Astronomy clicker question: stellar distance

Astronomy 210, Fall Semester 2008
Cuesta College, San Luis Obispo, CA

Students were asked the following clicker question (Classroom Performance System, einstruction.com) at the end of their learning cycle:

Antares is a star that has an apparent magnitude m = +0.92 and an absolute visual magnitude M_v = –4.5. Approximately how far away is Antares from the Earth?
(A) Much farther away than 10 parsecs.
(B) A little farther away than 10 parsecs.
(C) Exactly 10 parsecs away.
(D) Closer than 10 parsecs away.
(E) (I'm lost, and don't know how to answer this.)

Section 70158
(A) : 39 students
(B) : 13 students
(C) : 2 students
(D) : 3 students
(E) : 0 students

This question was asked again after displaying the tallied results with the lack of consensus, with the following results. (Comment from student, as to whether the pair-share follow-up is necessary: "I think it [the response distribution, shown to the class] already looks pretty." Retort from instructor: "Then make it look prettier...or if you think it looks ugly, then fix it!") No (other) comments were made by the instructor, in order to see if students were going to be able to discuss and determine the correct answer among themselves.

Section 70158
(A) : 54 students
(B) : 2 students
(C) : 0 students
(D) : 0 students
(E) : 1 student

Correct answer: (A)

When brought to the "fair distance" of 10 parsecs (thus changing its apparent magnitude to absolute visual magnitude), Antares now seems to be brighter, indicating that it must have moved closer to the Earth during this process. Since this is a substantive gain in brightness, Antares must be much farther away than this fair distance of 10 parsecs.

Pre- to post- peer-interaction gains:
pre-interaction correct = 68%
post-interaction correct = 95%
Hake (normalized) gain <g> = 83%