1. Dependency Matrix and Duration in Time Based Composition of Learning Paths Ayman Moghnieh, Fabien Girardin, Joseph Blat Department of Technologies, Pompeu Fabra University, Barcelona, Spain

2. Planning Learning Paths for L.L.L. Environment –Digital, Collaborative, Asynchronous, Social, Personalized, Interest-Based.... Challenges –Immersiveness, Learner Support, Sustainability, Usability, communication...

3. Context of work, an introduction Contemporary challenges in L.L.L. –Curriculum planning and development –Learner’s learning path composition –Contingency planning in competence development –Providing tools for learner support Simple approach suggested –Based on R.D.M. –Addresses a basic scenario –Provides an infrastructure for automation

4. Basic Scenario A professional planning to study virtual sets production technologies Effort: average of 6 h/week Curriculum: –Small set of interdependent CDPs –Accredited Tasks: –Explore learner’s possible choices –Partially automate process planning

5. Computing Dependency Matrix Each CDP represented as a vector of competences prerequisite competences define a transitive relation CDPs can be sorted by dependency relations RDM can also encompass the learning goal and the learner’s current position

6. Path existance Path Existance –CDPs with no prerequisite competences offer a set of competences C0  C /  c  C0, A0(c) = 1.  Starting points –A1 = step(A0) represents the set of CDPs accessible from A0 –Path(A0, A1) = true if CR1  , CR1 = {  c  C0 / A1(c) = -1}. –a goal is attainable by RCDP if  A0   / Path(A0, G) = true.

7. Path segmentation and length Path Steps and Segmentation –Any segmentation of Path(A0, G) is a composition of these unitary steps: A0  A1  A2 ……. An  G –Segments are more or less homogeneous in time and respect dependency relations among CDPs. Path length –LENGTH( Path(A0, G) ) =  LENGTH( Path(Ai, Aj) ) =  TIME(Ai)

8. Pre-planning: identifying choices

9. Conclusions Two main factors govern the planning process –Time restrictions / requirements –Competence dependency and prerequisites This work forms a foundation for learner support in learning path planning Visual aspects and interaction are key for success of the planning process