Some reflections on argumentations and mathematics in scenarios devoid of aristotelian influence and their importance in the mathematics classroom

This paper presents a characterization of cultural scenarios that are devoid of Aristotelian influence and whose argumentations differ from those originated in Greece. In these cultures, mathematical concepts such as the zero and infinity - whose scientific acceptance and treatment required various centuries in Western culture - were addressed and elaborated. The cultural construction nature of forms of argumentation is evidenced, as well as the possibility of constructing mathematical concepts on the basis of other forms of thought. Additionally, certain forms of argumentation are detected in the mathematics classroom which are incorrect from the viewpoint of Aristotelian logic, and which are neither learned nor elaborated in scholastic scenarios. Our Aristotelian-based culture has constructed specific forms of argumentation. The socioepistemological approach used in this research allows us to propose the need to pay attention to the non-classical forms of argumentation that arise in the classroom, and analyze how they could contribute to the construction of scholar mathematical concepts.