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

Introduction

Fast development ICT +

Changes in learner’s behaviour

Educational institutions have toevaluate technological & pedagogical approaches

to (F2F and VLE) learning + teaching

Math teaching & learning

(F2F & VLE)

Didactical tools, materialsPedagogical strategies

PersonalizationCollaborative

Technologicalcontext

& advances

Pedagogicalcontext

& advances

Learning 2.0

Math teaching & learning

(F2F & VLE)

Didactical tools, materialsPedagogical strategies

PersonalizationCollaborative

Technologicalcontext

& advances

Pedagogicalcontext

& advances

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

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

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

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

Interaction and mathematical processes

• Problem-solving• Mathematical modelling• Reasoning• Communicating• Making connections (applying maths)• Using tools

Experiences at the UOC.Really web based materials

• Browser support finally allows us to offer web based materials in XHTML + MathML formatLaTeX 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

Experiences at the UOC. Interactive math materials

• Case 1: Functions of complex variable

• Case 2: Precalculus

Conclusions & Much More Future Work

Satisfactory experience but it is necessaryimprovement

– 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

To be continued…