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FCI Gain Factor



In his 10/20/99 enigmatically titled "PDT Gain Factor," (What's PDT ???), Gene Mosca wrote "At the Anaheim AAPT meeting someone gave a talk on the g factor for the PTD (FCI) exam......"

The original presenter was Jeff Marx who was then at RPI but, the last I heard, is now at the Univ. of Oregon. Unfortunately, the Anaheim abstract (1) fails to give a recipe for calculating the Marx-Cummins Normalized Gain (MCNG). According to Marx's PhysLrnR posts, MCNG is simply an average of individual student gains, where the gain of each student is calculated in accord with the standard equation (2)

g = (%post-%pre)/(100% - %pre),

except that:
If post = pre = 100%, drop,
If post = or > pre, <g> = (post-pre)/(100-pre),
if post < pre, <g> = (post-pre)/pre.

More information on the MCNG and its rationale is contained in Marx's three PhysLrnR posts on this subject. To access these:

(a) go to the PhysLrnR archives at <http://listserv.boisestate.edu/archives/physlrnr.html,

(b) click on "search archives," feed "normalized gain" into subject slot,

(c) feed "Marx" into the address slot.

To access eight other PhysLrnR posts on this subject (including my own), simply delete "Marx" from the address slot. Unfortunately, the PhysLrnR archives are only accessible to those who are active members of the list. (Dewey Dykstra tells me that this serves to subvert spammers.)

In my opinion, a reasonable treatment of gains would be to calculate BOTH the "gain of the averages"(as done in ref. 2) and the "average of the gains," in accord with the standard formula (2) but omitting students who score 100% on the pretest. For most cases these two gains will be within 5% or so of one another and thus the difference is small in comparison with the random + systematic errors involved. Nevertheless the advantages of calculating both are:

(a) for large classes the difference yields information on the correlation of individual student g's with individual student pretest scores, (2,3)

(b) the unmassaged gain of the averages allows a good comparison with current <g> data bases, whereas idiosyncratically massaged averages of the gains will not,

(c) individual student g's and averages thereof are of interest in determining course effectiveness for various categories of students and in seeking diagnostic tests for the recognition and assistance of potential "low gainers," as discussed by Hake et al. (4) and Meltzer. (5)

It is noteworthy that the recent Cummings/Marx/Thornton/Kuhl paper (6) utilizes the gain of the averages as in ref. 2, because "First, it allowed us to keep students who achieved a 100% correct score on the pre-test in the study...... Second, calculating the average in this way reduces the skewing which occurs when students who pre-test with quite high scores then post-test with somewhat lower scores."

Richard Hake, Emeritus Professor of Physics, Indiana University
24245 Hatteras Street, Woodland Hills, CA 91367
PLEASE NOTE NEW ADDRESSES!
<rrhake@earthlink.net>
<http://www.physics.indiana.edu/~hake>
<http://www.physics.indiana.edu/~sdi>
<http://www.physics.indiana.edu/~redcube>


REFERENCES
1. J. Marx and K. Cummins, "Improved Normalized Gain," AAPT Announcer 28(4), 81 (1999).

2. R.R. Hake, "Interactive-engagement vs traditional methods: A six-thousand-student survey of mechanics test data for introductory physics courses," Am. J. Phys. 66, 64-74 (1998); on the Web at <http://physics.indiana.edu:80/~sdi/>.

3. R.R. Hake, "Errors in the Normalized Gain," 11/11/96, unpublished but
available as a pdf document upon request.

4. R.R. Hake, R. Wakeland, A. Bhattacharyya, and R. Sirochman, "Assessment
of Individual Student Performance in an Introductory Mechanics Course,"
AAPT Announcer 24(4), 76 (1994). Scatter plots of gains (posttest -
pretest) vs pretest scores for all students in a class delineate relatively
high-g (low-g) students for whom the course was (was not) effective. We
discuss various diagnostic tests (mechanics, mathematics, and spatial
visualization) given to incoming students which might be used to recognize
potential "low gainers" and thus initiate helpful intervention.

5. D. Meltzer, "Are There 'Hidden Variables' in Students' Initial Knowledge
States Which Correlate with Learning Gains?" AAPT Announcer 28(4), 81
(1999).

6. K. Cummings, J. Marx, R. Thornton, D. Kuhl, (1999" Evaluating innovations in studio physics," Physics Ed. Res., supplement 1 to the Am. J. Phys. 67(7), S38-S44.