For example, from the Pythagorean theorem we can define three skills as the association of this academic knowledge and several tasks:
  1. Knowledge: Pythagorean theorem, Task: calculating a distance
  2. Knowledge: Pythagorean theorem, Task: proving an angle is right
  3. Knowledge: Pythagorean theorem, Task: proving an angle is not right
Indeed, each of these tasks uses the theorem differently: its direct implication, its converse and its contra-position. Therefore there are different skills that may be trained specifically. The academic knowledge is necessary but not sufficient to conduct the task, and one skill does not transfer automatically to another.
The approach of teaching by competences has certain not been ignored by teachers: it specifically identifies what needs to be taught. But when pushed to an extreme, this approach brings the problem of an overwhelming list of competences to teach.

Dynabook implications

Competences are strongly tied to the domain to be taught. The Dynabook could propose a generic tool to represent such competences as the association of knowledge and task. This representation could take the form of a network of competences as explored in iStoa[1]. The links in the iStoa network are of two types: sufficient or precedence. A sufficient link between two competences A and B models a transfer in competence from A to B. A precedence links between two competences X and Y models the necessity to master X before Y. These relations are numerically tied to a learner cognitive model, they could be simplified without these numeric weights.
Such networks of competences could be shared among teachers or at least a local group of teachers. Then a teacher could adjust it to his or her specific vision.
The teaching resources available in the Dynabook will be linked to one or several nodes in this network of competences. New resources created by the teacher could be associated as well. This is expected to ease the search for specific resource to teach a given skill.
Any opinion on the topic? If so leave a comment for further reflection.

Thanks to David T Lewis for his editing.
 [1] H. Fernandes, iStoa, modèle notionnel de guidage macroscopique de l'apprentissage (Phd thesis), 2010