Semiotic Registers and Cognitive Obstacles Related to Solving Introductory Problems to Non-Euclidean Geometries Directed to the Preparation of Mathematics Teachers

Abstract

This investigation deals with selected aspects of an investigation regarding the acquisition of geometric concepts by in-service mathematics teachers at a very particular moment in their education or preparation: that of the transition between Euclidean and non-Euclidean geometric knowledge. Considering knowledge on Euclidean Geometry acquired by teachers as the subject to investigate, categories of mental representations and cognitive obstacles appearing in the process of resolution of introductory problems to non-Euclidean geometric concepts were researched. To cover the qualitative aspects, interviews with six in-service teachers and two undergraduates were conducted. Quantitative confirmation was pursued by means of a questionnaire administered to 45 in-service teachers. After a cognitive analysis of the conversion between semiotic registers, 14 categories of possible cognitive obstacles were identified as related to 7 semiotic registers of representation. Key-words: Cognitive Obstacles. Semiotic Registers. Preparation of Mathematics Teachers.