Item characteristics (e.g. item difficulty), and students' latent traits (e.g. student ability) are essential in a personalized learning system. In such system, items of different characteristics need to be recommended according to students' latent traits. The item response theory can fulfill such requirements. In this paper, we present a detailed description of the student ability and the item difficulty measurement based on an item response theory model. The model is evaluated using real data regarding the math and the English curriculum gathered from students' learning processes during the usage of the Squirrel AI Learning System. The data is regarding the math and the English curriculum. It is proved that the difficulty evaluated by teachers minus the difficulty estimated from the data approximately follows a normal distribution. The mean value of students' abilities approaches 0.50 as the numbers of their attempts on questions increase.