Recent work by Scherr, and her collaborators
determined student-held beliefs about the relativity of simultaneity and created
paper-and-pencil exercises to help aid student understanding of relativity.
Their research, which goes hand-in-hand with commentary by others reveals that
the teaching of introductory special relativity should focus less on the Lorentz
transformations and more on the relativity of simultaneity, length contraction,
and time dilation. Several textbook authors have already taken this
approach. A focus on Lorentz transformations can obscure the fact
that special relativity is about spatial and temporal intervals and not about
single position measurements and clock readings. In addition, an approach
based on spatial and temporal intervals leads to the metric in special and
general relativity while Lorentz transformations do not.

In our experience, pencil-and-paper exercises alone are often insufficient to
aid student understanding of abstract ideas, such as those in special
relativity. We believe that the level of visualization and interactivity
of carefully constructed Physlet-based exercises offers students a distinct
learning advantage over such traditional exercises. While there are other
computer programs that simulate phenomena in special relativity, most notably
Spacetime and RelLab, Physlets are free for noncommercial use and Physlet-based
curricular material can be written to specifically target concepts that students
find difficult. Because our material is Web-based, it is flexible enough
to be adapted to a variety of pedagogical strategies and local environments.
Finally, since Physlet-based material exists for all topics in introductory
physics, students can use Physlet-based material throughout the course, rather
than being forced to become familiar with numerous software packages.

For special relativity, we have incorporated the results from Scherr’s physics
education research into our development of several interactive Physlet-based
exercises that focus on visualizing the relativity of simultaneity, length
contraction, time dilation, and spacetime diagrams. These exercises can be
used as interactive reading assignments, in-class demonstrations, interactive
tutorials, and as part of an introductory physics laboratory in special
relativity. The material described in this paper and the laboratory version of
these exercises can be found at
http://webphysics.davidson.edu/physlet_resources. A brief description of
each exercise follows.

[1] M. H. Dancy, W. Christian, and M. Belloni, “Teaching with Physlets®:
Examples From Optics,” *Phys Teach.* **40**, 40 (Nov. 2002).

[2] W. Christian and M. Belloni, *Physlets: Teaching Physics with Interactive
Curricular Material *(Prentice Hall, Upper Saddle River, NJ, 2001). See also:
http://webphysics.davidson.edu/applets/applets.html.

[3] W. Christian and M. Belloni, *Physlet® Physics: Interactive Illustrations,
Explorations, and Problems for Introductory Physics* (Prentice Hall, Upper
Saddle River, NJ, 2004).

[4] A. J. Cox, M. Belloni, W. Christian, and M. H. Dancy, “Teaching
Thermodynamics with Physlets® in Introductory Physics,” *Phys. Ed. ***38**,
433 (September 2003).

[5] R. E. Scherr, P. S. Shaffer, and S. Vokos, “The Challenge of Changing Deeply
Held Student Beliefs about the Relativity of Simultaneity,” *Am. J. Phys.*
**70**, 1238 (2002).

[6] R. E. Scherr, P. S. Shaffer, and S. Vokos, “Student Understanding of Time in
Special Relativity: Simultaneity and Reference Frames,” *Phys. Educ. Res., Am.
J. Phys. Suppl. ***69**, S24 (2001).

[7] A. J. Malincrott, “Relativity Theory Versus the Lorentz Transformations,” *
Am. J. Phys. ***61**, 760 (1993).

[8] N. D. Mermin, “Lapses in Relativistic Pedagogy,” *Am. J. Phys.,* **62**
11 (1994).

[9] E. F. Taylor and J. A. Wheeler, *Spacetime Physics: An Introduction to
Special Relativity*, 2nd ed. (W. H. Freeman and Company, New York, 1992).

[10] K. Krane, *Modern Physics*, 2nd ed. (John Wiley and Sons, New York,
1997).

[11] T. A. Moore, *Six Ideas That Shaped Physics, Unit R: The Laws of Physics
are Frame-Independent,* 2nd ed. (McGraw-Hill, New York, 2003).

[12] T. A. Moore, *A Traveler’s Guide to Spacetime: An Introduction to the
Special Theory of Relativity*, 2nd ed. (McGraw-Hill, New York, 1995).

[13] See M. Belloni and W. Christian, “Physlets for Quantum Mechanics,” *Comp.
Sci. Eng. ***5**, 90 (2003) for our Force Concept Inventory (FCI) and
Quantum Mechanics Visualization Instrument (QMVI) data that support this
conclusion.

[14] P. Horwitz, E. F. Taylor, and P. Hickman, “‘Relativity Readiness’ Using the
RelLab Program,” *Phys. Teach.* **32**, 81 (Feb. 1994).

[15] Another way to do this is to synchronize all of the clocks at the location
of the master clock and then slowly move all of the clocks into place, so that
we do not incur any time-dilation errors due to their transport. An animated
version of this method can be found on our website.

[16] E. F. Taylor and J. A. Wheeler, *Exploring Black Holes: An Introduction
to General Relativity* (Addison Wesley Longman, New York, 2000).

[17] For all of the algebra, either visit the full exercise on our website or
see pages 26-29 of Ref. [10].

[18] In “An Introduction to Space-Time Diagrams,” *Am. J. Phys.* **65**,
476 (1997), Mermin suggests that the axes in spacetime diagrams are not
necessary and are actually a source of confusion for students.

[19] The Open Source Physics code library, documentation, and curricular
material can be downloaded from the website:
http://www.opensourcephysics.org/default.html.