Making use of
Rarely Given Wrong Answers
on the
Force Concept Inventory
A. John Mallinckrodt
Cal Poly Pomona
[email protected]
The Problem
 Many administer the FCI in ungraded,
“credit for completion” mode.
 How do we establish that the test has
been taken in good faith?
One Solution
 Have a way to identify exams that are
not taken in good faith and …
 … tell the class about it!
Rarely Given Wrong Answers
 The FCI has a large number of
distractors that are rarely chosen by
students—RGWAs
 Random choice leads to an
anomalously high occurrence frequency
for RGWAs
Defining RGWAs
 Choice of database
Large set of previous results
Current cohort
 Choice of frequency
(My “discriminator” = 1/f = minimum
number of exams expected to yield one
instance of the specific RGWA)
Procedure
 Collect frequencies for all answers
 Decide on a set of RGWAs
 Determine expected number of RGWAs
 For random guessing (=Total number of RGWAs/5)
 For good faith effort (= Sum of p’s for each
RGWA)
 Compare with individual results
(Note: We can always expect random guessing to produce 6
correct answers.)
Examples
Now what?
 To confront or not to confront?
 To deny credit or not to deny credit?
Conclusions
 RGWAs seem to provide a relatively robust
method of identifying bad faith efforts
 Still needed
 Larger databases
 Better statistical analyses
 More user-friendly (user-friendlier?) interface
 Interest from FCI community (?)
Making use of
Rarely Given Wrong Answers
on the
Force Concept Inventory
A. John Mallinckrodt
Cal Poly Pomona
[email protected]