Modified Item Response Theory (IRT) model and k means clustering for agent based E learning system

North Central Province is the largest province in Sri Lanka. But gaining poor results for Mathematics in General Certificate in ordinary level (G.C.E. - O/L) is an intense problem in the province. (Table 01) Many reports including reports from the Department of Examination national Evaluation Testing Services show that more than fifty percent of students have obtained poor (W) grade for the mathematics subject in the G.C.E. - O/L Examination. Therefore, it is conducted several surveys to find the root courses for this situation and suggested a remedy to overcome the situation. From these surveys, it is revealed that poor knowledge of primary level mathematics concepts is one of leading factor for this situation. So, it is suggested an Agent based E learning system as a remedy. In any E learning system, taking psychometric measurements and data clustering are very important. In this paper, it is shown the new Item response Theory model that suit for E learning and clustering probability values that calculated from new IRT model using k means algorithm.