Numerical representations and technologies: possibilities from a configuration formed by teachers-with-GeoGebraRepresentações numéricas e tecnologias: possibilidades a partir de uma configuração formada por professores-com-GeoGebra - Oliveira, Gerson Pastre de (Educação Matemática Pesquisa: Revista do Programa de Estudos Pós-Graduados em Educação Matemática, 2015)
This paper reports a qualitative research whose subjects were a group of public basic education teachers who took part in a workshop approaching, as its main subjects, primality of positive integers and the Fundamental Theorem of Arithmetic, relevant topics in the number theory, dealt with from different technological perspectives and analysed under a theoretical proposal connected to the concepts of transparency and opacity of numerical representations and to the construct humans-with-media. The session where interactions occurred took place in a computing lab, in the framework of the Study Program for Post Graduates in Mathematics Education at PUC university, in São Paulo, and it consisted of two activities: during the first one, participants had to tell, from a specific representation, if a given positive integer would be prime or not; during the second one, teachers used an application from GeoGebra to determine, through different representations, which numbers in a random list would be prime. The analysis showed that participants had difficulties in the mobilization of knowledge related to the FTA, which led them to adopt strategies with a high cognitive cost and make mistakes. Likewise, data showed that similar hindrances were overcome on the basis of the educational proposal planned from a configuration of human-beings-with-GeoGebra.