Abstract:

Increasingly the notion that it is no longer possible to teach at the university in the same way teachers did in the sixties is deepening. It is being carried out an effective change in the policies, contents and methodology in higher education.

From the Spanish perspective, regulatory changes after the Bologna Declaration and the creation of the European Higher Education Area, have led to an epistemological renewal: university education should be centered on the student and must be based on the acquisition of competencies. This implies a change in the way to teach: from traditional education where the main goal was the learning of heavy collections of theorems, corollaries and mathematical problems (disconnected from the real life) to an educational model that emphasizes, not only generic competencies, such as team work and self-learning problem solving, but also specific skills, such as the application of mathematical concepts to engineering problems.
To a greater or lesser extent, these reflections are taking shape at different ways and in different countries. Also it is reinforced the idea to create supranational groupings in education within the Latin American Higher Education Area with the purpose of generating a close collaboration between the different university systems.

In this new context, where different ways of teaching and learning are being promoted, the new technologies are emerging more and more in mathematical teaching and learning processes. It is possible to develop educational materials adapted to the new scenario. The traditional distinction between face to face and distance learning no longer makes sense. It is possible to shift the classroom from a traditional to non-traditional context.
Universities today offer many courses where the study materials and notes can be obtained online through different mechanisms. The terms e-learning and b-learning are being overshadowed by u-learning (ubiquitous learning), since the learning scenario is any place and any device can be used to get the materials.

The task of preparing the appropriate material in this new context cannot be addressed individually and, consequently, international collaborative process can be very fruitful. The main goal is to develop adapted study material to several Universities, with institutional endorsement for any University involved in the collaborative process and with the acceptance and incorporation of other Universities interested in the use of such development.

We will present an ongoing experience which involves the National Technological University (UTN) in Buenos Aires, Argentina, and Spanish universities: Salamanca University (USAL) and Pontificia Comillas University (UPCOMILLAS) in Madrid.

The authors of this paper have updated a virtual Multivariable Calculus course, hosted in STUDIUM (https://moodle.usal.es/) to be used by the students from the three universities. The assembled material contain theoretical notes, presentations, lectures, proposed and solved problems, applications, use of some Computer Algebra System (CAS) to be applied in Multivariable Calculus and also some assessment questionnaires.
Finally, we will present the state of the art of the experience and we will give some ideas and milestones for the further development of this collaborative project.

Keywords:

Collaborative processes, e-learning, b-learning, u-learning