Auteur principal			Co-auteurs(s)
Nom :	Ph.D Luis Moreno-Armella		Nom :
Courriel :	lmorenoa@prodigy.net.mx		Courriel :
Institution ou compagnie:	Cinvestav		Nom :
Département:	Matematica Educativa		Courriel :
Ville :	Mexico D.F.		Nom :
État/Province :			Courriel :
Pays :	Mexico		Nom :
Type de présentation:	Conférence :  25 minutes.		Courriel :
Conférence et numéro :	ACDCA ,    Numéro : A21		Horaire :   Local :	samedi, 11h30   1302
Site Internet :
Titre de la communication :	Mathematical Reasoning and its formalization within a Dynamic World
Résumé de la communication :
Recent curriculum reforms have pointed out the relevance of using technology in Mathematics Education. The NCTM (2000) identifies the use of technology as one of the key organizer principles of the curriculum. Working within a dynamic environment (Cabri, for instance) has been important to enhance students’ capacity to explore geometric problems and to provide them with adequate tools for conjecturing and proving mathematical propositions. Computational representations allow the exploration of mathematical objects with new strategies, different from the strategies in a world of paper, as mathematical objects to be identified with the (executable) representation provided by the dynamic software. In consequence, mathematical thinking is enriched. Within the framework sketched here, we will present empirical work done with students (18-20 years olds) related to activities of exploring, conjecturing, and proving. Our results are part of an ongoing longitudinal study that has already led to several master and Ph.D theses and workshops in Mexico. To substantiate our assertions, we will present a genuine formal proof within Cabri World, of the Napoleon Theorem and explore other related results. We understand we are studying the “ecology” of mathematical propositions and the ways to find the natural context of generalization. Working within a computational environment forces us to adopt a different strategy: we have to resort to the nature of the mediating tools we have at our disposal, for instance the internal mathematical universe residing in the computer/calculator.