1. Interactive Calculus in a Virtual Learning Environment César Córcoles, Antoni Gomà, M. Antonia Huertas Department of Computer Science Open University of Catalonia (UOC) e+Calculus JEM-TN Workshop I Lisboa 9-10 February 2007

2. Introduction Fast development ICT + Changes in learner’s behaviour Educational institutions have to evaluate technological & pedagogical approaches to (F2F and VLE) learning + teaching

4. Learning 2.0

5. Technical context (web 2.0) –Web as a platform / applications on the web –Collaborative & interactive applications –User centred model Pedagogical context (connectivism) –Learning is a constant building of a network –Capacity to learn more imp. than contents –Knowledge rests within the network Learning 2.0 paradigm –Learner-centred design –Teachers and learners as peers in a network –From traditional learning applications to an open learning environment

6. The Open University Of Catalonia (UOC) Distance learning – Web based learning (12 years) Completely VLE 30.000+ students Typical student: –>25 y/o –Fully employed –Long forgotten math

7. Experiences at the UOC. Technological & pedagogical improvements Our advantage (VLE): We already “live” inside a computer lab, even if it’s a widely distributed one, so integration of ICT in the classroom is not the problem Some experiences at the course of Calculus for Computer Science Students at the UOC

8. Experiences at the UOC. Technological & pedagogical improvements Semantical mark-up mathematical repository on the web (MathML, OpenMath, Ontologies, Learning standards) –UOC: Web based learning materials with MathML and Wiris Interactive math materials and mathematical learning processes –UOC: interactive Calculus with Wiris

9. Interaction and mathematical processes Problem-solving Mathematical modelling Reasoning Communicating Making connections (applying maths) Using tools

10. Experiences at the UOC. Really web based materials Browser support finally allows us to offer web based materials in XHTML + MathML format LaTeX based authoring + TeX4ht + …allow us to embed Wiris applets in order to have a symbolic calculator in the material We can teach mathematical processes, and forget about [some] algorithms and memorization

11. Experiences at the UOC. Interactive math materials Case 1: Functions of complex variableCase 1 Case 2: PrecalculusCase 2

12. Conclusions & Much More Future Work Satisfactory experience but it is necessary improvement –New curriculum & methodology in the content/process debate in teaching mathematics –Interface usability of new tools –Temporal costs of interaction –Students motivation for learning to learn vs. to learning contents –New assessments and certification systems

13. To be continued…