Gerardo Rodríguez

Changing assessment methods: New rules, new roles

Over the past 20 years, the use of Computer Algebra Systems (CAS) has helped with the teaching of mathematics in engineering schools. However the traditional use of CAS only in math labs has led to a narrow view by the student: the CAS is an additional work, not included in the learning process. The didactic guidelines of the European Higher Education Area (EHEA) propose a new teaching-learning model based on competencies. We suggest the use of the CAS be adapted to the new rules. In this paper, we present a model for the integrated use of the CAS, and we describe and analyze two experiments carried out in the academic year 2011-2012. Our analysis suggests that the use of CAS in all learning and assessment activities has the potential to positively influence the development of competencies.

dMath: A European Project for the Restatement of Mathematics Teaching

In this article the main characteristics of the dMath project are introduced. With the mathematical modules developed within this project a new tool is made available to the different users as a support of the teaching and learning of mathematics in the context of EHEA and of the Bologna declaration.

A SIS Epidemiological Model Based on Cellular Automata on Graphs

The main goal of this work is to introduce a new SIS epidemic model based on a particular type of finite state machines called cellular automata on graphs. The state of each cell stands for the fraction of the susceptible and infected individuals of the cell at a particular time step and the evolution of these classes is given in terms of a local transition function.

Using technology in mathematical courses: some possibilities

The use of technology to support the teaching of mathematics in engineering schools has been increasing in recent years, not only restricted to math labs, where certain software was used to develop different practical sessions. The versatility and the power of the current technological tools allow many possibilities of usage and promote new ways of assessing the different competencies to be acquired by the students. In this paper some examples developed in two Spanish universities with first year students of various Engineering degrees are presented. The examples selected were performed under different assumptions and conditions and using different technological tools. The study of the Cornu spiral or clothoid, one of the special curves used in the layout of roads, is carried out by the students of Civil Engineering at the University of Salamanca as team work supervised by the teacher. Mathematica has been the software used in the experience. At the Polytechnic University of Madrid some students of Mechanical Engineering have to research a real problem of their choice and solve it using different methods of systems of linear equations with several procedures implemented with the software MAXIMA. Students of Computer Sciences of the same University participated in a competition organized by math professors. The students, working in teams of two or three people, developed projects freely chosen by them. The mathematical topics and the technology used are free. The winning team has implemented an Android application for the study of graphs.

Facing the challenges of the European higher education area: the dMath project

Adaptation to the structure of the different University studies to the European Higher Education Area (EHEA) implies a deep reform affecting the structure of University studies. A brain storming about the mathematical courses will also be analysed. After some considerations about e-learning and b-learning we will describe the main features of the project: Building a European Database of Mathematical e-learning Modules: dMath. We pay attention to the general characteristics of the project and the different modules comprising it.