Slides from Vokos' talk,
"Student Understanding (and Misunderstanding) of Important Concepts in
Relativity" are given here in five web pages. In the narrative below
Click on any subject to go to its page or here for a
pg. 1 Vokos noted
that Peter Saulson’s fine
account of a physicist building and extending his understanding
shows that understanding is a subtle, complex process.
Students construct their understanding differently than professionals,
but their process is also subtle and complex, and it is often impeded by
basic misconceptions. Vokos and his physics education research (PER)
colleagues have probed and
analyzed how students
learn and understand ideas basic to GR. Vokos described
efforts to identify and assess
misconceptions, and then to devise methods of teaching that reduce
barriers to a student’s further
Vokos showed that
Hilbert's remark is not true for
American students (and probably not for Göttingen students either).
After instruction about the Schwarzschild metric,
47 out of 49 students in a
junior-level relativity course could not satisfactorily answer a
basic question requiring them
to connect local coordinates and Schwarz-schild coordinates.
Study of student responses to this and other
PER analyses shows that
pg. 2 students
need to understand basic concepts from
special relativity (SR) if they are to understand
GR concepts. A key idea is the
spacetime event which is the basis of all
measurements. The SR ideas of a
reference frame and clock synchronization are also of key importance.
To examine how well SR instruction had prepared them for GR, students
(1) A rocket passes two
volcanoes that erupt at the same time in the frame of an observer at
rest midway between them. Which one erupts first in the moving frame?
Because students can answer
incomplete reasoning, proper interpretation of their responses
requires careful analyses of
what students are thinking
as they formulate their answers to such PER test questions. The
results show generally
poor understanding by graduate students as well as undergraduates.
(2) Do students think simultaneity depends on
the location of an observer relative to a pair of events? The
eruption question was used to study this question. The
data show that both
graduate and undergraduate students are confused about this.
How might we improve students’ understanding? Traditional instruction
shows small improvement; tutorials
yield larger improvement.
Here are examples of some tutorials and their goals:
(1) Construct a
reference frame from sound signals.
(2) Synchronize clocks
using sound signals
(3) Invariance of c
and its consequences
pg. 4 To what extent can
students relate ideas to a physical
context? See if they can say In what order
wave fronts of light from two lightning
strikes reach observers in different frames? See if they understand
that an event is the same in all frames.
Tape player started by light signals. Is an event the same event in
every reference frame? (Shows PER use of
student scripts to
Tutorials help. Some before and after data for
(5) the spacecraft question;
(6) The seismologist and
the order of the eruptions.
pg. 5 Conclusions:
Student preconceptions strongly
affect their learning of special and general relativity.
Without a coherent framework for the key ideas many students will
never understand SR or GR.