Auteur principal			Co-auteurs(s)
Nom :	Dr Thierry Dana-Picard		Nom :
Courriel :	dana@mail.jct.ac.il		Courriel :
Institution ou compagnie:	Jerusalem College of Technology		Nom :
Département:	Mathematiques Appliquees		Courriel :
Ville :	Jerusalem		Nom :
État/Province :			Courriel :
Pays :	Israel		Nom :
Type de présentation:	Conférence :  25 minutes.		Courriel :
Conférence et numéro :	ACDCA ,    Numéro : A51		Horaire :   Local :	vendredi, 12h00   1302
Site Internet :	ndp.jct.ac.il est le site general qui accompagne
Titre de la communication :	Three-fold activities for discovering conceptual connections within the cognitive neighborhood of a mathematical topic
Résumé de la communication :
New technologies provide an efficient tool for the discovery of a broader mathematical landscape than what is afforded through purely traditional ways of learning. Compound activities, including numerous techniques, should be developed by educators, in order to enhance the epistemic value of the learning process and enlarge the student's knowledge of the internal connections within the cognitive neighborhood of learned topics. We propose a canvas for multi-task activities, involving hand-work, CAS assisted computations and related websurfing. The talk will be illustrated by the following example: A definite integral is given, depending on an integer parameter. This integral can be studied in two ways: 1. Paper-and-pencil work leads to an induction formula, and further, to a closed form for the parametric integral, involving factorials. 2. CAS assisted work does not lead immediately to such a closed form, but shows the first terms of integer sequences. 3. A suitable web-search provides an interpretation of the obtained sequence in terms of Catalan numbers. This three-fold compound activity shows connections between parametric integrals, sequences and combinatorics within an enlarged cognitive neighborhhood. In particular, we show that the choice of the CAS, and of the specific commands that are used, lead to different pedagogical situations. As an illustration we give more details for the first example using Derive and Maple. An important achievement of such compound activities is to transform the student from an imitator of his/her teacher to a creative actor of the process. References: M. Artigue (1997): Le logiciel DERIVE comme revelateur de phenomenes didactiques lies a l'utilisation d'environnements informatiques pour l'apprentissage, Educ. Studies in Math. 33 (2), 133-169. Th. Dana-Picard (2004): Explicit closed forms for parametric integrals, to appear in iJMEST. Th. Dana-Picard and J. Steiner (2003): Enhancing conceptual insight using a CAS, Proc. of CAME meeting, Reims (France), http://ltsn.mathstore.ac.uk/came/events/reims/3-ShortPres-DanaPicard.pdf The On-Line Encyclopedia of Integer Sequences, http://www.research.att.com/~njas/sequences/ J.-B. Lagrange (2000): L'integration d'instruments informatiques dans l'enseignement: une approche par les techniques, Educ. Stud. in Math. 43 (1), 1-30. J. Steiner and Th. Dana-Picard (2004): Teaching Mathematical Integration: Human Computational Skills versus Computer Algebra, to appear in iJMEST.