Authors: Takenori Sakumura, Takayuki Kuwahata, Hideo Hirose
The item response theory (IRT) gives us the valuable information about the difficulties of problems as well as the abilities of students contrary to the classical test method. The adaptive online systems often use the problems and their difficulties via item banks provided in advance by different test results, and evaluate the students’ abilities immediately after tests were performed. The systems usually do not give the problem difficulty values because of incomplete data. We have estimated the score in [0, 1] to such unanswered problems by using a newly proposed limit IRT (LIRT), and given the students’ abilities in addition to the problem difficulties recomputed. The newly developed online adaptive system worked with only five problems successfully.
Therefore, this kind of system can be applied to many situations such as primary check systems, short-time tests, introductory online systems. We have used this system to an open-campus event to introduce the adaptive online IRT system to high school students. The application field was mathematics to the first grade in high schools.
Keywords: item response theory, adaptive system, online, limit IRT, difficulty