Thing-Oriented Learning: Application to Mathematical Objects

This paper is about diagrammatic representations and their role in the process of learning. It considers the problem that learning mathematical objects can be only conceptual learning, and, on the other hand, any activity on mathematical objects is made possible merely by means of semiotic representations. This is an important problem, since inability to build direct access to mathematical objects except through a semiotic representation leads to confusion. An approach that contributes to solving this problem, for some mathematical concepts, is a unifying diagrammatic representation that depicts all types of mental and other objects. This exploratory study suggests the viability of the representation in explicitly emphasizing abstract object features.