American Association of Physics Teachers

 Stamatis Vokos's TALK  -- p. 1
Student Understanding (and Misunderstanding) of Important Concepts in Relativity

from the AAPT Topical Workshop:
Teaching General Relativity to Undergraduates
Syracuse University, July 20-21, 2006

Stamatis Vokos

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 full PDF version.

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 progress.

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 were asked:
(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 correctly with 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.

pg. 3  (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.

(4) Tape player started by light signals. Is an event the same event in every reference frame? (Shows PER use of student scripts to probe understanding.)

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.




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