An example of competence-based learning: Use of Maxima in Linear Algebra for Engineers By Ana Díaz 1 , Alfonsa García 2 , Agustín de la Villa 3 1 Dpto. de Matemática Aplicada. Universidad Nacional de Educación a Distancia, Spain, adiaz@ind.uned.es 2 Dpto. de Matemática Aplicada, E.U. Informática, Universidad Politécnica de Madrid, Spain, alfonsa.garcia@eui.upm.es 3 Departamento de Matemática Aplicada y Computación, ETSI (ICAI), Universidad Pontificia Comillas and Departamento de Matemática Aplicada, E.U.I.T.I, Universidad Politécnica de Madrid, Spain, avilla@upcomillas.es This paper analyzes the role of Computer Algebra Systems (CAS) in a model of learning based on competences. The proposal is an e-learning model Linear Algebra course for Engineering, which includes the use of a CAS (Maxima) and focuses on problem solving. A reference model has been taken from the Spanish Open University. The proper use of CAS is defined as an indicator of the generic competence: Use of Technology. Additionally, we show that using CAS could help to enhance the following generic competences: Self Learning, Planning and Organization, Communication and Writing, Mathematical and Technical Writing, Information Management and Critical Thinking. A follow-up at several stages of the resolution of a problem- example shall be performed; analyzing each contribution of Maxima to the competences´ acquisition. The problem- example concerns an electronic device for a building surveillance system, with different possibilities according to the number of sides of the building and other parameters. 1 INTRODUCTION Adaptation to the European Area of Higher Education (EAHE) implies a new teaching and learning model with active methodologies. Therefore it will be necessary to adjust all methodological resources to this new scenario. The Tuning Project proposes programs which are described in terms of specific and generic competences. A specification of competences to be acquired is necessary for the design of effective learning activities. The concept of competence can be defined as the ability of carry out tasks or to deal with situations effectively using knowledge; skills and attitudes (see Weinert, 2001). According to Mulder et al (2006), knowledge is captured as cognitive competence, skills as functional competence and attitudes as social competence. Meta-competence is the overarching ability under which competence shelters (Brown, 1995). Meta-competence is described as the ability to apply competences effectively in many different situations. The meta-competence to be achieved by engineering students of is “to be a good engineer to fit into society”. Universities propose concrete competences that need to be developed through the study of different subjects. One of the basic courses in engineering degrees is Mathematics, which is usually distributed across various subjects. It could be said that the meta-competence associated with this matter is the ability to master the mathematical techniques that allow students to solve engineering problems. These techniques are beyond mathematical concepts. Thus, the teaching of mathematics should always be mindful of problem-solving strategies, and hence in each mathematical discipline the habit of previously discussing the use of continuous or discrete, analytical or numerical methods, should be encouraged. Furthermore, it may be appropriate to start a simplified problem-solving model by using well known techniques, such as linearizing a non-linear model, etc. The methodology of problem-based learning is closely related to the style of teaching proposed. However, problem-based learning methodology must be subject to a careful analysis in order to ensure its effectiveness. In the first year of a degree course it may be highly desirable to introduce concepts and basic training skills before proposing problems. Here we focus on the Linear Algebra subject, proposing the use of a CAS in an e-learning model. Our reference course is carried out at the Spanish Open University with engineering students. This course is associated with the development of the following competences: Generic competences • G1: Self Learning. • G2: Analysis and Synthesis. • G3: Planning and Organization • G4: Communication and Writing. • G5: Mathematical and Technical Writing. • G6: Use of Technology. • G7: Information Management. • G8: Critical Thinking. Specific competences • S1: Knowledge, understanding and use of the principles of basic training in Linear Algebra. • S2: The ability to apply knowledge, calculation and technology to solve mathematical problems in engineering. In order to assess each competence, different measurable indicators are defined. Learning activities are planned taking into account these competences to define their content and to decide on the resources and methodologies to be used.