties in connecting graphs and physics: Examples from kinematics
,” Am. J. Phys.
55
, 503
–513
(1987
).7.
L. C. McDermott, P. S. Shaffer, and the Physics Education Group at the University of Washington, Tutorials in Introductory Physics, Preliminary Edition (Prentice-Hall, Upper Saddle River, NJ, 1998).
T. O’Brien
Pride
, S.
Vokos
, and L. C.
McDermott
, “The challenge of matching learning assessments to teaching goals: An example from the work-energy and impulse-momentum theorems
,” Am. J. Phys.
66
, 147
–157
(1998
).10.
The students were not expected to recognize that the axis of polarization affects the diffraction pattern. For a discussion of this effect, see
T. J.
Mayes
and B. F.
Melton
, “Fraunhofer diffraction of visible light by a narrow slit
,” Am. J. Phys.
62
, 397
–403
(1994
) andT. J.
Racey
, P.
Rochon
, and N.
Gauthier
, “Effect of light polarization on the diffraction pattern of small wires
,” Am. J. Phys.
53
, 783
–786
(1985
).11.
K.
Wosilait
, P. R. L.
Heron
, P. S.
Shaffer
, and L. C.
McDermott
, “Development and assessment of a research-based tutorial on light and shadow
,” Am. J. Phys.
66
, 906
–913
(1998
).12.
P. R. L.
Heron
and L. C.
McDermott
, “Bridging the gap between teaching and learning in geometrical optics: The role of research
,” Opt. Photonics News
9
, 30
–36
(1998
).13.
For a discussion of a related difficulty in the context of springs, see R. N. Steinberg, M. C. Wittmann, and E. F. Redish, “Sample class on mathematical tutorials in introductory physics” in Proceedings of the International Conference on Undergraduate Physics Education (ICUPE), College Park, MD, July 31–Aug. 3, 1996, edited by E. F. Redish and J. S. Rigden, AIP Conf. Proc. 399 (AIP, Woodbury, NY, 1997).
14.
Student difficulties with the field-line representation have been documented in electrostatics. See, for example,
S.
Törnkvist
, K. A.
Pettersson
and G.
Tranströmer
, “Confusion by representation: On students’ comprehension of the electric field concept
,” Am. J. Phys.
61
, 335
–338
(1993
) andR. R. Harrington, “An investigation of student understanding of electric concepts in the introductory university physics course,” Ph.D. dissertation, Department of Physics, University of Washington, 1995 (unpublished).
15.
In most introductory courses, conductivity (σ) is treated as a scalar quantity. Thus the current and the electric field can be assumed to be collinear. In addition, students were not expected to treat the antenna as a radiating body.
16.
Some student difficulties with mechanical waves are discussed in
M. C.
Wittmann
, R. N.
Steinberg
, and E. F.
Redish
, “Making sense of how students make sense of mechanical waves
,” Phys. Teach.
37
, 15
–21
(1999
).17.
It has been our experience that, after working through a tutorial, the success rate of the graduate TA’s on post-test questions is close to 100%. See, for example, the last article in Ref. 8.
18.
For other examples, see Ref. 11
and the last paper in Ref. 8.
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1999
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