Onto-semiotic analysis of diagrammatic reasoning

Abstract

Diagrams and in general the use of visualization and manipulative material play an important role in mathematics teaching and learning processes. Although several authors warn that mathematics objects should be distinguished from their possible material representations, the relations between these objects are still conflictive both from an epistemological point of view as well as an educational one. In this paper, we apply theoretical tools of the onto-semiotic approach of mathematics knowledge to analyze the diversity of objects and processes implied in mathematics activity, which is carried out with diagrammatic representations. This enables us to appreciate the synergic relations between ostensive (visual and sequential languages) and non-ostensive objects (abstract and mental entities) overlapping in mathematics practices. The analysis of the characteristics of diagrammatic reasoning and its interpretation in onto-semiotic terms is contextualized by means of the analysis of solving a problem about fractions by applying three procedures that involve diagrams.