This first post intends to open a thread of discussion, clarification and investigation of a proposal for modelling students' "knowledge" in a way which should satisfy two requests: (i) to make sense from a learning perspective, (ii) to be accessible to computational representations. Indeed this is a challenge since the beginning of research in AI in Education. Anyway, let's try...

The model, which we have called cK¢ , is constructed on the pragmatic definitions of  the words "conception", "knowing" and "concept". By pragmatic, I mean that these definitions intend to serve the purpose of the model, not to close two thousands years of philosophical investigations of the related epistemological issues. Here they are:

- "Conception" takes the place of the famous "misconception" which is used since the beginning of the 80s to refer to faulty meanings students may hold and witness in certain tasks. The idea is not to consider that students are wrong, but that they have possibly constructed meaning which works only in specific context but can be demonstrated faulty in certain situations. To make it simple, if learning is adaptation then its outcome cannot be completely wrong! There are limits to this claim, but it may be worthwhile to consider it seriously.

- "knowing" -- as a noun -- takes here the place of "knowledge". This innovative proposal, for a genuine English speaker, is an attempt at finding a solution to get rid of the usual connotation of the word knowledge seen as an authoritative reference being imposed on learners (although one may speak of the "learner's knowledge"). Then we will use "knowing" to refer to knowledge when it is considered from a learner perspective, and keep the word knowledge for the corresponding institutional or social reference. One may remark that we had the word "conception" and that it might have been sufficient. Actually it is not the case, since it is often possible to change the behavior of a learner by changing some characteristics of a situation, so ascribing to him or her a different conception, while for an "expert" the same conception should have been mobilized. Let's say that a knowing is a set of conceptions which could be used in different situations from the point of view of the learner, while from the observer these situations should have been recognised as being similar so as to allow the use of the same conception (note here the need for an observer point of view, we will come back to this aspect)

- "concept" is a word we will use in a way which is rather classical: it is a label which points to a set of knowings (and so a set of conceptions...). The difficulty will be to characterise this set... This will not be too difficult, once we have said more about the characterisation of a conception.

These three unformal defiintions give us a ground to make some progress. The newt step now is to characterise a conception in a way which matches both the expectations and the requirements of a researcher in the learning science and in computer science.