Abstract
The issue of comparing theories is one of the most relevant and debated research topic in mathematics education, which brings to the fore the epistemological foundations of this discipline. In this study, the authors examine and compare two of the most important theories that have characterized the development of mathematics education: the theory of objectification (TO) and the theory of didactical situations (TDS). The TDS has marked the birth of mathematics education in the modern sense, by focusing its interest on the classroom situations (the triangle of didactics, effects, clauses, didactical contract). The TO has marked the transition from a mentalist to a holistic approach to learning. Against the background of a pragmatic conception of human activity, historically and socially established, the TO takes into account not only the role of the body’s sensorimotor activity that broadens the range of semiotic resources by including gestures, material artefacts, bodily movements and postures – namely the so-called semiotic means of objectification – but also the individual’s emotional dimension. The authors present a thorough analysis of the foundational elements of the two theories, which are useful for an ontological and epistemological comparison. On the basis of the recent research results on the networking of theories in mathematics education and the distinction, proposed by Agazzi, between referential component and contextual component of the meaning of the terms or predicates that characterize a theory, this study shows that the two theories are partially comparable and partially compatible, and have partially similar explanatory aims; therefore it is shown that there is comparability and not contradiction, despite the different ontological and epistemological assumptions.