"1.1 Background and Related Works. In our own university and in most universities at least in Germany, LMS are used both in distance education and face to face teaching. They are becoming a must-have in distance education [18]. They are more and more used in face to face teaching as they make the administration of a course much easier for teachers, and provide a handy way to cater for special needs. Experienced teachers can handle better a diverse classroom as supplementary learning materials can easily be made available through them for example. LMS provide a virtual place where students can find learning materials, study guides as well as an overview of their results, and where they can communicate with teachers and with other students. The functionality of an LMS can be divided in three main parts: Management of learning resources, management of users, and communication between users [18]. However statistics and reports are usually basic. To illustrate this last point, we list below a few questions that reporting facilities of most of the currently used LMS cannot handle: 1.How many students have never viewed Learning Resource A? 2.If students do well on activity B, do they also do well on activity C? 3.If students solve exercise D, do they also solve exercise E? 4.What is the average mark on quiz G got by students who have viewed resource F? 5.Which courses use a lot of Audio Learning Resources? To manage properly learners, especially distance learners, it is quite important to gain a good overview of their learning behaviours. To manage properly degrees, it is important to harmonize the different modules offered in a degree. The aim of our work is to complement LMS in all aspects dealing with data analysis and mining. Many works to analyse and mine data stored by LMS have been undertaken, see [17, 1] for some overview. To the best of our knowledge, all these works do some ad hoc preprocessing of the data. They do not aim at proposing some data model for analysis and mining that could be shared by all LMS independently of their internal structure. The work undertaken in [16] bears similarity with our work in the sense that it considers all data stored by an institution in higher education and unifies it into a model to explore behaviours of students. Another work that bears similarities to our work is PSLC Datashop [9], an open repository of educational data. The analysis tools offered in Datashop are more suited for educational software such as intelligent tutoring systems. Our work is not concerned with discovering or sharing learning objects as other works such as [19, 7] do. It is concerned with describing and structuring the interactions of users with learning objects as stored in LMS. Our vocabulary to describe these interactions is partly borrowed from the vocabulary adopted by the LMS Moodle [14], as Moodle is used by a large community worldwide. The part related to the interactions of users with quizzes contains elements that the IMS specification [8] also contains, though it is much simpler that [8]. This paper is organised as follows. The following section introduces our data model. The third section gives an overview of the export tool that exports the data stored by an LMS into this data model. Section 4 presents a case study in analysing data stored in a specific course using our tool. Last section concludes this paper. 2 The Data Model. The data model we present is quite close to a fact constellation schema [4]. It contains three kinds of tables: tables to describe objects found in LMS, these tables can be seen as dimension tables; tables to describe interactions with learning objects, these tables can be seen as fact tables; and third, association tables to describe associations between objects. The choice of having a table per object comes from the observation that most LMS have a limited set of objects that teachers are used to handle. Adopting this same set should make it easier for teachers to analyse usage of resources by students. 2.1 The schema. Our data model makes several general assumptions that we expose now. First we assume that an LMS contains users and courses. Users can enroll or sign in courses and sign off courses. Users can have roles like “lecturer”, “administrator”, “tutor”, “student” and so on. A user may have different roles in different courses. For example a user can be a tutor in the course “Introduction to Programming” and a student in the course “Early American History”. An LMS may contain groups that are associated to courses. Students enroll in those groups. An LMS contains forums, wikis, resources and quizzes. We call a quiz any kind of assignment, exercise or test a lecturer may wish to give to students. Forums, wikis, resources and quizzes are associated to courses. Thus a resource for example, can be used in several courses. A quiz may contain one or more questions that are also contained in the LMS. Questions are associated to quizzes and a given question can be associated to several quizzes. These general assumptions cover the particular case of LMS where resources, forums, wikis or quizzes exist only inside a given course. In this particular case an association table contains only one tuple. We assume that an LMS logs or stores interactions of users. For any given interaction, the LMS stores the identification of the user, of the course, of the resource, forum, wiki, quiz, as well as the timestamp, the nature of the interaction (“view”, “modification”, “creation”, “attempt”, “submit” and so on), the marks and the contribution when relevant. We present now in more details the tables that are the most useful for our case study, see Figure 1. For the current full set of tables, we refer to [11, 12]. Every table contains an element id, which is the key or identifier of the tuple. The five tables below describe objects usually found in LMS. Table user: This table describes users registered in the LMS. The elements firstaccess and lastaccess are the times and dates when a user first and last accessed any kind of learning object, such as a resource, a quiz etc. in the LMS. The elements lastlogin and currentlogin are the times and dates a user logged in the LMS for the last time, respectively currently. Note that a user can log in without accessing any learning object. Table course: This table describes courses existing in the LMS. We assume that a course exists for a given period of time. The element timecreated is the date and time the course has been created, usually by the administrator. The element startdate is the time and date the course is supposed to start, this time is usually fixed by the lecturer in charge. The element enrolstart is the date users are allowed to enroll in this course, and the element enrolend is the date users can not enroll anymore in the course. The element timemodified is the time and date this course has been last modified. The elements title and shortname are self explanatory. Table quiz: This table describes quizzes existing in the LMS. As already mentioned, we call a quiz any kind of assignment or test a lecturer gives to students. The element qtype is the type of the quiz. It can take values such as “assignment”, “SCORM” and so on, according to the different kinds of quizzes an LMS makes available. The elements qid combined with type make up the identification of a quiz. A quiz may contain one or more questions, see table question. The element title is a title the lecturer in charge gives to this quiz. The elements timeopen and timeclose refer to the dates and times students are allowed to answer the quiz, while the element timecreated is the date and time the quiz has been created and the element timemodified is the date and time the quiz has been last modified. Figure 1. Snapshot of the relational schema. Table question: This table describes questions that make up quizzes. The element title is the title of the question, while the element text is the actual text of the problem to solve. The element type is a category like “multiple-choice”, “true-false” etc. The elements timecreated and timemodified are as described in the table quiz. Table resource: This table describes resources available in the LMS that lecturers may use in courses. The element type describes the type of the resource like “file”, “uri”, “directory”, “audio”, “picture” and so on. The elements timecreated and timemodified are as for quiz. The element title is the title of this resource like “transparencies01”. The three following tables describe interactions with learning objects. They are the facts that are stored while users use objects of an LMS. Table quiz_log: This table describes the information that a LMS stores when users interact with quizzes. The element user is the id (the key) of the user who interacted. The element course is the id (the key) of the course in which the interaction took place. The elements qid and qtype refer to the quiz that was tackled. The element grade is the mark obtained in the quiz. The element timestamp gives the date and time of the interaction. The element action gives the kind of action that took place. An action can be “view”, in that case the user simply looked at the quiz, “attempt”, in that case the user attempted the quiz, “submit”, in that case the user attempted and finished the quiz, “modify” if the quiz has been modified etc. . Table question_log: This table describes the information that a LMS stores when users interact with a question of a quiz, and contains all elements already included in the table quiz_log. The element penalty gives the penalty marks given in that interaction. If a quiz is run in adaptive mode then a student is allowed to try again the question after a wrong answer. In this case one may want to impose a penalty for each wrong answer to be subtracted from the final mark for the question. The amount of penalty is chosen individually for each question when setting up or editing the question. The element raw_grade gives the raw mark obtained in that interaction. The element grade gives the marks for that question in that interaction when penalty has been taken into account. It includes also an element question, the id of the question that was tackled, the elements type, which can take values like “multiple choice”, “true/false” and the element answers, the actual answer or answers, when several answers are allowed, given by the user in the interaction. Table resource_log: This table describes the information that a LMS stores when users interact with resources. This table contains elements that are similar to the ones of table quiz_log. Finally our data model contains a number of association tables to associate objects with each other, see [11,12]. 3 System Architecture. Figure 2 presents an overview of the system architecture. The central part of the system is the abstract class “ExtractAndMap” that describes and partly implements functionalities concerning data extraction from an LMS and data generation for the data model. To create the present data model with an LMS, what is needed is to implement the abstract extract methods according to the features of the LMS. The concrete save function can be inherited as is. The system contains an implementation for Moodle. It is implemented in Java, uses the Database Mysql [15] and the persistence framework Hibernate [6]. Figure 2. System architecture. 4 First Results. We have used our system to analyze the course “Introductory Programming with Java” taught in face to face teaching to first semester students enrolled in the degree “Computer Science and Media” at the Beuth University of Applied Sciences, Berlin, in winter semester 2009/2010. In that semester 65 students were enrolled in this course. The teaching of this course is supported by the use of the Learning Management System Moodle in which mandatory as well as additional resources are uploaded for students. A list of 8 exercises belongs to the mandatory resources. Students have to solve these 8 exercises to get a mark for the practical part of the course. The lecturer has additionally offered gradually in the semester 7 self-evaluation exercises on key concepts of Java programming like methods, arrays, statements etc.. These exercises are not compulsory. Solving them is left to the sole discretion of the students. The lecturer is interested to know whether students have used these self-evaluation exercises and, most importantly, whether solving or attempting them could have a positive impact on the marks obtained in the final exam. Figure 3, obtained by simple queries, gives an overview of how students have used these exercises. For each exercise the column on the left means view, the column in the middle means attempt and the column in the right means close attempt. Note that view means that students have clicked on the resource, attempt means that they have submitted a solution and close attempt means that they have finished the exercise. Figure 3. Access to self-evaluation exercises. One notices a pattern that we have already observed in other courses regarding optional self-evaluation exercises [13, 11]: As the semester progresses always less students make use of them. We are interested in investigating whether a dedicated group of students emerges that keep doing the exercises during the semester. Therefore we want to know whether associations such as “if students complete exercise 2, they complete exercise 1” or , “if students complete exercise 3, they complete exercise 2”, and so on, hold. For that we have used the method exposed in [10]. Indeed, the answer is positive as Table 1 shows. The association rule 2→1 means “if students complete exercise 2, they complete exercise 1”. All rules have a rather high confidence and are rated as interesting both by lift and cosine. We recall that confidence is a number between 0 and 1 (highest is 1), that lift rates a rule as interesting if its value is above 1, and that cosine rates a rule as interesting if its value is above 0.66. Support gives the proportion of the data involved in the rule. Table 1. Association rules “if students attempt exercise x, they also attempt exercise x-1” To investigate whether solving these self-evaluation exercises has a positive impact on the marks in the final exam cannot be achieved by correlation or regression analysis as not so many students have solved them. That means for many students we would have missing data, since 45 students have written the final exam. We have simply queried our data and looked at the average mark on each group of students. The result is given in Table 2. Table 2. Completing self-evaluation exercises and marks in the exam. The line General is the minimum, maximum, mean and standard deviation obtained taking all students who have taken part in the final exam. The last column gives the mean for students who have not solved any exercise. The line Ex1 gives similar results restricting the population to students who have completed the first self-evaluation exercise. The last column gives the mean for students who have not solved the first self- evaluation exercise. And so on till Ex7. One notices that the highest average and smallest standard deviation in the final exam is obtained in the group of students who have completed exercise 7 (11.67 and 1.41 respectively), while smallest average is obtained in the group that has not solved any exercise (7). Given the results of the association rules, students who have completed exercise 7 have most probably completed all optional self- evaluation exercises. These results may speak for a positive impact on the final mark of the self-evaluation exercises. However our small population prevents of making any strong conclusion since statistical tests to check the significance of the difference in the average, like t-test, usually require a sample of size 30 or more. The line for exercise 4 looks different and requires more investigation. 5 Conclusion and Future Work. In this paper we have presented a data model to structure and export the data that most LMS usually store in scattered places into an homogeneous schema. The first aim of our data model is to automate and alleviate the preprocessing that is needed to explore, analyse and mine these data. We have designed an architecture of the tool that does the actual structure/export functionality, and implemented it for the LMS Moodle. Finally we have used our tool to analyse the data stored in the course “Programming 1” in our university. We have focused our analysis on the optional self-evaluation exercises. The analysis shows that, as the semester progresses, less students solve them. It shows also that a group emerges that keeps solving them and that reaches slightly better marks in the final exam. Another aim of this data model is to couple loosely an LMS and the analysis of the data it stores. If the persistence functionality of an LMS is changed, only the structure/export tool needs to be changed, not the analysis tools linked to the data model. Note that the implementation of the module that performs the export functionality for a concrete LMS has to be programmed with particular consideration regarding performance as the data stored inside an institution can be huge. However this programming happens only once. As noticed in [5] on-line learning is likely to grow, and so is the use of LMS. As pointed out in [1] the number of works tackling data stored by LMS is increasing. We hope that this work will help boost results and best practices in that area. We have used this data model mainly to explore thoroughly how students use learning resources in a course. Results of such an exploration are enlightening for teachers and are necessary to conduct a better informed data mining afterwards. Will this model be robust enough to answer any pedagogical question using data mining techniques? It depends on who is asking. Our data model contains all interactions that users perform with any object of the LMS along with the timestamp. Therefore a whole range of pedagogical questions related to navigation, performance prediction, activity of students for instance should be treatable. We begin to notice recurring questions that users of LMS are interested in. A future work is to continue enhancing and structuring those questions, so that we try out our data model further. We aim also at not restricting our data model to LMS, but consider other learning software as well. Our next step in that direction is to consider learning portals. We are also working on a graphical user interface for users to query and mine the data model in an intuitive way. This interface should work as an adaptive front-end for the user, the real analysis work will be done by connecting suitable queries and mining tool already available. Our work is open for the community and will be released soon on [12]. Acknowledgment. We thank warmly our colleague Prof. Dr. Ripphausen-Lippa for her cooperation in analyzing the data of her course “Introductory Programming with Java”."