Antonia Huertas

Mathematical E-Learning: State of the Art and Experiences at the Open University of Catalonia

In this article we present a review of the state of the art in mathematical e-learning and some personal experiences on this area developed during the last eleven years at the Open University of Catalonia (UOC), a completely online university located in Spain. The article discusses important aspects related to online mathematics courses offered in higher education programs, including: benefits and challenges, universities offering this type of education, methodological considerations, emergent technologies, learning projects and environments, etc. Also, key aspects of the UOC mathematical e-learning model and its historical evolution are described and analysed. Special attention is paid to mathematical curricula in computer sciences degrees, where a lot of work needs to be done in order to adapt mathematics courses to the continuously changing educational necessities of students. A curricula design proposal, based on a top-down approach, is presented as a best practice. Finally, some trends and future perspectives on the subject are suggested.

Teaching and Learning Logic in a Virtual Learning Environment

Teaching and learning in a virtual learning environment (VLE) poses some difficulties, but also challenges and opportunities to rethink the whole learning process, particularly in abstract subjects like logic or high level mathematics. On the other hand, resources and ways to work, now available in VLEs, might soon extend to all kinds of environments. In this paper, we will present experiences at the Open University of Catalonia (UOC), a particular VLE, concerning the whole process of teaching logic and mathematics. In addition, we will discuss some challenges and we will present some innovation projects allowed by the present and near future technologies.

Teaching Mathematics Online in the European Area of Higher Education: An Instructor's Point of View.

This article first discusses how information technologies are changing the way knowledge is delivered at universities worldwide. Then, the article reviews some of the most popular learning management systems available today and some of the most useful online resources in the areas of Mathematics and Statistics. After that, some long-term experiences regarding the teaching of online courses in those areas at the Open University of Catalonia are discussed. Finally, the article presents the results of a large-scale survey performed in Spain that aims to reflect instructors’ opinions and feelings about potential benefits and challenges of teaching mathematics online, as well as the role of emergent technologies in the context of the European Area of Higher Education. Therefore, this article contributes to the existing literature as an additional reference point, one based on our long-term experience in a large-scale online environment, for discussions involving mathematical e-learning.

Completeness in Hybrid Type Theory

We show that basic hybridization (adding nominals and @ operators) makes it possible to give straightforward Henkin-style completeness proofs even when the modal logic being hybridized is higher-order. The key ideas are to add nominals as expressions of type t, and to extend to arbitrary types the way we interpret

The sell project: a learning tool for e-learning logic

@_i

Ten years of computer-based tutors for teaching logic 2000-2010: lessons learned

in propositional and first-order hybrid logic. This means: interpret

Henkin and Hybrid Logic

@_i\alpha _a

Hybrid Type Theory: A Quartet in Four Movements

, where

TOOL DEVELOPMENT TO SUPPORT LEARNING, IMMEDIATE FEEDBACK, AND CONTINUOUS ASSESSMENT IN LOGIC

\alpha _a

Completeness in Equational Hybrid Propositional Type Theory

is an expression of any type