En open access sur http://www.springerlink.com/content/k2k616x254q34236/?p=fa97ce28e2884c20834f83d7d8f92a2e&pi=1International audienceE-Exercise Bases (EEB) are now used in the teaching of mathematics, especially at university. We discuss here the consequences of their use on the students' activity during computer lab sessions. Results stem from observations of several teaching designs organised in different French universities with three e-exercise bases. The analysis focuses on new tasks and on specific solving strategies, which appear using these resources. Moreover, specific didactic contract clauses are studied

Mathematics education as a research domain is characterized by a plurality of theoretical approaches. Acknowledging the existence of such diversity and the risks of an excessive theoretical fragmentation does not mean to search for a unifying theory but to urge the community to develop strategies for coping with this diversity. This article is meant to show the potential of a “cross-analysis” methodology for establishing connections between different theoretical approaches to mathematics education with technology. Within the frame of the ReMath European Project, two Teaching Experiments were realized, centred on the use of a same ICT tool—Casyopée. Two distinct theoretical approaches shaped both the Teaching Experiments design and their enactments: the Theory of Didactical Situations and the Theory of Semiotic Mediation. The two Teaching Experiments have then been analysed from both theoretical points of view. In this article we will provide some examples drawn from this cross-analysis that show the synergy which can be established between the aforementioned theoretical approaches. Beyond contributing to a deeper understanding of the observed “didactical phenomena”, that synergy allows establishing connections between the two approaches that lead to their reciprocal enrichment

This article presents a synthesis of international research in mathematics education about the secondarytertiary transition, with a specific interest in the most recent works. These studies may concern students' difficulties, and investigate different factors causing these difficulties: notions become more abstract, expected practices refer to those of mathematicians, the institutional culture changes. Some studies analyze more broadly the practices of teachers and students at the end of high school or at the beginning of post-secondary level. Research in mathematics education provides keys to understanding current practices and their consequences, whether in ordinary courses or in teaching device specially designed to improve the transition from secondary to tertiary education. In some cases, it also proposes innovative courses fostering active student involvement, and highlights the benefits of these courses. The development of initial and in-service training for university teachers could help extend such teaching beyond experimental contexts. Cet article présente une synthèse de travaux de recherche internationaux en didactique des mathématiques à propos de la transition secondaire-supérieur, avec un intérêt spécifique porté aux travaux les plus récents. Ces travaux peuvent concerner les difficultés des étudiants, et en donner diverses interprétations : les notions deviennent plus abstraites, les pratiques attendues se réfèrent à celles des mathématiciens, la culture institutionnelle change. Certaines études analysent plus largement les pratiques des enseignants et des élèves en fin de lycée ou étudiants au début du supérieur. La recherche en didactique des mathématiques donne des clefs pour comprendre l’existant, qu’il s’agisse de cours ordinaires ou de dispositifs spécialement conçus pour accompagner la transition secondaire-supérieur. Elle propose aussi dans certains cas des enseignements innovants qui permettent une implication active des étudiants, et met en évidence les apports de ces dispositifs. Le développement de la formation initiale et continue des enseignants de l’université pourrait contribuer à étendre de tels enseignements au-delà de contextes expérimentaux.

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