Mathematical and neuro-mathematical connections activated by a teacher and his student in the geometric problems-solving: A view of networking of theories

Abstract

The research goal is twofold: to articulate neuro-mathematics with the extended theory of mathematical connections that uses onto-semiotic approach tools and to explore the connections established by a teacher and his student when solving a problem about the volume of two boxes, one of toothpaste and the other of tomato. This research was developed in two stages: the theories were articulated assuming concordances and complementarities, highlighting the notion of connection, and a context of reflection was considered carried out in three phases where the participants were selected, participant observation was carried out in the classroom during solving a problem and then analyzing the data with the new tool to explore mathematical and neuro-mathematical connections. The findings present the mathematical connections established by the teacher and the student of meaning, feature, procedural, different representations (alternate, equivalent, and from a horizontal mathematization view), and part-whole, as well as neuro-mathematical connections of: recognition of terms and symbols; visual perception, spatial skills and motor coordination; association of mathematical concepts and formulas; intermediate calculations and unit conversion; solve operations step by step and understand the process; verification and conclusion, activated in the brain areas linked to each mathematical practice sequentially.