Parameters were learned for each skill problem set individually. The parameters were unbounded and initial parameters were set to a Guess of 0.14, Slip of 0.09, Prior of 0.50 and Learn of 0.14, these initial values were the average parameter values across all skills in prior modeling work conducted on the ASSISTments tutor. For parameter learning, the new day observation (0 or 1) was presented as evidence in addition to the student responses. After training, the time and actual response values were given to the model as evidence for our new models to do the prediction one student at a time. In order to predict every response of each student in the test set, the student data for prediction was presented to the network in the following fashion:

• for predicting the first question, no evidence was entered;
• for the second question, the new day information for that question and the actual response of first question were entered as evidence;
• for the third question, the first two new day information and responses information were entered as evidence.

Apply this procedure until the prediction of the last question. This predicting process is shown in Fig. 2. By applying this prediction process, the probability of student answering each question correctly was computed and saved. Fig. 2. The process of entering evidence data. Finally, we calculated the Residuals and AUC values between predictions and actual responses on same day events, new day events as well as overall events of the whole problem set.