Session F1A 0-7803-7444-4/02/$17.00 © 2002 IEEE November 6 - 9, 2002, Boston, MA 32 nd ASEE/IEEE Frontiers in Education Conference F1A-1 A MATHEMATICAL MODEL FOR REUSING STUDENT LEARNING SKILLS ACROSS DIDACTICAL UNITS M. Carmen Fernández Panadero 1 , Abelardo Pardo 1 , Javier Fernández Panadero 1 , Andrés Marín López 1 1 Carlos III University of Madrid (UC3M), Avda. Universidad, 30. 28911 Leganés. Madrid. {mcfp, abel, amarin}@it.uc3m.es, javierf.p.@wanadoo.es Abstract  In this paper a mathematical model to capture information about learning capabilities of students for reusing across didactical units is presented. The model is based on the definition of a set of generic objectives related to the concepts, skills and attitudes the student is expected to assimilate by the end of a unit. Each objective is represented as an axis in a n-dimensional mathematical space. A relationship is established between the topics and each of the objectives. The grading process is modified to reflect how the student performs with respect to these objectives. The expected and obtained grades are then represented in this mathematical space. The proposed model provides support for diagnostics, facilitates the course characterization and comparison (even adaptive ones) and is suitable to be adopted in both new and on-going courses, because requires only the definition of the relationship between topics, evaluation and objectives. Index Terms  user modeling, evaluation, course sequencing, learning skills, adaptability. INTRODUCTION Today's computer science and computer engineering curricula include a significant part of student assignments. Grading of such assignments provide insight not only into the students’ proficiency but also into their generic learning capabilities. This information is typically used only at the course level. However, information about generic learning capabilities is very valuable toward providing a degree of personalization across different courses. There has been a significant effort to encourage the reuse of educational material across different courses and educational institutions. There is an equally important potential in reusing the information obtained during the evaluation process. But, as in the case of reuse of educational material, the main challenge is to provide a framework simple enough to facilitate its adoption and at the same time powerful enough to justify its use. Students encounter similar difficulties in different courses. This is specially true in engineering education since courses are extremely related. In this paper we present a mathematical model to capture through evaluation information about generic learning capabilities of each student for reusing accross didactical units. The model is suitable to be adopted in both new and on-going courses because requires only the definition of the relationship between topics, evaluation and objetives. The rest of the paper is structured as follows. First a brief introduction to user modeling and model reusability is outlined. Next, both the model and the evaluation process is presented. Finally, conclusions and future research venues are discused. RELATED RESEARCH In 1984 Bloom [1] reported that students working with a “good” human tutor obtained an average performance two standard desviations higher than students in conventional instruction. This is known as “The 2 Sigma Problem”. Since 1984 several research groups studied how to acomplish the same performance under more practical conditions than the one-to-one tutoring. In [2] Corbett proposes to accomplish this by customizing certain aspects like content, feedback, or providing personalized instruction pacing. All these techniques require an underlying student model or student profile that allows to diagnose the student characteristics, such as skills and knowledge level. There are multiple studies on how to collect information to create a student profile (i.e. background knowledge, experience, plans, preferences, etc) [3]. This student profile is tightly coupled with the course so each new course requires a different model. Reusing student models accross different courses would simplify this task, but a significant effort is required to define models suitable to be used in different contexts. The first step in this direction has been to create integrated environments such as WebCT [4], Blackboard [5] or TopClass [6] that allow the creation of course content and offer facilities to collect student information. These platforms can reuse student information as long as the course remains in the same platform. Taking student information from one platform to another remains being a difficult task . In the last decade there have been several groups like IEEE P1484.2 [7] or IMS project [8] devoted to specify generic user models (PAPI and IMS Learner Information