Learning gain comparison in MIRT

[Micha van den Enk]

For my master thesis within Educational Science and Technology, I have an experimental design with students divided over a control and an experimental group based on an educational intervention, and all students wrote both a pre- and posttest. Both tests consists of 5 non overlapping questions, drawn randomly from an itembank consisting of all 10 questions. Therefore, all students have answered the same 10 questions, however they differ in whether the question was answered on the pretest or posttest.

My question is: how can I determine the item difficulties and the students' learning gains, and compare these learning gains between the two groups?