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

摘要

The main idea behind this work is the study of the potential of resorting to othermodels of Plane Geometry (e.g. Hyperbolic Geometry, Taxicab Geometry) to helpstudents to progress towards a proper/better understanding of what amathematical proof is about. A teaching experiment carried out with students of15 to 17 years-old attending the 10th and11thgrade (the two first years ofsecondary school) of a Portuguese school. The experience started in the10thgrade and lasted in the 11thgrade. Our main focus is the analysis of primary andsecondary relationships of geometric objects involved in argumentation andproof (in the sense of Godino et al. and Gutiérrez et al.) activated by the studentsduring production of arguments.