1. INTRODUCTION. An ITS system has four main components: interface which provides the means for the students to interact with the ITS through a GUI, expert model which describes the knowledge that represents expertise in the subject matter domain the ITS is teaching, a tutor model that takes or suggests corrective action when necessary and a student model that describes student behavior or knowledge, including his/her misconceptions. Though a lot of work has been done on student model data that describes their cognitive skills like knowledge on a particular concept [2], not too much attention has been paid to outside factors like examples that can be provided as help to students while they use the tutoring system and how they can improve student engagement and their skill level. WebEx [1] is a web-based tool for exploring programming examples that enable teachers to use example-based approach in order to maximize learning opportunity for every student, weak or strong by allowing them to explore program examples in his or her own pace and order. We propose to differ from this approach by rating the examples. 2. DATA MINING TECHNIQUES AND TOOLS IN STUDENT MODELING. A correlation between objectives of creating a student model and the mining methods used for the respective objectives is shown in Table 1. If the student model design is directed towards teaching strategies / course planning, where the stakeholder is an educator, the most effective mining methods are clustering and association rule mining, whereas if the student model design is directed towards student learning and improving, then the mining method most effective is classification and prediction. With student as a stakeholder, the most commonly used classification algorithms used are decision tree algorithms like C4.5 and J48 and Bayesian classifiers such as Bayesian networks. To experiment on the comparative analysis of these mining methods, we used two data mining tools: WEKA (http://www.cs.waikato.ac.nz/ml/weka/) and Bayes Server (http://www.bayesserver.com). Table 1: mining methods used in student model. 2.1 Overview of Bayesian Networks. A Bayesian Network is a directed acyclic graph (DAG) of random variables (such as concepts, e.g., Add2Fracs) that uses Bayes theorem to depict probabilistic relationships between these variables. BNs used in student models typically have their DAGs designed by experts and the probabilistic relationships between variables are estimated by using some training data such as that in Table 2. Here, it is assumed that Add2Fracs is probabilistically dependent on find_LCM and Attempt_made, hence Add2Fracs has these two as its parents. Table 2: An Example BN Training Dataset. For a given sample X=(find_LCM=False, Attempts_made=2), we have to compute P(X|Ci) for each value of class attribute Ci (In table 2, C is Add2Fracs that can have 2 values Pass and Fail) and find the maximum of them. Since Ci has 2 values and X has 2 attributes, the number of such posterior probabilities is 4, as given in the Table 3. Using these probability values, we can compute P(X|Add2Fracs = Pass) = 1/6* 4/6=0.11 and P(X|Add2Fracs=Fail) = 2/4*2/4 = 0.75. This indicates that the probability of failing Add2Fracs is higher for the given sample X. A variable in BN is conditionally independent of all its nondescendants given its parents. The joint probability of the network computed by multiplying the conditional probabilities of each variable given its parents is P(X1 ... XN) = πi P(Xi | Pa(Xi)) where Pa stands for parents of, i.e., P(Xi ) = P(Xi | Pa(Xi)). Table 3: Posterior probabilities for Sample X. When building a student model for the domain of adding fractions, each variable (concepts, tests and other student attributes) is assigned a conditional probability (CPT). Root(s) of the BN will store only prior probabilities in their CPTs. All other variables that are child nodes store conditional probabilities in their respective CPTs. This is shown in figures 1, 2 and 3. 3. PROPOSED ALGORITHM. We are currently working on algorithms to study the effect of relevant examples on student performance. A relational table of examples stores the domain and topic to which they belong, input fraction numbers, detailed solution of the example, its difficulty level and rating. Table 4 shows a sample table. Table 4: Sample example table (CD = Common denominator, DD= Different Denominator). When a student uses the ITS for the first time, a new student model is created. This model stores the attributes describing the student and the initial Bayesian network with the respective probabilities for each node. A table of examples is also given as input to the student model. A student is recommended to use examples before attempting a certain activity or task. A comparison of the scores he/she achieves is then made. Thereby, if the student’s skill level has increased, the rating of the example is increased. A student is then presented with examples of higher difficulty depending on the skill level he/she has achieved. This method has a two-fold advantage. Examples help students learn a skill better and faster. Secondly, from the logged table of examples, we mine the most useful example (measured by the rating) using an association rule (e.g., Apriori-like or FP-growth like) or sequential pattern algorithm. This information can then be accessed by other student models to help them pick more useful examples. As future work, we propose to use K-means algorithm to cluster examples into different groups so that examples that come before constructing the BN for the student model will ascertain the relationships between variables. Sequential pattern mining can also be applied to the examples to ascertain an effective order in which they are recommended to students. An algorithm is shown below. Initial BN Example DB 1. Student chooses a module (for example Add fractions with Common denominator (eg. current_module=ADD_CD)) 2. If student wishes to see examples before attempting a task: Until task is achieved or number of example exceeds 3, do - show next example E from current_module - student attempts task from current_module - if task is done successfully, rating of example E is incremented by 1 3. If number of example exceeds 3 and the task is still not achieved, then the tutor module is informed (and the student is asked to repeat the module). 4. EXAMPLE STUDENT MODELING. We used WEKA and Bayes Server to describe student attributes and their probabilities. The training dataset D consisted of 100 rows or instances and 10 attributes in a domain of adding fractions. WEKA classified 76% of our instances. There are two steps in creating a Bayesian network: creating DAG and assigning prior and conditional probabilities to each node. These steps can be either done manually by an expert or can be learnt automatically. We preferred to create the DAG manually and input it as an xml file to WEKA but use WEKA to compute the initial probabilities for each node using an input csv file with our dataset D. We used Bayes Server for creating and studying Bayesian networks. Bayes Server does not learn the structure of DAG automatically, but like WEKA, it computes the probabilities from a training data set given as an excel file. figure 1 shows the DAG generated by Bayes Server for the training set given in table 2. figure 2 shows the detailed CPT for node Add2Fracs where State1 = False and State2 = True. figure 1: BN for table 2. figure2: CPT for Add2Fracs. As evidence is introduced, the CPTs of each node get updated. figure 3 shows the updated BN when evidence Age = False. figure 3: Updated BN (indicates an evidence). 5. CONCLUSION. ITS Systems have progressed greatly in terms of adjusting instruction, using individualized strategies that are effective for students. However, there is little work done on how aids like examples help students improve their learning skills. This paper attempts to analyze the tools and techniques used in ITS’s student models. Future work proposed is to mine up the most important example from several and present it to the student to enhance learning and understanding.