Resorting to non euclidean plane geometries to develop deductive reasoning an onto-semiotic approach

Abstract

The main idea behind this work is the study of the potential of resorting to other models of Plane Geometry (e.g. Hyperbolic Geometry, Taxicab Geometry) to help students to progress towards a proper/better understanding of what a mathematical proof is about. A teaching experiment carried out with students of 15 to 17 years-old attending the 10th and11thgrade (the two first years of secondary school) of a Portuguese school. The experience started in the10th grade and lasted in the 11thgrade. Our main focus is the analysis of primary and secondary relationships of geometric objects involved in argumentation and proof (in the sense of Godino et al. and Gutiérrez et al.) activated by the students during production of arguments.