LO = Learning Objects

It seems natural to think that a single LO can cover the concepts that the student intends to learn, depending on the granularity of these concepts. In this case, there is no need to recommend more than one LO to cover these concepts. At the opposite extreme, there is the case where an OA is required for each concept. Note that if the number of LOs was greater than the number of concepts, this would only insert unnecessary redundancy if we consider that each concept does not contain other concepts and therefore does not need to be covered by more than one LO.

Therefore, the ideal is to recommend as few LOs as possible so as not to saturate the student with unnecessary LOs and also to avoid redundancy. In fact, we will see that this recommendation process is characterized as a minimization problem. Before this problem is formally defined, an example is given below.

Imagine a situation where a student needs to learn five concepts, which belong to the set X = {C1, C2, C3, C4, C5}. Consider a collection of subsets of X given by F = {LO1, LO3, LO4, LO5, LO6, LO7}, where LO1 = {C1, C2}, LO2 = {C3}, LO3 = {C4}, LO4 = C5, LO5 = {C2, C3, C4, C5} and LO6 = {C2, C3}. Each element of F is a learning object that covers a set of concepts. LO1, for example, covers concepts C1 and C2. The objective is to find the least number of LOs that together cover all the elements (concepts) of X.