visualizations, the diagrammatic reasoning and the configurations of practices, objects and processes in additive problems with natural numbers

Abstract

Within the model of mathematical cognition proposed by the Ontosemiotic Approach (EOS) and using visualizations, diagrammatic reasoning and the configuration of objects and processes, we study the different objects, processes and practices put into play in the study of the addition of natural numbers. Students when learning put into play a set of personal and institutional meanings that must be described and used to solve problems. Both institutional and personal meanings need to be interpreted (processes of semiosis) in order to be learned. Under the described context, we analyze three additive problems with natural numbers in which we show the mathematical practices, both the operative ones and the discursive ones, we make the non-obvious objects public and we describe the use and intentionality of said practices. The analyzed problems corresponding to the second grade of primary education.