Although the item response theory (IRT) has been widely used to
test systems such as the Test of English as a Foreign Language
(TOEFL), it is not as well known to teachers of mathematics in
universities and colleges. The superiority of the IRT over the
classical test method is also valid in mathematics in universities
and high schools. Since the number of problems in mathematics to
be tested in a short time period is strictly limited, particularly
in universities, an accurate and efficient method to evaluate the
abilities of students is strongly required. In this paper, we propose
to use the stress-strength model to estimate the students' abilities.
To perform the optimal test, the up-and-down method by Dixon and
Mood is incorporated. Then, the proposed model becomes a generalized
test model that includes the stratified adaptive test method by
Weiss and the up-and-down method.
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